Related papers: An Impossibility Result for High Dimensional Super…

We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are "sub-Gaussian"~even when the randomness of the…

Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…

When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the…

The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…

We study asymptotically minimax predictive distributions in an infinite sequence model. First, we discuss the connection between the prediction in the infinite sequence model and the prediction in the function model. Second, we construct an…

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

We study ``selective'' or ``conditional'' classification problems under an agnostic setting. Classification tasks commonly focus on modeling the relationship between features and categories that captures the vast majority of data. In…

This paper studies the probability of error associated with the social machine learning framework, which involves an independent training phase followed by a cooperative decision-making phase over a graph. This framework addresses the…

High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…

Most modern learning problems are over-parameterized, where the number of learnable parameters is much greater than the number of training data points. In this over-parameterized regime, the training loss typically has infinitely many…

This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\to\delta$) drawn from a…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

Few Bayesian methods for analyzing high-dimensional sparse survival data provide scalable variable selection, effect estimation and uncertainty quantification. Such methods often either sacrifice uncertainty quantification by computing…

The prominent Bernstein -- von Mises (BvM) result claims that the posterior distribution after centering by the efficient estimator and standardizing by the square root of the total Fisher information is nearly standard normal. In…

We consider three problems in high-dimensional Gaussian linear mixed models. Without any assumptions on the design for the fixed effects, we construct an asymptotic $F$-statistic for testing whether a collection of random effects is zero,…

Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This…

While the Bayesian decision-theoretic framework offers an elegant solution to the problem of decision making under uncertainty, one question is how to appropriately select the prior distribution. One idea is to employ a worst-case prior.…