Ensembles of randomized decision trees, usually referred to as random forests, are widely used for classification and regression tasks in machine learning and statistics. Random forests achieve competitive predictive performance and are computationally efficient to train and test, making them excellent candidates for real-world prediction tasks. The most popular random forest variants (such as Breiman's random forest and extremely randomized trees) operate on batches of training data. Online methods are now in greater demand. Existing online random forests, however, require more training data than their batch counterpart to achieve comparable predictive performance. In this work, we use Mondrian processes (Roy and Teh, 2009) to construct ensembles of random decision trees we call Mondrian forests. Mondrian forests can be grown in an incremental/online fashion and remarkably, the distribution of online Mondrian forests is the same as that of batch Mondrian forests. Mondrian forests achieve competitive predictive performance comparable with existing online random forests and periodically re-trained batch random forests, while being more than an order of magnitude faster, thus representing a better computation vs accuracy tradeoff.
We propose a new method, named isolation Mondrian forest (iMondrian forest), for batch and online anomaly detection. The proposed method is a novel hybrid of isolation forest and Mondrian forest which are existing methods for batch anomaly detection and online random forest, respectively. iMondrian forest takes the idea of isolation, using the depth of a node in a tree, and implements it in the Mondrian forest structure. The result is a new data structure which can accept streaming data in an online manner while being used for anomaly detection. Our experiments show that iMondrian forest mostl…
The stable under iterated tessellation (STIT) process is a stochastic process that produces a recursive partition of space with cut directions drawn independently from a distribution over the sphere. The case of random axis-aligned cuts is known as the Mondrian process. Random forests and Laplace kernel approximations built from the Mondrian process have led to efficient online learning methods and Bayesian optimization. In this work, we utilize tools from stochastic geometry to resolve some fundamental questions concerning STIT processes in machine learning. First, we show that a STIT process…
University of Warwick（华威大学）；University of Cambridge（剑桥大学）；Amazon（亚马逊）
Anomaly detection at scale is an extremely challenging problem of great practicality. When data is large and high-dimensional, it can be difficult to detect which observations do not fit the expected behaviour. Recent work has coalesced on variations of (random) $k$\emph{d-trees} to summarise data for anomaly detection. However, these methods rely on ad-hoc score functions that are not easy to interpret, making it difficult to asses the severity of the detected anomalies or select a reasonable threshold in the absence of labelled anomalies. To solve these issues, we contextualise these methods…
$Q$-learning is the most fundamental model-free reinforcement learning algorithm. Deployment of $Q$-learning requires approximation of the state-action value function (also known as the $Q$-function). In this work, we provide online random forests as $Q$-function approximators and propose a novel method wherein the random forest is grown as learning proceeds (through expanding forests). We demonstrate improved performance of our methods over state-of-the-art Deep $Q$-Networks in two OpenAI gyms (`blackjack' and `inverted pendulum') but not in the `lunar lander' gym. We suspect that the resilie…
Interpretability of learning algorithms is crucial for applications involving critical decisions, and variable importance is one of the main interpretation tools. Shapley effects are now widely used to interpret both tree ensembles and neural networks, as they can efficiently handle dependence and interactions in the data, as opposed to most other variable importance measures. However, estimating Shapley effects is a challenging task, because of the computational complexity and the conditional expectation estimates. Accordingly, existing Shapley algorithms have flaws: a costly running time, or…
INRIA（法国国家信息与自动化研究所）；INSERM（法国国家健康与医学研究院）；Univ. Bordeaux（波尔多大学）；Univ. Paris-Sud Orsay（巴黎第十一大学）；Univ. Paris Descartes（巴黎第五大学）；Université Côte d’Azur（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；Université de Toulouse（图卢兹大学）；INRA（法国国家农业研究院）
Variable importance measures are the main tools to analyze the black-box mechanisms of random forests. Although the mean decrease accuracy (MDA) is widely accepted as the most efficient variable importance measure for random forests, little is known about its statistical properties. In fact, the definition of MDA varies across the main random forest software. In this article, our objective is to rigorously analyze the behavior of the main MDA implementations. Consequently, we mathematically formalize the various implemented MDA algorithms, and then establish their limits when the sample size i…
Beyond Point Prediction: Artificial Representative Trees with Uncertainty
University of Luebeck（吕贝克大学）；University Medical Center Göttingen（哥廷根大学医学中心）；Lower Saxony Center for Artificial Intelligence and Causal Methods in Medicine（下萨克森州医学人工智能与因果方法中心）；Jönköping University（延雪平大学）
This transformation of food delivery businesses to online platforms has gained high attention in recent years. This due to the availability of customizing ordering experiences, easy payment methods, fast delivery, and others. The competition between online food delivery providers has intensified to attain a wider range of customers. Hence, they should have a better understanding of their customers' needs and predict their purchasing decisions. Machine learning has a significant impact on companies' bottom line. They are used to construct models and strategies in industries that rely on big dat…
Electromyography signals can be used as training data by machine learning models to classify various gestures. We seek to produce a model that can classify six different hand gestures with a limited number of samples that generalizes well to a wider audience while comparing the effect of our feature extraction results on model accuracy to other more conventional methods such as the use of AR parameters on a sliding window across the channels of a signal. We appeal to a set of more elementary methods such as the use of random bounds on a signal, but desire to show the power these methods can ca…
Online Hierarchical Forecasting for Power Consumption Data
EDF R&D（法国电力公司研发中心）；INRIA - Département d’Informatique de l’École Normale Supérieure, PSL Research University（法国国家信息与自动化研究所 - 巴黎高等师范学院信息系，巴黎文理研究大学）；Laboratoire de mathématiques d’Orsay, CNRS, Université Paris-Saclay（奥赛数学实验室，法国国家科学研究中心，巴黎萨克雷大学）
Didi Chuxing（滴滴出行）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Uplift modeling is a rapidly growing approach that utilizes causal inference and machine learning methods to directly estimate the heterogeneous treatment effects, which has been widely applied to various online marketplaces to assist large-scale decision-making in recent years. The existing popular models, like causal forest (CF), are limited to either discrete treatments or posing parametric assumptions on the outcome-treatment relationship that may suffer model misspecification. However, continuous treatments (e.g., price, duration) often arise in marketplaces. To alleviate these restrictio…
Reliable Real-Time Value at Risk Estimation via Quantile Regression Forest with Conformal Calibration
Institute of Statistics and Big Data, Renmin University of China（统计与大数据研究院，中国人民大学）；Department of Decision Analytics and Operations, City University of Hong Kong（决策分析与运营部门，香港城市大学）；School of Information, Renmin University of China（信息学院，中国人民大学）
