We propose online debiasing, a novel approach for reliable statistical inference for settings with high-dimensional adaptively collected data. In particular, in two concrete contexts (i) time series analysis and (ii) batched data collection, we demonstrate that online debiasing optimally debiases the LASSO estimate when the underlying parameter has sparsity of certain order. We study the performance of our method in a marketing application via Chicago-area grocery store chain Dominick’s dataset and evaluate the cross-category effect of products on each other.

Over the past few years, several adversarial training methods have been proposed to improve the robustness of data-driven models against adversarial perturbations in the input. Despite remarkable progress in this regard, adversarial training is often observed to drop the standard test accuracy. This phenomenon has intrigued the research community to investigate the potential tradeoff between standard accuracy (a.k.a generalization) and robust accuracy (a.k.a robust generalization) as two performance measures. In this paper, we revisit this tradeoff for latent models and argue that this tradeoff is mitigated when the data enjoy a low-dimensional structure. We develop a theory to show that the low-dimensional manifold structure allows one to obtain models that are nearly optimal with respect to both, the standard accuracy and the robust accuracy measures.

The performance of classifiers is often measured in terms of average accuracy on test data. Despite being a standard measure, average accuracy fails in characterizing the fit of the model to the underlying conditional law of labels on the input feature vectors (Y|X), e.g. due to model misspecification, overfitting, and high-dimensionality. In this work, we consider the fundamental problem of assessing the goodness-of-fit of a general classifier. Our framework does not make any parametric assumption on the conditional law Y|X  and treats that as a black box oracle model which can be accessed only through queries.  We formulate the goodness-of-fit assessment as a tolerance hypothesis testing problem.  We propose a novel test, called GRASP, which works in finite sample settings, no matter the features (distribution-free). We also propose model-X GRASP designed for model-X settings where the joint distribution of the features X is known. Model-X GRASP uses this distributional information to achieve better power.

 We propose a low complexity procedure that is designed to be used generically on top of any sub-optimal baseline support recovery algorithm to improve its statistical accuracy. This can be achieved at the cost of a relatively small computational overhead. Interestingly, adding this module to orthogonal matching pursuit (OMP) yields a support recovery procedure that is more accurate and significantly faster than basis pursuit (BP). 

We propose Pearson Chi-squared conditional randomization test for studying the statistical association between variables while controlling for the effect of high-dimensional confounding factors. The proposed test requires a very small number of conditional randomizations but still outputs high-resolution p-values. In high multiplicity problems with thousands of explanatory variables, this can drastically speed up the process of identifying the significant variables. In addition, our test in some cases enjoys a significantly higher statistical power in comparison with other conditional independence tests.