Variable selection has been played a critical role in contemporary statistics and scientific discoveries. Numerous regularization and Bayesian variable selection methods have been developed in the past two decades for variable selection, but they mainly target at only one response. As more data being collected nowadays, it is common to obtain and analyze multiple correlated responses from the same study. Running separate regression for each response ignores their correlation thus multivariate analysis is recommended. Existing multivariate methods select variables related to all responses without considering the possible heterogeneous sparsity of different responses, i.e. some features may only predict a subset of responses but not the rest. In this paper, we develop a novel Bayesian indicator variable selection method in multivariate regression model with a large number of grouped predictors targeting at multiple correlated responses with possibly heterogeneous sparsity patterns. The method is motivated by the multi-trait fine mapping problem in genetics to identify the variants that are causal to multiple related traits. Our new method is featured by its selection at individual level, group level as well as specific to each response. In addition, we propose a new concept of subset posterior inclusion probability for inference to prioritize predictors that target at subset(s) of responses. Extensive simulations with varying sparsity and heterogeneity levels and dimension have shown the advantage of our method in variable selection and prediction performance as compared to existing general Bayesian multivariate variable selection methods and Bayesian fine mapping methods. We also applied our method to a real data example in imaging genetics and identified important causal variants for brain white matter structural change in different regions.
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The rising growth of deep neural networks (DNNs) and datasets in size motivates the need for efficient solutions for simultaneous model selection and training. Many methods for hyperparameter optimization (HPO) of iterative learners, including DNNs, attempt to solve this problem by querying and learning a response surface while searching for the optimum of that surface. However, many of these methods make myopic queries, do not consider prior knowledge about the response structure, and/or perform a biased cost-aware search, all of which exacerbate identifying the best-performing model when a total cost budget is specified. This paper proposes a novel approach referred to as {\bf B}udget-{\bf A}ware {\bf P}lanning for {\bf I}terative Learners (BAPI) to solve HPO problems under a constrained cost budget. BAPI is an efficient non-myopic Bayesian optimization solution that accounts for the budget and leverages the prior knowledge about the objective function and cost function to select better configurations and to take more informed decisions during the evaluation (training). Experiments on diverse HPO benchmarks for iterative learners show that BAPI performs better than state-of-the-art baselines in most cases.
Federated Learning (FL) recently emerges as a paradigm to train a global machine learning model across distributed clients without sharing raw data. Knowledge Graph (KG) embedding represents KGs in a continuous vector space, serving as the backbone of many knowledge-driven applications. As a promising combination, federated KG embedding can fully take advantage of knowledge learned from different clients while preserving the privacy of local data. However, realistic problems such as data heterogeneity and knowledge forgetting still remain to be concerned. In this paper, we propose FedLU, a novel FL framework for heterogeneous KG embedding learning and unlearning. To cope with the drift between local optimization and global convergence caused by data heterogeneity, we propose mutual knowledge distillation to transfer local knowledge to global, and absorb global knowledge back. Moreover, we present an unlearning method based on cognitive neuroscience, which combines retroactive interference and passive decay to erase specific knowledge from local clients and propagate to the global model by reusing knowledge distillation. We construct new datasets for assessing realistic performance of the state-of-the-arts. Extensive experiments show that FedLU achieves superior results in both link prediction and knowledge forgetting.
Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models inadequate. Yet even for parametric regression models, approximations such as MCMC typically are needed for posterior inference. This paper introduces a Bayesian modeling and algorithmic framework that enables semiparametric regression analysis for discrete data with Monte Carlo (not MCMC) sampling. The proposed approach pairs a nonparametric marginal model with a latent linear regression model to encourage both flexibility and interpretability, and delivers posterior consistency even under model misspecification. For a parametric or large-sample approximation of this model, we identify a class of conjugate priors with (pseudo) closed-form posteriors. All posterior and predictive distributions are available analytically or via direct Monte Carlo sampling. These tools are broadly useful for linear regression, nonlinear models via basis expansions, and variable selection with discrete data. Simulation studies demonstrate significant advantages in computing, prediction, estimation, and selection relative to existing alternatives. This novel approach is applied successfully to self-reported mental health data that exhibit zero-inflation, overdispersion, boundedness, and heaping.
Deep neural networks (DNNs) are sensitive to adversarial examples, resulting in fragile and unreliable performance in the real world. Although adversarial training (AT) is currently one of the most effective methodologies to robustify DNNs, it is computationally very expensive (e.g., 5-10X costlier than standard training). To address this challenge, existing approaches focus on single-step AT, referred to as Fast AT, reducing the overhead of adversarial example generation. Unfortunately, these approaches are known to fail against stronger adversaries. To make AT computationally efficient without compromising robustness, this paper takes a different view of the efficient AT problem. Specifically, we propose to minimize redundancies at the data level by leveraging data pruning. Extensive experiments demonstrate that the data pruning based AT can achieve similar or superior robust (and clean) accuracy as its unpruned counterparts while being significantly faster. For instance, proposed strategies accelerate CIFAR-10 training up to 3.44X and CIFAR-100 training to 2.02X. Additionally, the data pruning methods can readily be reconciled with existing adversarial acceleration tricks to obtain the striking speed-ups of 5.66X and 5.12X on CIFAR-10, 3.67X and 3.07X on CIFAR-100 with TRADES and MART, respectively.
The Dirichlet-multinomial (DM) distribution plays a fundamental role in modern statistical methodology development and application. Recently, the DM distribution and its variants have been used extensively to model multivariate count data generated by high-throughput sequencing technology in omics research due to its ability to accommodate the compositional structure of the data as well as overdispersion. A major limitation of the DM distribution is that it is unable to handle excess zeros typically found in practice which may bias inference. To fill this gap, we propose a novel Bayesian zero-inflated DM model for multivariate compositional count data with excess zeros. We then extend our approach to regression settings and embed sparsity-inducing priors to perform variable selection for high-dimensional covariate spaces. Throughout, modeling decisions are made to boost scalability without sacrificing interpretability or imposing limiting assumptions. Extensive simulations and an application to a human gut microbiome data set are presented to compare the performance of the proposed method to existing approaches. We provide an accompanying R package with a user-friendly vignette to apply our method to other data sets.
Machine learning models that are developed with invariance to certain types of data transformations have demonstrated superior generalization performance in practice. However, the underlying mechanism that explains why invariance leads to better generalization is not well-understood, limiting our ability to select appropriate data transformations for a given dataset. This paper studies the generalization benefit of model invariance by introducing the sample cover induced by transformations, i.e., a representative subset of a dataset that can approximately recover the whole dataset using transformations. Based on this notion, we refine the generalization bound for invariant models and characterize the suitability of a set of data transformations by the sample covering number induced by transformations, i.e., the smallest size of its induced sample covers. We show that the generalization bound can be tightened for suitable transformations that have a small sample covering number. Moreover, our proposed sample covering number can be empirically evaluated, providing a practical guide for selecting transformations to develop model invariance for better generalization. We evaluate the sample covering numbers for commonly used transformations on multiple datasets and demonstrate that the smaller sample covering number for a set of transformations indicates a smaller gap between the test and training error for invariant models, thus validating our propositions.
Calibration weighting has been widely used to correct selection biases in non-probability sampling, missing data, and causal inference. The main idea is to calibrate the biased sample to the benchmark by adjusting the subject weights. However, hard calibration can produce enormous weights when an exact calibration is enforced on a large set of extraneous covariates. This article proposes a soft calibration scheme, in which the outcome and the selection indicator follow mixed-effects models. The scheme imposes an exact calibration on the fixed effects and an approximate calibration on the random effects. On the one hand, our soft calibration has an intrinsic connection with best linear unbiased prediction, which results in a more efficient estimation compared to hard calibration. On the other hand, soft calibration weighting estimation can be envisioned as penalized propensity score weight estimation, with the penalty term motivated by the mixed-effects structure. The asymptotic distribution and a valid variance estimator are derived for soft calibration. We demonstrate the superiority of the proposed estimator over other competitors in simulation studies and a real-data application.
Precision medicine is an emerging field that takes into account individual heterogeneity to inform better clinical practice. In clinical trials, the evaluation of treatment effect heterogeneity is an important component, and recently, many statistical methods have been proposed for stratifying patients into different subgroups based on such heterogeneity. However, the majority of existing methods developed for this purpose focus on the case with a dichotomous treatment and are not directly applicable to multi-arm trials. In this paper, we consider the problem of patient stratification in multi-arm trial settings and propose a two-stage procedure within the Bayesian nonparametric framework. Specifically, we first use Bayesian additive regression trees (BART) to predict potential outcomes (treatment responses) under different treatment options for each patient, and then we leverage Bayesian profile regression to cluster patients into subgroups according to their baseline characteristics and predicted potential outcomes. We further embed a variable selection procedure into our proposed framework to identify the patient characteristics that actively "drive" the clustering structure. We conduct simulation studies to examine the performance of our proposed method and demonstrate the method by applying it to a UK-based multi-arm blood donation trial, wherein our method uncovers five clinically meaningful donor subgroups.
Causal discovery and causal reasoning are classically treated as separate and consecutive tasks: one first infers the causal graph, and then uses it to estimate causal effects of interventions. However, such a two-stage approach is uneconomical, especially in terms of actively collected interventional data, since the causal query of interest may not require a fully-specified causal model. From a Bayesian perspective, it is also unnatural, since a causal query (e.g., the causal graph or some causal effect) can be viewed as a latent quantity subject to posterior inference -- other unobserved quantities that are not of direct interest (e.g., the full causal model) ought to be marginalized out in this process and contribute to our epistemic uncertainty. In this work, we propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning, which jointly infers a posterior over causal models and queries of interest. In our approach to ABCI, we focus on the class of causally-sufficient, nonlinear additive noise models, which we model using Gaussian processes. We sequentially design experiments that are maximally informative about our target causal query, collect the corresponding interventional data, and update our beliefs to choose the next experiment. Through simulations, we demonstrate that our approach is more data-efficient than several baselines that only focus on learning the full causal graph. This allows us to accurately learn downstream causal queries from fewer samples while providing well-calibrated uncertainty estimates for the quantities of interest.
Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.
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