You might have heard about random forests as a somewhat-new analytical method in forestry. But how do they work?

We investigate the challenge of multi-output learning, where the goal is to learn a vector-valued function based on a supervised data set. This includes a range of important problems in Machine Learning including multi-target regression, multi-class classification and multi-label classification. We begin our analysis by introducing the self-bounding Lipschitz condition for multi-output loss functions, which interpolates continuously between a classical Lipschitz condition and a multi-dimensional analogue of a smoothness condition. We then show that the self-bounding Lipschitz condition gives rise to optimistic bounds for multi-output learning, which are minimax optimal up to logarithmic factors. The proof exploits local Rademacher complexity combined with a powerful minoration inequality due to Srebro, Sridharan and Tewari. As an application we derive a state-of-the-art generalization bound for multi-class gradient boosting.

This release marks a major milestone for the XGBoost project. In this release, we introduce an experimental support of using JSON for serializing (saving/loading) XGBoost models and related hyperparameters for training. We would like to eventually replace the old binary format with JSON, since it is an open format and parsers are available in many programming languages and platforms. See the documentation for model I/O using JSON. Previously, users often ran into issues where the model file produced by one machine could not load or run on another machine.

A novel gradient boosting framework is proposed where shallow neural networks are employed as "weak learners". General loss functions are considered under this unified framework with specific examples presented for classification, regression and learning to rank. A fully corrective step is incorporated to remedy the pitfall of greedy function approximation of classic gradient boosting decision tree. The proposed model rendered state-of-the-art results in all three tasks on multiple datasets. An ablation study is performed to shed light on the effect of each model components and model hyperparameters.

Time series data is all around us; some examples are the weather, human behavioral patterns as consumers and members of society, and financial data. In this course, you'll learn how to calculate technical indicators from historical stock data, and how to create features and targets out of the historical stock data. You'll understand how to prepare our features for linear models, xgboost models, and neural network models. We will then use linear models, decision trees, random forests, and neural networks to predict the future price of stocks in the US markets. You will also learn how to evaluate the performance of the various models we train in order to optimize them, so our predictions have enough accuracy to make a stock trading strategy profitable.

We combine random forest (RF) and conditional random field (CRF) into a new computational framework, called random forest random field (RF) 2. Inference of (RF) 2 uses the Swendsen-Wang cut algorithm, characterized by Metropolis-Hastings jumps. A jump from one state to another depends on the ratio of the proposal distributions, and on the ratio of the posterior distributions of the two states. Prior work typically resorts to a parametric estimation of these four distributions, and then computes their ratio. Our key idea is to instead directly estimate these ratios using RF. RF collects in leaf nodes of each decision tree the class histograms of training examples.

Inspired by the big ol' long list of deep learning models I saw this morning, and @SpaceWhaleRider's love of science-y A-Z lists, I've decided to create an A to Z series of tweets on popular #MachineLearning and #DeepLearning methods / algorithms. A is for... the Apriori Algorithm! Ex: if someone purchases the same products as you, in general, then you'd probably purchase something they've purchased. B is for... Bootstrapped Aggregation (Bagging)! This is an ensemble meta-algorithm designed to improve the stability and accuracy of machine learning algorithms used in statistical classification regression.

Multi-layered distributed representation is believed to be the key ingredient of deep neural networks especially in cognitive tasks like computer vision. While non-differentiable models such as gradient boosting decision trees (GBDTs) are still the dominant methods for modeling discrete or tabular data, they are hard to incorporate with such representation learning ability. In this work, we propose the multi-layered GBDT forest (mGBDTs), with an explicit emphasis on exploring the ability to learn hierarchical distributed representations by stacking several layers of regression GBDTs as its building block. The model can be jointly trained by a variant of target propagation across layers, without the need to derive backpropagation nor differentiability. Experiments confirmed the effectiveness of the model in terms of performance and representation learning ability.

Gradient Boosting Decision Tree (GBDT) is a popular machine learning algorithm, and has quite a few effective implementations such as XGBoost and pGBRT. Although many engineering optimizations have been adopted in these implementations, the efficiency and scalability are still unsatisfactory when the feature dimension is high and data size is large. A major reason is that for each feature, they need to scan all the data instances to estimate the information gain of all possible split points, which is very time consuming. To tackle this problem, we propose two novel techniques: \emph{Gradient-based One-Side Sampling} (GOSS) and \emph{Exclusive Feature Bundling} (EFB). With GOSS, we exclude a significant proportion of data instances with small gradients, and only use the rest to estimate the information gain.

Random forests are learning algorithms that build large collections of random trees and make predictions by averaging the individual tree predictions. In this paper, we consider various tree constructions and examine how the choice of parameters affects the generalization error of the resulting random forests as the sample size goes to infinity. We show that subsampling of data points during the tree construction phase is important: Forests can become inconsistent with either no subsampling or too severe subsampling. As a consequence, even highly randomized trees can lead to inconsistent forests if no subsampling is used, which implies that some of the commonly used setups for random forests can be inconsistent. As a second consequence we can show that trees that have good performance in nearest-neighbor search can be a poor choice for random forests.