This paper presents a novel ensemble learning approach called Residual Likelihood Forests (RLF). Our weak learners produce conditional likelihoods that are sequentially optimized using global loss in the context of previous learners within a boosting-like framework (rather than probability distributions that are measured from observed data) and are combined multiplicatively (rather than additively). This increases the efficiency of our strong classifier, allowing for the design of classifiers which are more compact in terms of model capacity. We apply our method to several machine learning classification tasks, showing significant improvements in performance. When compared against several ensemble approaches including Random Forests and Gradient Boosted Trees, RLFs offer a significant improvement in performance whilst concurrently reducing the required model size.
Empirical Likelihood for Random Forests and Ensembles
Department of Economics University of Wisconsin–Madison（威斯康星大学麦迪逊分校经济系）；Graduate School of Economics Hitotsubashi University（早稻田大学经济学研究生院）；Department of Economics London School of Economics（伦敦经济学院经济系）
The issue of estimating residual variance in regression models has experienced relatively little attention in the machine learning community. However, the estimate is of primary interest in many practical applications, e.g. as a primary step towards the construction of prediction intervals. Here, we consider this issue for the random forest. Therein, the functional relationship between covariates and response variable is modeled by a weighted sum of the latter. The dependence structure is, however, involved in the weights that are constructed during the tree construction process making the mod…
In this paper we propose using the principle of boosting to reduce the bias of a random forest prediction in the regression setting. From the original random forest fit we extract the residuals and then fit another random forest to these residuals. We call the sum of these two random forests a \textit{one-step boosted forest}. We show with simulated and real data that the one-step boosted forest has a reduced bias compared to the original random forest. The paper also provides a variance estimate of the one-step boosted forest by an extension of the infinitesimal Jackknife estimator. Using thi…
Random forest and deep neural network are two schools of effective classification methods in machine learning. While the random forest is robust irrespective of the data domain, the deep neural network has advantages in handling high dimensional data. In view that a differentiable neural decision forest can be added to the neural network to fully exploit the benefits of both models, in our work, we further combine convolutional autoencoder with neural decision forest, where autoencoder has its advantages in finding the hidden representations of the input data. We develop a gradient boost modul…
Monash University（莫纳什大学）；ARC Centre of Excellence for Robotic Vision（澳大利亚研究理事会机器人视觉卓越中心）
In recent times, many of the breakthroughs in various vision-related tasks have revolved around improving learning of deep models; these methods have ranged from network architectural improvements such as Residual Networks, to various forms of regularisation such as Batch Normalisation. In essence, many of these techniques revolve around better conditioning, allowing for deeper and deeper models to be successfully learned. In this paper, we look towards better conditioning Generative Adversarial Networks (GANs) in an unsupervised learning setting. Our method embeds the powerful discriminating …
In short, our experiments suggest that yes, on average, rotation forest is better than the most common alternatives when all the attributes are real-valued. Rotation forest is a tree based ensemble that performs transforms on subsets of attributes prior to constructing each tree. We present an empirical comparison of classifiers for problems with only real-valued features. We evaluate classifiers from three families of algorithms: support vector machines; tree-based ensembles; and neural networks tuned with a large grid search. We compare classifiers on unseen data based on the quality of the …
Feature Space Selection and Heterogeneous Effect Estimation for Blood-Brain Barrier Permeability: A Random Forest to the Generalized Random Forest Pipeline
University of Pretoria（比勒陀利亚大学）；Ferdowsi University of Mashhad（马什哈德菲尔多西大学）
Random forests have become an established tool for classification and regression, in particular in high-dimensional settings and in the presence of complex predictor-response relationships. For bounded outcome variables restricted to the unit interval, however, classical random forest approaches may severely suffer as they do not account for the heteroscedasticity in the data. A random forest approach is proposed for relating beta distributed outcomes to explanatory variables. The approach explicitly makes use of the likelihood function of the beta distribution for the selection of splits duri…
Vanderbilt University（范德堡大学）；University of Notre Dame（圣母大学）；Department of Psychology and Human Development（心理与人类发展系）；Department of Applied and Computational Mathematics & Statistics（应用与计算数学及统计学系）；Nashville, TN（纳什维尔，田纳西州）；Notre Dame, IN（圣母大学，印第安纳州）
We propose a novel tree-based ensemble method named Selective Cascade of Residual ExtraTrees (SCORE). SCORE draws inspiration from representation learning, incorporates regularized regression with variable selection features, and utilizes boosting to improve prediction and reduce generalization errors. We also develop a variable importance measure to increase the explainability of SCORE. Our computer experiments show that SCORE provides comparable or superior performance in prediction against ExtraTrees, random forest, gradient boosting machine, and neural networks; and the proposed variable i…
University of Pennsylvania（宾夕法尼亚大学）；Apple Inc.（苹果公司）
There is a large literature explaining why AdaBoost is a successful classifier. The literature on AdaBoost focuses on classifier margins and boosting's interpretation as the optimization of an exponential likelihood function. These existing explanations, however, have been pointed out to be incomplete. A random forest is another popular ensemble method for which there is substantially less explanation in the literature. We introduce a novel perspective on AdaBoost and random forests that proposes that the two algorithms work for similar reasons. While both classifiers achieve similar predictiv…
We introduce random spatial forests, a method of bagging regression trees allowing for spatial correlation. Our main contribution is the development of a computationally efficient tree building algorithm which selects each split of the tree adjusting for spatial correlation. We evaluate two different approaches for estimation of random spatial forests, a pseudo-likelihood approach combining random forests with kriging and a non-parametric version for a general class of spatial smoothers. We show improved prediction accuracy of our method compared to existing two-step approaches combining rando…
Regression models for supervised learning problems with a continuous target are commonly understood as models for the conditional mean of the target given predictors. This notion is simple and therefore appealing for interpretation and visualisation. Information about the whole underlying conditional distribution is, however, not available from these models. A more general understanding of regression models as models for conditional distributions allows much broader inference from such models, for example the computation of prediction intervals. Several random forest-type algorithms aim at est…
This document is an invited chapter covering the specificities of ABC model choice, intended for the incoming Handbook of ABC by Sisson, Fan, and Beaumont (2017). Beyond exposing the potential pitfalls of ABC based posterior probabilities, the review emphasizes mostly the solution proposed by Pudlo et al. (2016) on the use of random forests for aggregating summary statistics and and for estimating the posterior probability of the most likely model via a secondary random fores.
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Pittsburgh（匹兹堡大学）
Standard supervised learning procedures are validated against a test set that is assumed to have come from the same distribution as the training data. However, in many problems, the test data may have come from a different distribution. We consider the case of having many labeled observations from one distribution, $P_1$, and making predictions at unlabeled points that come from $P_2$. We combine the high predictive accuracy of random forests (Breiman, 2001) with an importance sampling scheme, where the splits and predictions of the base-trees are done in a weighted manner, which we call Local…
An important issue when using Machine Learning algorithms in recent research is the lack of interpretability. Although these algorithms provide accurate point predictions for various learning problems, uncertainty estimates connected with point predictions are rather sparse. A contribution to this gap for the Random Forest Regression Learner is presented here. Based on its Out-of-Bag procedure, several parametric and non-parametric prediction intervals are provided for Random Forest point predictions and theoretical guarantees for its correct coverage probability is delivered. In a second part…
Tractable yet expressive density estimators are a key building block of probabilistic machine learning. While sum-product networks (SPNs) offer attractive inference capabilities, obtaining structures large enough to fit complex, high-dimensional data has proven challenging. In this paper, we present random sum-product forests (RSPFs), an ensemble approach for mixing multiple randomly generated SPNs. We also introduce residual links, which reference specialized substructures of other component SPNs in order to leverage the context-specific knowledge encoded within them. Our empirical evidence d…
A fully nonparametric approach for making probabilistic predictions in multi-response regression problems is introduced. Random forests are used as marginal models for each response variable and, as novel contribution of the present work, the dependence between the multiple response variables is modeled by a generative neural network. This combined modeling approach of random forests, corresponding empirical marginal residual distributions and a generative neural network is referred to as RafterNet. Multiple datasets serve as examples to demonstrate the flexibility of the approach and its impa…
A conditional independence graph is a concise representation of pairwise conditional independence among many variables. Graphical Random Forests (GRaFo) are a novel method for estimating pairwise conditional independence relationships among mixed-type, i.e. continuous and discrete, variables. The number of edges is a tuning parameter in any graphical model estimator and there is no obvious number that constitutes a good choice. Stability Selection helps choosing this parameter with respect to a bound on the expected number of false positives (error control). The performance of GRaFo is evaluat…
The uncertainties in future Bitcoin price make it difficult to accurately predict the price of Bitcoin. Accurately predicting the price for Bitcoin is therefore important for decision-making process of investors and market players in the cryptocurrency market. Using historical data from 01/01/2012 to 16/08/2019, machine learning techniques (Generalized linear model via penalized maximum likelihood, random forest, support vector regression with linear kernel, and stacking ensemble) were used to forecast the price of Bitcoin. The prediction models employed key and high dimensional technical indi…
Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that correspond to subforests. For these singularities, we compute the real log-canonical thresholds (also known as stochastic complexities or learning coefficients) that quantify the large-sample behavior of the marginal likelihood in Bayesian inference. This provides the information needed for a recently introduced generalization of the Bayesian information criterion. Our mathematical developments treat the general set…
This paper extends recent work on boosting random forests to model non-Gaussian responses. Given an exponential family $\mathbb{E}[Y|X] = g^{-1}(f(X))$ our goal is to obtain an estimate for $f$. We start with an MLE-type estimate in the link space and then define generalised residuals from it. We use these residuals and some corresponding weights to fit a base random forest and then repeat the same to obtain a boost random forest. We call the sum of these three estimators a \textit{generalised boosted forest}. We show with simulated and real data that both the random forest steps reduces test-…
University of Bremen（不来梅大学）；Vector Institute（向量研究所）；University of Toronto（多伦多大学）
We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting network architectures. In contrast, our approach only requires adding a simple normalization step during training, already available in standard frameworks. Invertible ResNets define a generative model which can be trained by maximum likelihood on unlabeled data. To compute likelihoods, we introduce a tractable approximation to the Jacobian log-determinant …
The oblique random survival forest (RSF) is an ensemble supervised learning method for right-censored outcomes. Trees in the oblique RSF are grown using linear combinations of predictors to create branches, whereas in the standard RSF, a single predictor is used. Oblique RSF ensembles often have higher prediction accuracy than standard RSF ensembles. However, assessing all possible linear combinations of predictors induces significant computational overhead that limits applications to large-scale data sets. In addition, few methods have been developed for interpretation of oblique RSF ensemble…
