We introduce instancewise feature selection as a methodology for model interpretation. Our method is based on learning a function to extract a subset of features that are most informative for each given example. This feature selector is trained to maximize the mutual information between selected features and the responsevariable, where the conditional distribution of the response variable given the input is the model to be explained. We develop an efficient variational approximation to the mutual information, and show the effectiveness of our method on a variety of synthetic and real data sets using both quantitative metrics and human evaluation.

Variable selection is a classic problem in machine learning (ML), widely used to find important explanatory factors, and improve generalization performance and interpretability of ML models. In this paper, we consider variable selection for models where multiple responses are to be predicted based on the same set of covariates. Since each response is relevant to a unique subset of covariates, we desire the selected variables for different responses have small overlap. We propose a regularizer that simultaneously encourage orthogonality and sparsity, which jointly brings in an effect of reducing overlap. We apply this regularizer to four model instances and develop efficient algorithms to solve the regularized problems. We provide a formal analysis on why the proposed regularizer can reduce generalization error. Experiments on both simulation studies and real-world datasets demonstrate the effectiveness of the proposed regularizer in selecting less-overlapped variables and improving generalization performance.

It is one typical and general topic of learning a good embedding model to efficiently learn the representation coefficients between two spaces/subspaces. To solve this task, $L_{1}$ regularization is widely used for the pursuit of feature selection and avoiding overfitting, and yet the sparse estimation of features in $L_{1}$ regularization may cause the underfitting of training data. $L_{2}$ regularization is also frequently used, but it is a biased estimator. In this paper, we propose the idea that the features consist of three orthogonal parts, \emph{namely} sparse strong signals, dense weak signals and random noise, in which both strong and weak signals contribute to the fitting of data. To facilitate such novel decomposition, \emph{MSplit} LBI is for the first time proposed to realize feature selection and dense estimation simultaneously. We provide theoretical and simulational verification that our method exceeds $L_{1}$ and $L_{2}$ regularization, and extensive experimental results show that our method achieves state-of-the-art performance in the few-shot and zero-shot learning.

Analyzing large-scale, multi-experiment studies requires scientists to test each experimental outcome for statistical significance and then assess the results as a whole. We present Black Box FDR (BB-FDR), an empirical-Bayes method for analyzing multi-experiment studies when many covariates are gathered per experiment. BB-FDR learns a series of black box predictive models to boost power and control the false discovery rate (FDR) at two stages of study analysis. In Stage 1, it uses a deep neural network prior to report which experiments yielded significant outcomes. In Stage 2, a separate black box model of each covariate is used to select features that have significant predictive power across all experiments. In benchmarks, BB-FDR outperforms competing state-of-the-art methods in both stages of analysis. We apply BB-FDR to two real studies on cancer drug efficacy. For both studies, BB-FDR increases the proportion of significant outcomes discovered and selects variables that reveal key genomic drivers of drug sensitivity and resistance in cancer.

We propose a variable selection method for high dimensional regression models, which allows for complex, nonlinear, and high-order interactions among variables. The proposed method approximates this complex system using a penalized neural network and selects explanatory variables by measuring their utility in explaining the variance of the response variable. This measurement is based on a novel statistic called Drop-Out-One Loss. The proposed method also allows (overlapping) group variable selection. We prove that the proposed method can select relevant variables and exclude irrelevant variables with probability one as the sample size goes to infinity, which is referred to as the Oracle Property. Experimental results on simulated and real world datasets show the efficiency of our method in terms of variable selection and prediction accuracy.