XGBoost

Presented by

• Chun Waan Loke
• Peter Chong
• Clarice Osmond
• Zhilong Li

System Design

Column Block for Parallel Learning

The most time consuming part of tree learning is to get the data into sorted order. To overcome this problem, XGBoost stores the data in blocks where each block performs the sorting operation in parallel. The results are then merged together.

1. For the exact greedy algorithm, XGBoost stores the entire dataset in a single block

   • Original spase aware algorithm costs: [math]\displaystyle{ O(Kd∥x∥_0 log(n)) }[/math]
   • Tree boosting on block structure costs: [math]\displaystyle{ O(Kd∥x∥_0 + ∥x∥_0 log(n)) }[/math]
   • Hence, block structure helps to save an additional [math]\displaystyle{ log(n) }[/math] factor

2. For approximate algorithms, XGBoost stores the dataset in multiple blocks

   • Original algorithm with binary search costs: [math]\displaystyle{ O(Kd∥x∥_0 log(q)) }[/math]
   • With block structure costs: [math]\displaystyle{ O(Kd∥x∥_0 + ∥x∥_0 log(B)) }[/math]
   • Hence, block structure helps to save an additional [math]\displaystyle{ log(q) }[/math] factor

K = total number of trees
d = maximum depth of the tree
[math]\displaystyle{ ∥x∥_0 }[/math] = number of non-missing entries in the training data
n = number of rows in the dataset
q = number of proposal candidates in the dataset, usually between 32 to 100
B = maximum number of rows in each block

Cache-aware Access

The proposed block structure optimizes the computation complexity but requires indirect fetches of gradient statistics by row index. XGBoost optimizes the process by using the following methods.

1. For the exact greedy algorithm, XGBoost uses a cache-aware prefetching algorithm

   • It stores Gradient and Hessians in the cache to make calculations fast
   • It runs twice as fast as the naive method when the dataset is large

2. For approximate algorithms, XGBoost chooses a specific block size

   • Choosing a small block size results in inefficient parallelization
   • Choosing a large block size results in cache misses
   • Various choices of block size are compared and the results are shown in Figure 9
   • XGBoost chose [math]\displaystyle{ 2^{16} }[/math] as the block size

Blocks for Out-of-core Computation

When the dataset is too large for the cache and main memory, XGBoost utilizes disk spaces as well. Since reading and writing data to the disks are slow, XGBoost optimizes the process by using the following two methods.

1. Block Compression

   • Blocks are compressed by columns
   • Although decompressing takes time, it is still faster than reading from the disks

2. Block Sharding

   • If multiple disks are available, data is split into those disks
   • When the CPU needs data, all the disks can be read at the same time

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