In many applications, it is of interest to assess the relative contribution of features (or subsets of features) toward the goal of predicting a response -- in other words, to gauge the variable importance of features. Most recent work on variable importance assessment has focused on describing the importance of features within the confines of a given prediction algorithm. However, such assessment does not necessarily characterize the prediction potential of features, and may provide a misleading reflection of the intrinsic value of these features. To address this limitation, we propose a general framework for nonparametric inference on interpretable algorithm-agnostic variable importance. We define variable importance as a population-level contrast between the oracle predictiveness of all available features versus all features except those under consideration. We propose a nonparametric efficient estimation procedure that allows the construction of valid confidence intervals, even when machine learning techniques are used. We also outline a valid strategy for testing the null importance hypothesis. Through simulations, we show that our proposal has good operating characteristics, and we illustrate its use with data from a study of an antibody against HIV-1 infection.
Inference on summaries of a model-agnostic longitudinal variable importance trajectory with application to suicide prevention
Kaiser Permanente Washington Health Research Institute（凯撒永久华盛顿健康研究所）；Fred Hutchinson Cancer Center（弗雷德·哈钦森癌症中心）；University of Washington（华盛顿大学）；McGill University（麦吉尔大学）；Kaiser Permanente Bernard J. Tyson School of Medicine（凯撒永久伯纳德·J·泰森医学院）；HealthPartners Institute（健康伙伴研究所）
Wasserman et al. (2020, PNAS, vol. 117, pp. 16880-16890) constructed estimator agnostic and finite-sample valid confidence sets and hypothesis tests, using split-data likelihood ratio-based statistics. We demonstrate that the same approach extends to the use of split-data composite likelihood ratios as well, and thus establish universal methods for conducting multivariate inference when the data generating process is only known up to marginal and conditional relationships between the coordinates. Always-valid sequential inference is also considered.
LOCO Feature Importance Inference without Data Splitting via Minipatch Ensembles
Department of Statistics, Rice University（理查德·伊尔·米勒大学统计系）；Department of Statistics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校统计系）；Department of Statistics, Columbia University（哥伦比亚大学统计系）
Models in the supervised learning framework may capture rich and complex representations over the features that are hard for humans to interpret. Existing methods to explain such models are often specific to architectures and data where the features do not have a time-varying component. In this work, we propose TIME, a method to explain models that are inherently temporal in nature. Our approach (i) uses a model-agnostic permutation-based approach to analyze global feature importance, (ii) identifies the importance of salient features with respect to their temporal ordering as well as localize…
We consider Bayesian inference by importance sampling when the likelihood is analytically intractable but can be unbiasedly estimated. We refer to this procedure as importance sampling squared (IS2), as we can often estimate the likelihood itself by importance sampling. We provide a formal justification for importance sampling when working with an estimate of the likelihood and study its convergence properties. We analyze the effect of estimating the likelihood on the resulting inference and provide guidelines on how to set up the precision of the likelihood estimate in order to obtain an opti…
Kernel methods have revolutionized the fields of pattern recognition and machine learning. Their success, however, critically depends on the choice of kernel parameters. Using Gaussian process (GP) classification as a working example, this paper focuses on Bayesian inference of covariance (kernel) parameters using Markov chain Monte Carlo (MCMC) methods. The motivation is that, compared to standard optimization of kernel parameters, they have been systematically demonstrated to be superior in quantifying uncertainty in predictions. Recently, the Pseudo-Marginal MCMC approach has been proposed …
Sequential importance sampling algorithms have been defined to estimate likelihoods in models of ancestral population processes. However, these algorithms are based on features of the models with constant population size, and become inefficient when the population size varies in time, making likelihood-based inferences difficult in many demographic situations. In this work, we modify a previous sequential importance sampling algorithm to improve the efficiency of the likelihood estimation. Our procedure is still based on features of the model with constant size, but uses a resampling technique…
This article presents new methodology for sample-based Bayesian inference when data are partitioned and communication between the parts is expensive, as arises by necessity in the context of "big data" or by choice in order to take advantage of computational parallelism. The method, which we call the Laplace enriched multiple importance estimator, uses new multiple importance sampling techniques to approximate posterior expectations using samples drawn independently from the local posterior distributions (those conditioned on isolated parts of the data). We construct Laplace approximations fro…
University of South Australia（南澳大学）；Hefei University of Technology（合肥工业大学）
This paper studies the problem of estimating the contributions of features to the prediction of a specific instance by a machine learning model and the overall contribution of a feature to the model. The causal effect of a feature (variable) on the predicted outcome reflects the contribution of the feature to a prediction very well. A challenge is that most existing causal effects cannot be estimated from data without a known causal graph. In this paper, we define an explanatory causal effect based on a hypothetical ideal experiment. The definition brings several benefits to model agnostic exp…
