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Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…

Many statistical learning problems can be posed as minimization of a sum of two convex functions, one typically a composition of non-smooth and linear functions. Examples include regression under structured sparsity assumptions. Popular…

We explore a new type of sparsity for the generalized moment problem (GMP) that we call ideal-sparsity. This sparsity exploits the presence of equality constraints requiring the measure to be supported on the variety of an ideal generated…

Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity…

In this article we use techniques of proof mining to analyse a result, due to Yonghong Yao and Muhammad Aslam Noor, concerning the strong convergence of a generalized proximal point algorithm which involves multiple parameters. Yao and…

We identify a phenomenon, which we refer to as multi-model forgetting, that occurs when sequentially training multiple deep networks with partially-shared parameters; the performance of previously-trained models degrades as one optimizes a…

A new prior is proposed for learning representations of high-level concepts of the kind we manipulate with language. This prior can be combined with other priors in order to help disentangling abstract factors from each other. It is…

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

Online Convex Optimization plays a key role in large scale machine learning. Early approaches to this problem were conservative, in which the main focus was protection against the worst case scenario. But recently several algorithms have…

Due to the vast testing space, the increasing demand for effective and efficient testing of deep neural networks (DNNs) has led to the development of various DNN test case prioritization techniques. However, the fact that DNNs can deliver…

On a compact group the Haar probability measure plays the role of uniform distribution. The entropy and rate distortion theory for this uniform distribution is studied. New results and simplified proofs on convergence of convolutions on…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

Sparsity-based methods are widely used in machine learning, statistics, and signal processing. There is now a rich class of structured sparsity approaches that expand the modeling power of the sparsity paradigm and incorporate constraints…

We give a method for proactively identifying small, plausible shifts in distribution which lead to large differences in model performance. These shifts are defined via parametric changes in the causal mechanisms of observed variables, where…

This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…

Submodular maximization has been widely studied over the past decades, mostly because of its numerous applications in real-world problems. It is well known that the standard greedy algorithm guarantees a worst-case approximation factor of…

Self-supervised representation learning has seen remarkable progress in the last few years, with some of the recent methods being able to learn useful image representations without labels. These methods are trained using backpropagation,…

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…

By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…

Training datasets for machine learning often have some form of missingness. For example, to learn a model for deciding whom to give a loan, the available training data includes individuals who were given a loan in the past, but not those…