In surveys, the interest lies in estimating finite population parameters such as population totals and means. In most surveys, some auxiliary information is available at the estimation stage. This information may be incorporated in the estimation procedures to increase their precision. In this article, we use random forests to estimate the functional relationship between the survey variable and the auxiliary variables. In recent years, random forests have become attractive as National Statistical Offices have now access to a variety of data sources, potentially exhibiting a large number of observations on a large number of variables. We establish the theoretical properties of model-assisted procedures based on random forests and derive corresponding variance estimators. A model-calibration procedure for handling multiple survey variables is also discussed. The results of a simulation study suggest that the proposed point and estimation procedures perform well in term of bias, efficiency, and coverage of normal-based confidence intervals, in a wide variety of settings. Finally, we apply the proposed methods using data on radio audiences collected by Médiamétrie, a French audience company.
Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；Technical University of Munich（慕尼黑工业大学）
In this investigation, we outline a data-assisted approach that employs random forest classifiers for local and dynamic combustion submodel assignment in turbulent-combustion simulations. This method is applied in simulations of a single-element GOX/GCH4 rocket combustor; a priori as well as a posteriori assessments are conducted to (i) evaluate the accuracy and adjustability of the classifier for targeting different quantities-of-interest (QoIs), and (ii) assess improvements, resulting from the data-assisted combustion model assignment, in predicting target QoIs during simulation runtime. Res…
We consider applying multi-armed bandits to model-assisted designs for dose-finding clinical trials. Multi-armed bandits are very simple and powerful methods to determine actions to maximize a reward in a limited number of trials. Among the multi-armed bandits, we first consider the use of Thompson sampling which determines actions based on random samples from a posterior distribution. In the small sample size, as shown in dose-finding trials, because the tails of posterior distribution are heavier and random samples are too much variability, we also consider an application of regularized Thom…
In (\cite{zhang2014nonlinear,zhang2014nonlinear2}), we have viewed machine learning as a coding and dimensionality reduction problem, and further proposed a simple unsupervised dimensionality reduction method, entitled deep distributed random samplings (DDRS). In this paper, we further extend it to supervised learning incrementally. The key idea here is to incorporate label information into the coding process by reformulating that each center in DDRS has multiple output units indicating which class the center belongs to. The supervised learning method seems somewhat similar with random forests…
Prediction in high dimensional settings is difficult due to large by number of variables relative to the sample size. We demonstrate how auxiliary "co-data" can be used to improve the performance of a Random Forest in such a setting. Co-data are incorporated in the Random Forest by replacing the uniform sampling probabilities (used to draw candidate variables, the default for a Random Forest) by co-data moderated sampling probabilities. Co-data here is defined as any type information that is available on the variables of the primary data, but does not use its response labels. These moderated s…
Several studies have shown that combining machine learning models in an appropriate way will introduce improvements in the individual predictions made by the base models. The key to make well-performing ensemble model is in the diversity of the base models. Of the most common solutions for introducing diversity into the decision trees are bagging and random forest. Bagging enhances the diversity by sampling with replacement and generating many training data sets, while random forest adds selecting a random number of features as well. This has made the random forest a winning candidate for many…
CRIStAL Lab, UMR 9189, Université Charles de Gaulle, Lille 3（里尔第三大学（戴高乐大学）CRIStAL实验室）；Université Paris-Est, A3SI-ESIEE LIGM（巴黎东大学 ESIEE LIGM）
Random forests perform bootstrap-aggregation by sampling the training samples with replacement. This enables the evaluation of out-of-bag error which serves as a internal cross-validation mechanism. Our motivation lies in using the unsampled training samples to improve each decision tree in the ensemble. We study the effect of using the out-of-bag samples to improve the generalization error first of the decision trees and second the random forest by post-pruning. A preliminary empirical study on four UCI repository datasets show consistent decrease in the size of the forests without considerab…
Missing data are common in data analyses in biomedical fields, and imputation methods based on random forests (RF) have become widely accepted, as the RF algorithm can achieve high accuracy without the need for specification of data distributions or relationships. However, the predictions from RF do not contain information about prediction uncertainty, which was unacceptable for multiple imputation. Available RF-based multiple imputation methods tried to do proper multiple imputation either by sampling directly from observations under predicting nodes without accounting for the prediction erro…
CNRS（法国国家科学研究中心）；Télécom ParisTech（巴黎高等电信学院）；Université Paris-Saclay（巴黎萨克雷大学）；Institut Supérieur de l’Aéronautique et de l’Espace (ISAE-SUPAERO)（法国国立高等航空航天学院（ISAE-SUPAERO））；Université d’Évry val d’Essonne（埃夫里-瓦尔德埃松大学）
Random Forests (RFs) are strong machine learning tools for classification and regression. However, they remain supervised algorithms, and no extension of RFs to the one-class setting has been proposed, except for techniques based on second-class sampling. This work fills this gap by proposing a natural methodology to extend standard splitting criteria to the one-class setting, structurally generalizing RFs to one-class classification. An extensive benchmark of seven state-of-the-art anomaly detection algorithms is also presented. This empirically demonstrates the relevance of our approach.
We study the variability of predictions made by bagged learners and random forests, and show how to estimate standard errors for these methods. Our work builds on variance estimates for bagging proposed by Efron (1992, 2012) that are based on the jackknife and the infinitesimal jackknife (IJ). In practice, bagged predictors are computed using a finite number B of bootstrap replicates, and working with a large B can be computationally expensive. Direct applications of jackknife and IJ estimators to bagging require B on the order of n^{1.5} bootstrap replicates to converge, where n is the size o…
Random forest is widely exploited as an ensemble learning method. In many practical applications, however, there is still a significant challenge to learn from imbalanced data. To alleviate this limitation, we propose a deep dynamic boosted forest (DDBF), a novel ensemble algorithm that incorporates the notion of hard example mining into random forest. Specically, we propose to measure the quality of each leaf node of every decision tree in the random forest to determine hard examples. By iteratively training and then removing easy examples from training data, we evolve the random forest to fo…
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…
Random Forest remains one of Data Mining's most enduring ensemble algorithms, achieving well-documented levels of accuracy and processing speed, as well as regularly appearing in new research. However, with data mining now reaching the domain of hardware-constrained devices such as smartphones and Internet of Things (IoT) devices, there is continued need for further research into algorithm efficiency to deliver greater processing speed without sacrificing accuracy. Our proposed FastForest algorithm delivers an average 24% increase in processing speed compared with Random Forest whilst maintain…
The infinitesimal jackknife (IJ) has recently been applied to the random forest to estimate its prediction variance. These theorems were verified under a traditional random forest framework which uses classification and regression trees (CART) and bootstrap resampling. However, random forests using conditional inference (CI) trees and subsampling have been found to be not prone to variable selection bias. Here, we conduct simulation experiments using a novel approach to explore the applicability of the IJ to random forests using variations on the resampling method and base learner. Test data p…
Instituto Nacional de Estadística（国家统计局）；University of Southampton（南安普顿大学）；Statistisk sentralbyraa（中央统计局）；Universitetet i Oslo（奥斯陆大学）
Design-consistent model-assisted estimation has become the standard practice in survey sampling. However, a general theory is lacking so far, which allows one to incorporate modern machine-learning techniques that can lead to potentially much more powerful assisting models. We propose a subsampling Rao-Blackwell method, and develop a statistical learning theory for exactly design-unbiased estimation with the help of linear or non-linear prediction models. Our approach makes use of classic ideas from Statistical Science as well as the rapidly growing field of Machine Learning. Provided rich aux…
Columbia University（哥伦比亚大学）；Carnegie Mellon University（卡内基梅隆大学）
We study rare-event simulation for a class of problems where the target hitting sets of interest are defined via modern machine learning tools such as neural networks and random forests. This problem is motivated from fast emerging studies on the safety evaluation of intelligent systems, robustness quantification of learning models, and other potential applications to large-scale simulation in which machine learning tools can be used to approximate complex rare-event set boundaries. We investigate an importance sampling scheme that integrates the dominating point machinery in large deviations …
EPFL（洛桑联邦理工学院）；IBM Research Lab, Zurich（IBM苏黎世研究实验室）
We study the effectiveness of non-uniform randomized feature selection in decision tree classification. We experimentally evaluate two feature selection methodologies, based on information extracted from the provided dataset: $(i)$ \emph{leverage scores-based} and $(ii)$ \emph{norm-based} feature selection. Experimental evaluation of the proposed feature selection techniques indicate that such approaches might be more effective compared to naive uniform feature selection and moreover having comparable performance to the random forest algorithm [3]
Respondent-Driven Sampling is a method to sample hard-to-reach human populations by link-tracing over their social networks. Beginning with a convenience sample, each person sampled is given a small number of uniquely identified coupons to distribute to other members of the target population, making them eligible for enrollment in the study. This can be an effective means to collect large diverse samples from many populations. Inference from such data requires specialized techniques for two reasons. Unlike in standard sampling designs, the sampling process is both partially beyond the control …
Surrogate-assisted optimal sampling for risk prediction under measurement constraints
University of Seoul（首尔大学）；Department of Statistics and Data Science, University of Seoul（首尔大学统计与数据科学系）；Department of Statistics, University of Seoul（首尔大学统计系）
The aim of this paper is twofold. First, three theoretical principles are formalized: randomization, overrepresentation and restriction. We develop these principles and give a rationale for their use in choosing the sampling design in a systematic way. In the model-assisted framework, knowledge of the population is formalized by modelling the population and the sampling design is chosen accordingly. We show how the principles of overrepresentation and of restriction naturally arise from the modelling of the population. The balanced sampling then appears as a consequence of the modelling. Secon…
Few problems in statistics are as perplexing as variable selection in the presence of very many redundant covariates. The variable selection problem is most familiar in parametric environments such as the linear model or additive variants thereof. In this work, we abandon the linear model framework, which can be quite detrimental when the covariates impact the outcome in a non-linear way, and turn to tree-based methods for variable selection. Such variable screening is traditionally done by pruning down large trees or by ranking variables based on some importance measure. Despite heavily used …
A model-assisted semiparametric method of estimating finite population totals is investigated to improve the precision of survey estimators by incorporating multivariate auxiliary information. The proposed superpopulation model is a single-index model which has proven to be a simple and efficient semiparametric tool in multivariate regression. A class of estimators based on polynomial spline regression is proposed. These estimators are robust against deviation from single-index models. Under standard design conditions, the proposed estimators are asymptotically design-unbiased, consistent and …
Model-assisted estimation with complex survey data is an important practical problem in survey sampling. When there are many auxiliary variables, selecting significant variables associated with the study variable would be necessary to achieve efficient estimation of population parameters of interest. In this paper, we formulate a regularized regression estimator in the framework of Bayesian inference using the penalty function as the shrinkage prior for model selection. The proposed Bayesian approach enables us to get not only efficient point estimates but also reasonable credible intervals. R…
The goal of survey design is often to minimize the errors associated with inference: the total of bias and variance. Random surveys are common because they allow the use of theoretically unbiased estimators. In practice however, such design-based approaches are often unable to account for logistical or budgetary constraints. Thus, they may result in samples that are logistically inefficient, or infeasible to implement. Various balancing and optimal sampling techniques have been proposed to improve the statistical efficiency of such designs, but few models have attempted to explicitly incorpora…
A Unified Framework for Density Estimation under Right-Censored Point-Centred Quarter Sampling
East China Normal University（华东师范大学）；Zhejiang Tiantong Forest Ecosystem National Observation and Research Station, School of Ecological and Environmental Sciences, East China Normal University（浙江天目山森林生态系统国家野外科学观测研究站，华东大学生态与环境科学学院）；Zhejiang Zhoushan Island Ecosystem Observation and Research Station, School of Ecological and Environmental Sciences, East China Normal University（浙江舟山岛生态系统观测研究站，华东大学生态与环境科学学院）；KLATASDS-MOE, School of Statistics, East China Normal University（华东师范大学统计学院）
Many scientific and engineering challenges -- ranging from personalized medicine to customized marketing recommendations -- require an understanding of treatment effect heterogeneity. In this paper, we develop a non-parametric causal forest for estimating heterogeneous treatment effects that extends Breiman's widely used random forest algorithm. In the potential outcomes framework with unconfoundedness, we show that causal forests are pointwise consistent for the true treatment effect, and have an asymptotically Gaussian and centered sampling distribution. We also discuss a practical method fo…
