XGBoost: A Scalable Tree Boosting System

 
XGBoost: A Scalable Tree Boosting System
XGBoost: A Scalable Tree Boosting System

                                        Tianqi Chen                                                            Carlos Guestrin
                               University of Washington                                                     University of Washington
                        tqchen@cs.washington.edu                                                      guestrin@cs.washington.edu

ABSTRACT                                                                                      problems. Besides being used as a stand-alone predictor, it
Tree boosting is a highly effective and widely used machine                                   is also incorporated into real-world production pipelines for
learning method. In this paper, we describe a scalable end-                                   ad click through rate prediction [15]. Finally, it is the de-
to-end tree boosting system called XGBoost, which is used                                     facto choice of ensemble method and is used in challenges
widely by data scientists to achieve state-of-the-art results                                 such as the Netflix prize [3].
on many machine learning challenges. We propose a novel                                          In this paper, we describe XGBoost, a scalable machine
sparsity-aware algorithm for sparse data and weighted quan-                                   learning system for tree boosting. The system is available
tile sketch for approximate tree learning. More importantly,                                  as an open source package2 . The impact of the system has
we provide insights on cache access patterns, data compres-                                   been widely recognized in a number of machine learning and
sion and sharding to build a scalable tree boosting system.                                   data mining challenges. Take the challenges hosted by the
By combining these insights, XGBoost scales beyond billions                                   machine learning competition site Kaggle for example. A-
of examples using far fewer resources than existing systems.                                  mong the 29 challenge winning solutions 3 published at Kag-
                                                                                              gle’s blog during 2015, 17 solutions used XGBoost. Among
                                                                                              these solutions, eight solely used XGBoost to train the mod-
Keywords                                                                                      el, while most others combined XGBoost with neural net-
Large-scale Machine Learning                                                                  s in ensembles. For comparison, the second most popular
                                                                                              method, deep neural nets, was used in 11 solutions. The
                                                                                              success of the system was also witnessed in KDDCup 2015,
1.     INTRODUCTION                                                                           where XGBoost was used by every winning team in the top-
   Machine learning and data-driven approaches are becom-                                     10. Moreover, the winning teams reported that ensemble
ing very important in many areas. Smart spam classifiers                                      methods outperform a well-configured XGBoost by only a
protect our email by learning from massive amounts of s-                                      small amount [1].
pam data and user feedback; advertising systems learn to                                         These results demonstrate that our system gives state-of-
match the right ads with the right context; fraud detection                                   the-art results on a wide range of problems. Examples of
systems protect banks from malicious attackers; anomaly                                       the problems in these winning solutions include: store sales
event detection systems help experimental physicists to find                                  prediction; high energy physics event classification; web text
events that lead to new physics. There are two importan-                                      classification; customer behavior prediction; motion detec-
t factors that drive these successful applications: usage of                                  tion; ad click through rate prediction; malware classification;
effective (statistical) models that capture the complex data                                  product categorization; hazard risk prediction; massive on-
dependencies and scalable learning systems that learn the                                     line course dropout rate prediction. While domain depen-
model of interest from large datasets.                                                        dent data analysis and feature engineering play an important
   Among the machine learning methods used in practice,                                       role in these solutions, the fact that XGBoost is the consen-
gradient tree boosting [10]1 is one technique that shines                                     sus choice of learner shows the impact and importance of
in many applications. Tree boosting has been shown to                                         our system and tree boosting.
give state-of-the-art results on many standard classification                                    The most important factor behind the success of XGBoost
benchmarks [16]. LambdaMART [5], a variant of tree boost-                                     is its scalability in all scenarios. The system runs more than
ing for ranking, achieves state-of-the-art result for ranking                                 ten times faster than existing popular solutions on a single
1
  Gradient tree boosting is also known as gradient boosting                                   machine and scales to billions of examples in distributed or
machine (GBM) or gradient boosted regression tree (GBRT)                                      memory-limited settings. The scalability of XGBoost is due
                                                                                              to several important systems and algorithmic optimizations.
Permission to make digital or hard copies of all or part of this work for personal or
                                                                                              These innovations include: a novel tree learning algorithm
classroom use is granted without fee provided that copies are not made or distributed         is for handling sparse data; a theoretically justified weighted
for profit or commercial advantage and that copies bear this notice and the full cita-        quantile sketch procedure enables handling instance weights
tion on the first page. Copyrights for components of this work owned by others than           in approximate tree learning. Parallel and distributed com-
ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or re-
publish, to post on servers or to redistribute to lists, requires prior specific permission   puting makes learning faster which enables quicker model ex-
and/or a fee. Request permissions from permissions@acm.org.                                   ploration. More importantly, XGBoost exploits out-of-core
KDD ’16, August 13-17, 2016, San Francisco, CA, USA
                                                                                              2
c 2016 ACM. ISBN 978-1-4503-4232-2/16/08. . . $15.00                                              https://github.com/dmlc/xgboost
                                                                                              3
DOI: http://dx.doi.org/10.1145/2939672.2939785                                                    Solutions come from of top-3 teams of each competitions.
XGBoost: A Scalable Tree Boosting System
computation and enables data scientists to process hundred
millions of examples on a desktop. Finally, it is even more
exciting to combine these techniques to make an end-to-end
system that scales to even larger data with the least amount
of cluster resources. The major contributions of this paper
is listed as follows:

     • We design and build a highly scalable end-to-end tree
       boosting system.

     • We propose a theoretically justified weighted quantile       Figure 1: Tree Ensemble Model. The final predic-
       sketch for efficient proposal calculation.                   tion for a given example is the sum of predictions
                                                                    from each tree.
     • We introduce a novel sparsity-aware algorithm for par-
       allel tree learning.                                         it into the leaves and calculate the final prediction by sum-
                                                                    ming up the score in the corresponding leaves (given by w).
     • We propose an effective cache-aware block structure          To learn the set of functions used in the model, we minimize
       for out-of-core tree learning.                               the following regularized objective.
   While there are some existing works on parallel tree boost-                             X                  X
                                                                                    L(φ) =     l(ŷi , yi ) +   Ω(fk )
ing [22, 23, 19], the directions such as out-of-core compu-
                                                                                                     i                   k
tation, cache-aware and sparsity-aware learning have not                                                                                            (2)
                                                                                                           1
been explored. More importantly, an end-to-end system                                    where Ω(f ) = γT + λkwk2
that combines all of these aspects gives a novel solution for                                              2
real-world use-cases. This enables data scientists as well as       Here l is a differentiable convex loss function that measures
researchers to build powerful variants of tree boosting al-         the difference between the prediction ŷi and the target yi .
gorithms [7, 8]. Besides these major contributions, we also         The second term Ω penalizes the complexity of the model
make additional improvements in proposing a regularized             (i.e., the regression tree functions). The additional regular-
learning objective, which we will include for completeness.         ization term helps to smooth the final learnt weights to avoid
   The remainder of the paper is organized as follows. We           over-fitting. Intuitively, the regularized objective will tend
will first review tree boosting and introduce a regularized         to select a model employing simple and predictive functions.
objective in Sec. 2. We then describe the split finding meth-       A similar regularization technique has been used in Regu-
ods in Sec. 3 as well as the system design in Sec. 4, including     larized greedy forest (RGF) [25] model. Our objective and
experimental results when relevant to provide quantitative          the corresponding learning algorithm is simpler than RGF
support for each optimization we describe. Related work             and easier to parallelize. When the regularization parame-
is discussed in Sec. 5. Detailed end-to-end evaluations are         ter is set to zero, the objective falls back to the traditional
included in Sec. 6. Finally we conclude the paper in Sec. 7.        gradient tree boosting.

2.    TREE BOOSTING IN A NUTSHELL                                   2.2     Gradient Tree Boosting
   We review gradient tree boosting algorithms in this sec-            The tree ensemble model in Eq. (2) includes functions as
tion. The derivation follows from the same idea in existing         parameters and cannot be optimized using traditional opti-
literatures in gradient boosting. Specicially the second order      mization methods in Euclidean space. Instead, the model
                                                                                                                        (t)
method is originated from Friedman et al. [12]. We make mi-         is trained in an additive manner. Formally, let ŷi be the
nor improvements in the reguralized objective, which were           prediction of the i-th instance at the t-th iteration, we will
found helpful in practice.                                          need to add ft to minimize the following objective.
                                                                                           n
2.1     Regularized Learning Objective                                          L(t) =
                                                                                           X
                                                                                                  l(yi , yˆi (t−1) + ft (xi )) + Ω(ft )
  For a given data set with n examples and m features                                       i=1
D = {(xi , yi )} (|D| = n, xi ∈ Rm , yi ∈ R), a tree ensem-
ble model (shown in Fig. 1) uses K additive functions to            This means we greedily add the ft that most improves our
predict the output.                                                 model according to Eq. (2). Second-order approximation
                                                                    can be used to quickly optimize the objective in the general
                               K
                               X                                    setting [12].
              ŷi = φ(xi ) =         fk (xi ), fk ∈ F ,       (1)
                                                                                n
                               k=1                                              X                                            1
                                                                       L(t) '         [l(yi , ŷ (t−1) ) + gi ft (xi ) +       hi ft2 (xi )] + Ω(ft )
                                          m
where F = {f (x) = wq(x) }(q : R → T, w ∈ R ) is the      T
                                                                                i=1
                                                                                                                             2
space of regression trees (also known as CART). Here q rep-
resents the structure of each tree that maps an example to          where gi = ∂ŷ(t−1) l(yi , ŷ (t−1) ) and hi = ∂ŷ2(t−1) l(yi , ŷ (t−1) )
the corresponding leaf index. T is the number of leaves in the      are first and second order gradient statistics on the loss func-
tree. Each fk corresponds to an independent tree structure          tion. We can remove the constant terms to obtain the fol-
q and leaf weights w. Unlike decision trees, each regression        lowing simplified objective at step t.
tree contains a continuous score on each of the leaf, we use                               n
wi to represent score on i-th leaf. For a given example, we
                                                                                           X                      1
                                                                                L̃(t) =          [gi ft (xi ) +     hi ft2 (xi )] + Ω(ft )          (3)
will use the decision rules in the trees (given by q) to classify                          i=1
                                                                                                                  2
XGBoost: A Scalable Tree Boosting System
Algorithm 1: Exact Greedy Algorithm for Split Finding
                                                                                Input: I, instance set of current node
                                                                                Input: d, feature dimension
                                                                                gain ←
                                                                                     P0             P
                                                                                G ← i∈I gi , H ← i∈I hi
                                                                                for k = 1 to m do
                                                                                   GL ← 0, HL ← 0
                                                                                   for j in sorted(I, by xjk ) do
                                                                                       GL ← GL + gj , HL ← HL + hj
Figure 2: Structure Score Calculation. We only
                                                                                       GR ← G − GL , H R ← H − H L
need to sum up the gradient and second order gra-                                                             G2     G2    G2
dient statistics on each leaf, then apply the scoring                                  score ← max(score, HLL+λ + HRR+λ − H+λ  )
formula to get the quality score.                                                  end
                                                                                end
  Define Ij = {i|q(xi ) = j} as the instance set of leaf j. We                  Output: Split with max score
can rewrite Eq (3) by expanding Ω as follows
             n                                               T                 Algorithm 2: Approximate Algorithm for Split Finding
             X                      1                     1 X 2
   L̃(t) =         [gi ft (xi ) +     hi ft2 (xi )] + γT + λ    wj
                                    2                     2 j=1                 for k = 1 to m do
             i=1
                                                                     (4)            Propose Sk = {sk1 , sk2 , · · · skl } by percentiles on feature k.
              T
             X     X         1 X                                                    Proposal can be done per tree (global), or per split(local).
        =       [(   gi )wj + (     hi + λ)wj2 ] + γT                           end
             j=1 i∈I
                             2  i∈I
                        j                  j                                    for k = 1 to P
                                                                                             m do
                                                                                    Gkv ←= j∈{j|sk,v ≥xjk >sk,v−1 } gj
  For a fixed structure q(x), we can compute the optimal                                     P
weight wj∗ of leaf j by                                                             Hkv ←= j∈{j|sk,v ≥xjk >sk,v−1 } hj
                             P                                                  end
                      ∗        i∈Ij gi                                          Follow same step as in previous section to find max
                    wj = − P             ,           (5)                        score only among proposed splits.
                             i∈Ij hi + λ

and calculate the corresponding optimal value by
                          T
                              P       2                                    13], It is implemented in a commercial software TreeNet 4
             (t)       1 X ( i∈Ij gi )                                     for gradient boosting, but is not implemented in existing
           L̃ (q) = −       P            + γT.                       (6)
                       2 j=1 i∈Ij hi + λ                                   opensource packages. According to user feedback, using col-
                                                                           umn sub-sampling prevents over-fitting even more so than
   Eq (6) can be used as a scoring function to measure the                 the traditional row sub-sampling (which is also supported).
quality of a tree structure q. This score is like the impurity             The usage of column sub-samples also speeds up computa-
score for evaluating decision trees, except that it is derived             tions of the parallel algorithm described later.
for a wider range of objective functions. Fig. 2 illustrates
how this score can be calculated.
   Normally it is impossible to enumerate all the possible
                                                                           3.      SPLIT FINDING ALGORITHMS
tree structures q. A greedy algorithm that starts from a
single leaf and iteratively adds branches to the tree is used
                                                                           3.1       Basic Exact Greedy Algorithm
instead. Assume that IL and IR are the instance sets of left                  One of the key problems in tree learning is to find the
and right nodes after the split. Lettting I = IL ∪ IR , then               best split as indicated by Eq (7). In order to do so, a s-
the loss reduction after the split is given by                             plit finding algorithm enumerates over all the possible splits
            " P                                               #            on all the features. We call this the exact greedy algorithm.
                         2
                               ( i∈IR gi )2      ( i∈I gi )2
                                P
                                                                           Most existing single machine tree boosting implementation-
                                                  P
          1 ( i∈IL gi )
Lsplit =     P              +  P              − P               −γ         s, such as scikit-learn [20], R’s gbm [21] as well as the single
          2     i∈IL hi + λ      i∈IR hi + λ       i∈I hi + λ
                                                                           machine version of XGBoost support the exact greedy algo-
                                                            (7)            rithm. The exact greedy algorithm is shown in Alg. 1. It
This formula is usually used in practice for evaluating the                is computationally demanding to enumerate all the possible
split candidates.                                                          splits for continuous features. In order to do so efficiently,
                                                                           the algorithm must first sort the data according to feature
2.3    Shrinkage and Column Subsampling                                    values and visit the data in sorted order to accumulate the
   Besides the regularized objective mentioned in Sec. 2.1,                gradient statistics for the structure score in Eq (7).
two additional techniques are used to further prevent over-
fitting. The first technique is shrinkage introduced by Fried-             3.2       Approximate Algorithm
man [11]. Shrinkage scales newly added weights by a factor                    The exact greedy algorithm is very powerful since it enu-
η after each step of tree boosting. Similar to a learning rate             merates over all possible splitting points greedily. However,
in tochastic optimization, shrinkage reduces the influence of              it is impossible to efficiently do so when the data does not fit
each individual tree and leaves space for future trees to im-              entirely into memory. Same problem also arises in the dis-
prove the model. The second technique is column (feature)
                                                                           4
subsampling. This technique is used in RandomForest [4,                        https://www.salford-systems.com/products/treenet
0.83

                    0.82

                    0.81

                    0.80
         Test AUC

                    0.79

                    0.78
                                                         exact greedy           Figure 4: Tree structure with default directions. An
                    0.77                                 global eps=0.3         example will be classified into the default direction
                                                         local eps=0.3          when the feature needed for the split is missing.
                    0.76
                                                         global eps=0.05
                    0.75
                        0   10   20   30   40      50     60   70   80     90
                                       Number of Iterations                     ta. Formally, let multi-set Dk = {(x1k , h1 ), (x2k , h2 ) · · · (xnk , hn )}
                                                                                represent the k-th feature values and second order gradient
Figure 3: Comparison of test AUC convergence on                                 statistics of each training instances. We can define a rank
Higgs 10M dataset. The eps parameter corresponds                                functions rk : R → [0, +∞) as
to the accuracy of the approximate sketch. This
roughly translates to 1 / eps buckets in the proposal.                                                      1          X
                                                                                             rk (z) = P                           h,               (8)
We find that local proposals require fewer buckets,                                                     (x,h)∈Dk h
                                                                                                                       (x,h)∈Dk ,x
Figure 6: Block structure for parallel learning. Each column in a block is sorted by the corresponding feature
value. A linear scan over one column in the block is sufficient to enumerate all the split points.

                                                                                                     32
 Algorithm 3: Sparsity-aware Split Finding
                                                                                                     16                    Basic algorithm
  Input: I, instance set of current node
                                                                                                      8
  Input: Ik = {i ∈ I|xik 6= missing}                                                                  4

                                                                            Time per Tree(sec)
  Input: d, feature dimension                                                                         2
  Also applies to the approximate setting, only collect                                               1
  statistics of non-missing entries into buckets                                                     0.5
  gain ←P0             P                                                                            0.25
                                                                                                                       Sparsity aware algorithm

  G ← i∈I , gi ,H ← i∈I hi                                                                         0.125
  for k = 1 to m do                                                                               0.0625
      // enumerate missing value goto right                                                      0.03125
                                                                                                                                     8
                                                                                                           1   2          4                   16
      GL ← 0, HL ← 0                                                                                               Number of Threads

      for j in sorted(Ik , ascent order by xjk ) do
                                                                 Figure 5: Impact of the sparsity aware algorithm
          GL ← GL + g j , H L ← H L + h j
                                                                 on Allstate-10K. The dataset is sparse mainly due
          GR ← G − GL , H R ← H − H L
                                 G2       G2       G2
                                                                 to one-hot encoding. The sparsity aware algorithm
          score ← max(score, HLL+λ + HRR+λ − H+λ      )          is more than 50 times faster than the naive version
      end                                                        that does not take sparsity into consideration.
      // enumerate missing value goto left
      GR ← 0, HR ← 0                                             4.    SYSTEM DESIGN
      for j in sorted(Ik , descent order by xjk ) do
          GR ← GR + gj , HR ← HR + hj                            4.1   Column Block for Parallel Learning
          GL ← G − GR , HL ← H − HR
                                 G2       G2       G2
                                                                    The most time consuming part of tree learning is to get
          score ← max(score, HLL+λ + HRR+λ − H+λ      )          the data into sorted order. In order to reduce the cost of
      end                                                        sorting, we propose to store the data in in-memory units,
  end                                                            which we called block. Data in each block is stored in the
  Output: Split and default directions with max gain             compressed column (CSC) format, with each column sorted
                                                                 by the corresponding feature value. This input data layout
                                                                 only needs to be computed once before training, and can be
                                                                 reused in later iterations.
classified into the default direction. There are two choices        In the exact greedy algorithm, we store the entire dataset
of default direction in each branch. The optimal default di-     in a single block and run the split search algorithm by lin-
rections are learnt from the data. The algorithm is shown in     early scanning over the pre-sorted entries. We do the split
Alg. 3. The key improvement is to only visit the non-missing     finding of all leaves collectively, so one scan over the block
entries Ik . The presented algorithm treats the non-presence     will collect the statistics of the split candidates in all leaf
as a missing value and learns the best direction to handle       branches. Fig. 6 shows how we transform a dataset into the
missing values. The same algorithm can also be applied           format and find the optimal split using the block structure.
when the non-presence corresponds to a user specified value         The block structure also helps when using the approxi-
by limiting the enumeration only to consistent solutions.        mate algorithms. Multiple blocks can be used in this case,
   To the best of our knowledge, most existing tree learning     with each block corresponding to subset of rows in the dataset.
algorithms are either only optimized for dense data, or need     Different blocks can be distributed across machines, or s-
specific procedures to handle limited cases such as categor-     tored on disk in the out-of-core setting. Using the sorted
ical encoding. XGBoost handles all sparsity patterns in a        structure, the quantile finding step becomes a linear scan
unified way. More importantly, our method exploits the s-        over the sorted columns. This is especially valuable for lo-
parsity to make computation complexity linear to number          cal proposal algorithms, where candidates are generated fre-
of non-missing entries in the input. Fig. 5 shows the com-       quently at each branch. The binary search in histogram ag-
parison of sparsity aware and a naive implementation on an       gregation also becomes a linear time merge style algorithm.
Allstate-10K dataset (description of dataset given in Sec. 6).      Collecting statistics for each column can be parallelized,
We find that the sparsity aware algorithm runs 50 times          giving us a parallel algorithm for split finding. Importantly,
faster than the naive version. This confirms the importance      the column block structure also supports column subsam-
of the sparsity aware algorithm.                                 pling, as it is easy to select a subset of columns in a block.
128                                                           256                                                                8                                                                                         8
                                        Basic algorithm                                                  Basic algorithm                                                    Basic algorithm                                                                             Basic algorithm
                                        Cache-aware algorithm                        128                 Cache-aware algorithm                          4                   Cache-aware algorithm                                                 4                     Cache-aware algorithm
                        64
  Time per Tree(sec)

                                                                Time per Tree(sec)

                                                                                                                                 Time per Tree(sec)

                                                                                                                                                                                                                           Time per Tree(sec)
                                                                                      64                                                                2                                                                                         2
                        32
                                                                                      32                                                                1                                                                                         1

                        16
                                                                                      16                                                               0.5                                                                                       0.5

                         8                                                             8                                                              0.25                                                                                      0.25
                             1   2          4          8   16                              1      2          4          8   16                               1       2          4          8                    16                                     1         2          4          8   16
                                     Number of Threads                                                Number of Threads                                                  Number of Threads                                                                           Number of Threads

                             (a) Allstate 10M                                                  (b) Higgs 10M                                                     (c) Allstate 1M                                                                            (d) Higgs 1M
Figure 7: Impact of cache-aware prefetching in exact greedy algorithm. We find that the cache-miss effect
impacts the performance on the large datasets (10 million instances). Using cache aware prefetching improves
the performance by factor of two when the dataset is large.

                                                                                                                                                                                                    128
                                                                                                                                                                                                                                                           block size=2^12
                                                                                                                                                                                                                                                           block size=2^16
                                                                                                                                                                                                     64
                                                                                                                                                                                                                                                           block size=2^20
                                                                                                                                                                                                                                                           block size=2^24

                                                                                                                                                                               Time per Tree(sec)
                                                                                                                                                                                                     32

                                                                                                                                                                                                     16

Figure 8:   Short range data dependency pattern
that can cause stall due to cache miss.                                                                                                                                                               8

Time Complexity Analysis Let d be the maximum depth                                                                                                                                                   4
                                                                                                                                                                                                          1      2          4                                8            16
                                                                                                                                                                                                                     Number of Threads
of the tree and K be total number of trees. For the exac-
t greedy algorithm, the time complexity of original spase                                                                                                                                                     (a) Allstate 10M
aware algorithm is O(Kdkxk0 log n). Here we use kxk0 to
denote number of non-missing entries in the training data.                                                                                                                                          512
                                                                                                                                                                                                                                                           block size=2^12
On the other hand, tree boosting on the block structure on-                                                                                                                                         256                                                    block size=2^16
ly cost O(Kdkxk0 + kxk0 log n). Here O(kxk0 log n) is the                                                                                                                                                                                                  block size=2^20
                                                                                                                                                                                                    128
one time preprocessing cost that can be amortized. This                                                                                                                                                                                                    block size=2^24
                                                                                                                                                                               Time per Tree(sec)

analysis shows that the block structure helps to save an ad-                                                                                                                                         64
ditional log n factor, which is significant when n is large. For
                                                                                                                                                                                                     32
the approximate algorithm, the time complexity of original
algorithm with binary search is O(Kdkxk0 log q). Here q is                                                                                                                                           16

the number of proposal candidates in the dataset. While q
                                                                                                                                                                                                      8
is usually between 32 and 100, the log factor still introduces
overhead. Using the block structure, we can reduce the time                                                                                                                                           4
                                                                                                                                                                                                          1      2          4                                8            16
                                                                                                                                                                                                                     Number of Threads
to O(Kdkxk0 + kxk0 log B), where B is the maximum num-
ber of rows in each block. Again we can save the additional                                                                                                                                                    (b) Higgs 10M
log q factor in computation.
                                                                                                                                           Figure 9: The impact of block size in the approxi-
                                                                                                                                           mate algorithm. We find that overly small blocks re-
4.2                          Cache-aware Access                                                                                            sults in inefficient parallelization, while overly large
   While the proposed block structure helps optimize the                                                                                   blocks also slows down training due to cache misses.
computation complexity of split finding, the new algorithm
requires indirect fetches of gradient statistics by row index,
since these values are accessed in order of feature. This is                                                                               non cache-aware algorithm on the the Higgs and the All-
a non-continuous memory access. A naive implementation                                                                                     state dataset. We find that cache-aware implementation of
of split enumeration introduces immediate read/write de-                                                                                   the exact greedy algorithm runs twice as fast as the naive
pendency between the accumulation and the non-continuous                                                                                   version when the dataset is large.
memory fetch operation (see Fig. 8). This slows down split                                                                                   For approximate algorithms, we solve the problem by choos-
finding when the gradient statistics do not fit into CPU cache                                                                             ing a correct block size. We define the block size to be max-
and cache miss occur.                                                                                                                      imum number of examples in contained in a block, as this
   For the exact greedy algorithm, we can alleviate the prob-                                                                              reflects the cache storage cost of gradient statistics. Choos-
lem by a cache-aware prefetching algorithm. Specifically,                                                                                  ing an overly small block size results in small workload for
we allocate an internal buffer in each thread, fetch the gra-                                                                              each thread and leads to inefficient parallelization. On the
dient statistics into it, and then perform accumulation in                                                                                 other hand, overly large blocks result in cache misses, as the
a mini-batch manner. This prefetching changes the direct                                                                                   gradient statistics do not fit into the CPU cache. A good
read/write dependency to a longer dependency and helps to                                                                                  choice of block size balances these two factors. We compared
reduce the runtime overhead when number of rows in the                                                                                     various choices of block size on two data sets. The results
is large. Figure 7 gives the comparison of cache-aware vs.                                                                                 are given in Fig. 9. This result validates our discussion and
Table   1: Comparison of major tree boosting         systems.
                                exact     approximate approximate                      sparsity
              System                                              out-of-core                          parallel
                                greedy    global      local                            aware
              XGBoost           yes       yes         yes         yes                  yes             yes
              pGBRT             no        no          yes         no                   no              yes
              Spark MLLib       no        yes         no          no                   partially       yes
              H2O               no        yes         no          no                   partially       yes
              scikit-learn      yes       no          no          no                   no              no
              R GBM             yes       no          no          no                   partially       no

shows that choosing 216 examples per block balances the               There are several existing works on parallelizing tree learn-
cache property and parallelization.                                ing [22, 19]. Most of these algorithms fall into the approxi-
                                                                   mate framework described in this paper. Notably, it is also
4.3    Blocks for Out-of-core Computation                          possible to partition data by columns [23] and apply the ex-
  One goal of our system is to fully utilize a machine’s re-       act greedy algorithm. This is also supported in our frame-
sources to achieve scalable learning. Besides processors and       work, and the techniques such as cache-aware pre-fecthing
memory, it is important to utilize disk space to handle data       can be used to benefit this type of algorithm. While most
that does not fit into main memory. To enable out-of-core          existing works focus on the algorithmic aspect of paralleliza-
computation, we divide the data into multiple blocks and           tion, our work improves in two unexplored system direction-
store each block on disk. During computation, it is impor-         s: out-of-core computation and cache-aware learning. This
tant to use an independent thread to pre-fetch the block into      gives us insights on how the system and the algorithm can
a main memory buffer, so computation can happen in con-            be jointly optimized and provides an end-to-end system that
currence with disk reading. However, this does not entirely        can handle large scale problems with very limited computing
solve the problem since the disk reading takes most of the         resources. We also summarize the comparison between our
computation time. It is important to reduce the overhead           system and existing opensource implementations in Table 1.
and increase the throughput of disk IO. We mainly use two             Quantile summary (without weights) is a classical prob-
techniques to improve the out-of-core computation.                 lem in the database community [14, 24]. However, the ap-
Block Compression The first technique we use is block              proximate tree boosting algorithm reveals a more general
compression. The block is compressed by columns, and de-           problem – finding quantiles on weighted data. To the best
compressed on the fly by an independent thread when load-          of our knowledge, the weighted quantile sketch proposed in
ing into main memory. This helps to trade some of the              this paper is the first method to solve this problem. The
computation in decompression with the disk reading cost.           weighted quantile summary is also not specific to the tree
We use a general purpose compression algorithm for com-            learning and can benefit other applications in data science
pressing the features values. For the row index, we substract      and machine learning in the future.
the row index by the begining index of the block and use a
16bit integer to store each offset. This requires 216 examples
per block, which is confirmed to be a good setting. In most
                                                                   6.    END TO END EVALUATIONS
of the dataset we tested, we achieve roughly a 26% to 29%
compression ratio.
                                                                   6.1    System Implementation
Block Sharding The second technique is to shard the data              We implemented XGBoost as an open source package6 .
onto multiple disks in an alternative manner. A pre-fetcher        The package is portable and reusable. It supports various
thread is assigned to each disk and fetches the data into an       weighted classification and rank objective functions, as well
in-memory buffer. The training thread then alternatively           as user defined objective function. It is available in popular
reads the data from each buffer. This helps to increase the        languages such as python, R, Julia and integrates naturally
throughput of disk reading when multiple disks are available.      with language native data science pipelines such as scikit-
                                                                   learn. The distributed version is built on top of the rabit
                                                                   library7 for allreduce. The portability of XGBoost makes it
5.    RELATED WORKS                                                available in many ecosystems, instead of only being tied to
   Our system implements gradient boosting [10], which per-        a specific platform. The distributed XGBoost runs natively
forms additive optimization in functional space. Gradient          on Hadoop, MPI Sun Grid engine. Recently, we also enable
tree boosting has been successfully used in classification [12],   distributed XGBoost on jvm bigdata stacks such as Flink
learning to rank [5], structured prediction [8] as well as other   and Spark. The distributed version has also been integrated
fields. XGBoost incorporates a regularized model to prevent        into cloud platform Tianchi8 of Alibaba. We believe that
overfitting. This this resembles previous work on regularized      there will be more integrations in the future.
greedy forest [25], but simplifies the objective and algorithm
for parallelization. Column sampling is a simple but effective     6.2    Dataset and Setup
technique borrowed from RandomForest [4]. While sparsity-            We used four datasets in our experiments. A summary of
aware learning is essential in other types of models such as       these datasets is given in Table 2. In some of the experi-
linear models [9], few works on tree learning have considered
                                                                   6
this topic in a principled way. The algorithm proposed in            https://github.com/dmlc/xgboost
                                                                   7
this paper is the first unified approach to handle all kinds of      https://github.com/dmlc/rabit
                                                                   8
sparsity patterns.                                                   https://tianchi.aliyun.com
Table 2: Dataset used in the Experiments.                 Table 3: Comparison of Exact Greedy Methods with
     Dataset         n      m    Task                              500 trees on Higgs-1M data.
     Allstate      10 M 4227 Insurance claim classification         Method                  Time per Tree (sec) Test AUC
     Higgs Boson   10 M     28   Event classification               XGBoost                       0.6841         0.8304
     Yahoo LTRC 473K       700   Learning to Rank                   XGBoost (colsample=0.5)       0.6401         0.8245
     Criteo        1.7 B    67   Click through rate prediction      scikit-learn                   28.51         0.8302
                                                                    R.gbm                          1.032         0.6224

ments, we use a randomly selected subset of the data either                                      32
due to slow baselines or to demonstrate the performance of
the algorithm with varying dataset size. We use a suffix to                                      16
denote the size in these cases. For example Allstate-10K

                                                                            Time per Tree(sec)
means a subset of the Allstate dataset with 10K instances.                                        8                              pGBRT

   The first dataset we use is the Allstate insurance claim
                                                                                                  4
dataset9 . The task is to predict the likelihood and cost of
an insurance claim given different risk factors. In the exper-                                    2
                                                                                                                                 XGBoost
iment, we simplified the task to only predict the likelihood
of an insurance claim. This dataset is used to evaluate the                                       1
impact of sparsity-aware algorithm in Sec. 3.4. Most of the
sparse features in this data come from one-hot encoding. We                                      0.5
                                                                                                       1   2          4          8         16
randomly select 10M instances as training set and use the                                                      Number of Threads
rest as evaluation set.
                                                                   Figure 10: Comparison between XGBoost and pG-
   The second dataset is the Higgs boson dataset10 from high
                                                                   BRT on Yahoo LTRC dataset.
energy physics. The data was produced using Monte Carlo
simulations of physics events. It contains 21 kinematic prop-      Table 4: Comparison of Learning to Rank with 500
erties measured by the particle detectors in the accelerator.      trees on Yahoo! LTRC Dataset
It also contains seven additional derived physics quantities        Method                  Time per Tree (sec) NDCG@10
of the particles. The task is to classify whether an event          XGBoost                       0.826          0.7892
corresponds to the Higgs boson. We randomly select 10M              XGBoost (colsample=0.5)       0.506          0.7913
instances as training set and use the rest as evaluation set.       pGBRT [22]                    2.576          0.7915
   The third dataset is the Yahoo! learning to rank challenge
dataset [6], which is one of the most commonly used bench-
marks in learning to rank algorithms. The dataset contains         corresponding section. In all the experiments, we boost trees
20K web search queries, with each query corresponding to a         with a common setting of maximum depth equals 8, shrink-
list of around 22 documents. The task is to rank the docu-         age equals 0.1 and no column subsampling unless explicitly
ments according to relevance of the query. We use the official     specified. We can find similar results when we use other
train test split in our experiment.                                settings of maximum depth.
   The last dataset is the criteo terabyte click log dataset11 .
We use this dataset to evaluate the scaling property of the        6.3   Classification
system in the out-of-core and the distributed settings. The
                                                                     In this section, we evaluate the performance of XGBoost
data contains 13 integer features and 26 ID features of user,
                                                                   on a single machine using the exact greedy algorithm on
item and advertiser information. Since a tree based model
                                                                   Higgs-1M data, by comparing it against two other common-
is better at handling continuous features, we preprocess the
                                                                   ly used exact greedy tree boosting implementations. Since
data by calculating the statistics of average CTR and count
                                                                   scikit-learn only handles non-sparse input, we choose the
of ID features on the first ten days, replacing the ID fea-
                                                                   dense Higgs dataset for a fair comparison. We use the 1M
tures by the corresponding count statistics during the next
                                                                   subset to make scikit-learn finish running in reasonable time.
ten days for training. The training set after preprocessing
                                                                   Among the methods in comparison, R’s GBM uses a greedy
contains 1.7 billion instances with 67 features (13 integer, 26
                                                                   approach that only expands one branch of a tree, which
average CTR statistics and 26 counts). The entire dataset
                                                                   makes it faster but can result in lower accuracy, while both
is more than one terabyte in LibSVM format.
                                                                   scikit-learn and XGBoost learn a full tree. The results are
   We use the first three datasets for the single machine par-
                                                                   shown in Table 3. Both XGBoost and scikit-learn give bet-
allel setting, and the last dataset for the distributed and
                                                                   ter performance than R’s GBM, while XGBoost runs more
out-of-core settings. All the single machine experiments are
                                                                   than 10x faster than scikit-learn. In this experiment, we al-
conducted on a Dell PowerEdge R420 with two eight-core
                                                                   so find column subsamples gives slightly worse performance
Intel Xeon (E5-2470) (2.3GHz) and 64GB of memory. If not
                                                                   than using all the features. This could due to the fact that
specified, all the experiments are run using all the available
                                                                   there are few important features in this dataset and we can
cores in the machine. The machine settings of the distribut-
                                                                   benefit from greedily select from all the features.
ed and the out-of-core experiments will be described in the
9
   https://www.kaggle.com/c/ClaimPredictionChallenge               6.4   Learning to Rank
10                                                                    We next evaluate the performance of XGBoost on the
   https://archive.ics.uci.edu/ml/datasets/HIGGS
11                                                                 learning to rank problem. We compare against pGBRT [22],
   http://labs.criteo.com/downloads/download-terabyte-
 click-logs/                                                       the best previously pubished system on this task. XGBoost
4096                                                                                             32768

                                         Block compression                                                                       16384      H2O

                                2048
                                                                                                                                   8192

                                                                                                      Total Running Time (sec)
                                       Basic algorithm                                                                             4096
           Time per Tree(sec)

                                1024
                                                                                                                                   2048                     Spark MLLib

                                                                    Compression+shard
                                                                                                                                   1024
                                 512
                                                             Out of system file cache
                                                                                                                                    512
                                                             start from this point                                                                                            XGBoost

                                 256                                                                                                256

                                                                                                                                    128
                                                                                                                                      128          256             512          1024      2048
                                                                                                                                                  Number of Training Examples (million)
                                 128
                                   128          256            512         1024         2048
                                              Number of Training Examples (million)
                                                                                                     (a) End-to-end time cost include data loading
Figure 11: Comparison of out-of-core methods on
different subsets of criteo data. The missing data                                                                                 4096
points are due to out of disk space. We can find                                                                                   2048
that basic algorithm can only handle 200M exam-
ples. Adding compression gives 3x speedup, and                                                                                     1024

                                                                                                        Time per Iteration (sec)
sharding into two disks gives another 2x speedup.                                                                                   512
The system runs out of file cache start from 400M
                                                                                                                                    256
examples. The algorithm really has to rely on disk
                                                                                                                                                           Spark MLLib
after this point. The compression+shard method                                                                                      128
has a less dramatic slowdown when running out of
                                                                                                                                     64
file cache, and exhibits a linear trend afterwards.                                                                                          H2O

                                                                                                                                     32
                                                                                                                                                                             XGBoost
runs exact greedy algorithm, while pGBRT only support an                                                                             16
approximate algorithm. The results are shown in Table 4
and Fig. 10. We find that XGBoost runs faster. Interest-                                                                             8
                                                                                                                                     128        256            512         1024           2048
                                                                                                                                              Number of Training Examples (million)
ingly, subsampling columns not only reduces running time,
and but also gives a bit higher performance for this prob-                                                      (b) Per iteration cost exclude data loading
lem. This could due to the fact that the subsampling helps
prevent overfitting, which is observed by many of the users.                                   Figure 12: Comparison of different distributed sys-
                                                                                               tems on 32 EC2 nodes for 10 iterations on different
6.5      Out-of-core Experiment                                                                subset of criteo data. XGBoost runs more 10x than
                                                                                               spark per iteration and 2.2x as H2O’s optimized ver-
   We also evaluate our system in the out-of-core setting on
                                                                                               sion (However, H2O is slow in loading the data, get-
the criteo data. We conducted the experiment on one AWS
                                                                                               ting worse end-to-end time). Note that spark suffers
c3.8xlarge machine (32 vcores, two 320 GB SSD, 60 GB
                                                                                               from drastic slow down when running out of mem-
RAM). The results are shown in Figure 11. We can find
                                                                                               ory. XGBoost runs faster and scales smoothly to
that compression helps to speed up computation by factor of
                                                                                               the full 1.7 billion examples with given resources by
three, and sharding into two disks further gives 2x speedup.
                                                                                               utilizing out-of-core computation.
For this type of experiment, it is important to use a very
large dataset to drain the system file cache for a real out-
of-core setting. This is indeed our setup. We can observe a
transition point when the system runs out of file cache. Note                                  tems with various input size. Both of the baseline systems
that the transition in the final method is less dramatic. This                                 are in-memory analytics frameworks that need to store the
is due to larger disk throughput and better utilization of                                     data in RAM, while XGBoost can switch to out-of-core set-
computation resources. Our final method is able to process                                     ting when it runs out of memory. The results are shown
1.7 billion examples on a single machine.                                                      in Fig. 12. We can find that XGBoost runs faster than
                                                                                               the baseline systems. More importantly, it is able to take
6.6      Distributed Experiment                                                                advantage of out-of-core computing and smoothly scale to
  Finally, we evaluate the system in the distributed setting.                                  all 1.7 billion examples with the given limited computing re-
We set up a YARN cluster on EC2 with m3.2xlarge ma-                                            sources. The baseline systems are only able to handle subset
chines, which is a very common choice for clusters. Each                                       of the data with the given resources. This experiment shows
machine contains 8 virtual cores, 30GB of RAM and two                                          the advantage to bring all the system improvement togeth-
80GB SSD local disks. The dataset is stored on AWS S3                                          er and solve a real-world scale problem. We also evaluate
instead of HDFS to avoid purchasing persistent storage.                                        the scaling property of XGBoost by varying the number of
  We first compare our system against two production-level                                     machines. The results are shown in Fig. 13. We can find
distributed systems: Spark MLLib [18] and H2O 12 . We use                                      XGBoost’s performance scales linearly as we add more ma-
32 m3.2xlarge machines and test the performance of the sys-                                    chines. Importantly, XGBoost is able to handle the entire
                                                                                               1.7 billion data with only four machines. This shows the
12                                                                                             system’s potential to handle even larger data.
     www.h2o.ai
2048                                        of 30th International Conference on Machine Learning
                                                                                (ICML’13), volume 1, pages 436–444, 2013.
                                                                          [8]   T. Chen, S. Singh, B. Taskar, and C. Guestrin. Efficient
                                                                                second-order gradient boosting for conditional random
                                    1024
                                                                                fields. In Proceeding of 18th Artificial Intelligence and
         Time per Iteration (sec)

                                                                                Statistics Conference (AISTATS’15), volume 1, 2015.
                                                                          [9]   R.-E. Fan, K.-W. Chang, C.-J. Hsieh, X.-R. Wang, and
                                     512                                        C.-J. Lin. LIBLINEAR: A library for large linear
                                                                                classification. Journal of Machine Learning Research,
                                                                                9:1871–1874, 2008.
                                                                         [10]   J. Friedman. Greedy function approximation: a gradient
                                     256
                                                                                boosting machine. Annals of Statistics, 29(5):1189–1232,
                                                                                2001.
                                                                         [11]   J. Friedman. Stochastic gradient boosting. Computational
                                     128                                        Statistics & Data Analysis, 38(4):367–378, 2002.
                                           4    8             16    32
                                               Number of Machines        [12]   J. Friedman, T. Hastie, and R. Tibshirani. Additive logistic
                                                                                regression: a statistical view of boosting. Annals of
Figure 13: Scaling of XGBoost with different num-                               Statistics, 28(2):337–407, 2000.
ber of machines on criteo full 1.7 billion dataset.                      [13]   J. H. Friedman and B. E. Popescu. Importance sampled
Using more machines results in more file cache and                              learning ensembles, 2003.
makes the system run faster, causing the trend to                        [14]   M. Greenwald and S. Khanna. Space-efficient online
be slightly super linear. XGBoost can process the                               computation of quantile summaries. In Proceedings of the
entire dataset using as little as four machines, and s-                         2001 ACM SIGMOD International Conference on
cales smoothly by utilizing more available resources.                           Management of Data, pages 58–66, 2001.
                                                                         [15]   X. He, J. Pan, O. Jin, T. Xu, B. Liu, T. Xu, Y. Shi,
                                                                                A. Atallah, R. Herbrich, S. Bowers, and J. Q. n. Candela.
7.   CONCLUSION                                                                 Practical lessons from predicting clicks on ads at facebook.
  In this paper, we described the lessons we learnt when                        In Proceedings of the Eighth International Workshop on
building XGBoost, a scalable tree boosting system that is                       Data Mining for Online Advertising, ADKDD’14, 2014.
widely used by data scientists and provides state-of-the-art             [16]   P. Li. Robust Logitboost and adaptive base class (ABC)
                                                                                Logitboost. In Proceedings of the Twenty-Sixth Conference
results on many problems. We proposed a novel sparsity                          Annual Conference on Uncertainty in Artificial Intelligence
aware algorithm for handling sparse data and a theoretically                    (UAI’10), pages 302–311, 2010.
justified weighted quantile sketch for approximate learning.             [17]   P. Li, Q. Wu, and C. J. Burges. Mcrank: Learning to rank
Our experience shows that cache access patterns, data com-                      using multiple classification and gradient boosting. In
pression and sharding are essential elements for building a                     Advances in Neural Information Processing Systems 20,
scalable end-to-end system for tree boosting. These lessons                     pages 897–904. 2008.
can be applied to other machine learning systems as well.                [18]   X. Meng, J. Bradley, B. Yavuz, E. Sparks,
                                                                                S. Venkataraman, D. Liu, J. Freeman, D. Tsai, M. Amde,
By combining these insights, XGBoost is able to solve real-
                                                                                S. Owen, D. Xin, R. Xin, M. J. Franklin, R. Zadeh,
world scale problems using a minimal amount of resources.                       M. Zaharia, and A. Talwalkar. MLlib: Machine learning in
                                                                                apache spark. Journal of Machine Learning Research,
                                                                                17(34):1–7, 2016.
Acknowledgments                                                          [19]   B. Panda, J. S. Herbach, S. Basu, and R. J. Bayardo.
We would like to thank Tyler B. Johnson, Marco Tulio Ribeiro,                   Planet: Massively parallel learning of tree ensembles with
Sameer Singh, Arvind Krishnamurthy for their valuable feedback.                 mapreduce. Proceeding of VLDB Endowment,
We also sincerely thank Tong He, Bing Xu, Michael Benesty, Yuan                 2(2):1426–1437, Aug. 2009.
Tang, Hongliang Liu, Qiang Kou, Nan Zhu and all other con-               [20]   F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel,
tributors in the XGBoost community. This work was supported                     B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer,
in part by ONR (PECASE) N000141010672, NSF IIS 1258741                          R. Weiss, V. Dubourg, J. Vanderplas, A. Passos,
and the TerraSwarm Research Center sponsored by MARCO and                       D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay.
DARPA.                                                                          Scikit-learn: Machine learning in Python. Journal of
                                                                                Machine Learning Research, 12:2825–2830, 2011.
                                                                         [21]   G. Ridgeway. Generalized Boosted Models: A guide to the
8.   REFERENCES                                                                 gbm package.
 [1] R. Bekkerman. The present and the future of the kdd cup
                                                                         [22]   S. Tyree, K. Weinberger, K. Agrawal, and J. Paykin.
     competition: an outsider’s perspective.
                                                                                Parallel boosted regression trees for web search ranking. In
 [2] R. Bekkerman, M. Bilenko, and J. Langford. Scaling Up                      Proceedings of the 20th international conference on World
     Machine Learning: Parallel and Distributed Approaches.                     wide web, pages 387–396. ACM, 2011.
     Cambridge University Press, New York, NY, USA, 2011.
                                                                         [23]   J. Ye, J.-H. Chow, J. Chen, and Z. Zheng. Stochastic
 [3] J. Bennett and S. Lanning. The netflix prize. In                           gradient boosted distributed decision trees. In Proceedings
     Proceedings of the KDD Cup Workshop 2007, pages 3–6,                       of the 18th ACM Conference on Information and
     New York, Aug. 2007.                                                       Knowledge Management, CIKM ’09.
 [4] L. Breiman. Random forests. Maching Learning,                       [24]   Q. Zhang and W. Wang. A fast algorithm for approximate
     45(1):5–32, Oct. 2001.                                                     quantiles in high speed data streams. In Proceedings of the
 [5] C. Burges. From ranknet to lambdarank to lambdamart:                       19th International Conference on Scientific and Statistical
     An overview. Learning, 11:23–581, 2010.                                    Database Management, 2007.
 [6] O. Chapelle and Y. Chang. Yahoo! Learning to Rank                   [25]   T. Zhang and R. Johnson. Learning nonlinear functions
     Challenge Overview. Journal of Machine Learning                            using regularized greedy forest. IEEE Transactions on
     Research - W & CP, 14:1–24, 2011.                                          Pattern Analysis and Machine Intelligence, 36(5), 2014.
 [7] T. Chen, H. Li, Q. Yang, and Y. Yu. General functional
     matrix factorization using gradient boosting. In Proceeding
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