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In recent years, neural networks have achieved remarkable progress in various fields and have also drawn much attention in applying them on scientific problems. A line of methods involving neural networks for solving partial differential…

Stochastic descent methods (of the gradient and mirror varieties) have become increasingly popular in optimization. In fact, it is now widely recognized that the success of deep learning is not only due to the special deep architecture of…

We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…

Deep learning (DL) has shown promise for faster, high quality accelerated MRI reconstruction. However, supervised DL methods depend on extensive amounts of fully-sampled (labeled) data and are sensitive to out-of-distribution (OOD) shifts,…

Semi-supervised learning (SSL) has achieved remarkable performance with a small fraction of labeled data by leveraging vast amounts of unlabeled data from the Internet. However, this large pool of untrusted data is extremely vulnerable to…

We propose to address the issue of sample efficiency, in Deep Convolutional Neural Networks (DCNN), with a semi-supervised training strategy that combines Hebbian learning with gradient descent: all internal layers (both convolutional and…

The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…

Recent advancements in semi-supervised deep learning have introduced effective strategies for leveraging both labeled and unlabeled data to improve classification performance. This work proposes a semi-supervised framework that utilizes a…

An algorithm is said to be adaptive to a certain parameter (of the problem) if it does not need a priori knowledge of such a parameter but performs competitively to those that know it. This dissertation presents our work on adaptive…

Neuromorphic computing systems are set to revolutionize energy-constrained robotics by achieving orders-of-magnitude efficiency gains, while enabling native temporal processing. Spiking Neural Networks (SNNs) represent a promising…

The theory of deep learning focuses almost exclusively on supervised learning, non-convex optimization using stochastic gradient descent, and overparametrized neural networks. It is common belief that the optimizer dynamics, network…

Existing algorithms for human body part segmentation have shown promising results on challenging datasets, primarily relying on end-to-end supervision. However, these algorithms exhibit severe performance drops in the face of domain shifts,…

In this work, we propose Reciprocal Distribution Alignment (RDA) to address semi-supervised learning (SSL), which is a hyperparameter-free framework that is independent of confidence threshold and works with both the matched…

We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…

In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…

We consider quantile estimation in a semi-supervised setting, characterized by two available data sets: (i) a small or moderate sized labeled data set containing observations for a response and a set of possibly high dimensional covariates,…

Single-level reformulations of (non-convex) distributionally robust optimization (DRO) problems are often intractable, as they contain semiinfinite dual constraints. Based on such a semiinfinite reformulation, we present a safe…

Semi-supervised domain adaptation (SSDA) is quite a challenging problem requiring methods to overcome both 1) overfitting towards poorly annotated data and 2) distribution shift across domains. Unfortunately, a simple combination of domain…

The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…

Neural models have shown several state-of-the-art performances on Semantic Role Labeling (SRL). However, the neural models require an immense amount of semantic-role corpora and are thus not well suited for low-resource languages or…