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Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…
Domain Generalization (DG) is a fundamental challenge for machine learning models, which aims to improve model generalization on various domains. Previous methods focus on generating domain invariant features from various source domains.…
To address the challenges in learning deep generative models (e.g.,the blurriness of variational auto-encoder and the instability of training generative adversarial networks, we propose a novel deep generative model, named…
This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…
We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in…
Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…
We present a technique for developing a network of re-used features, where the topology is formed using a coarse learning method, that allows gradient-descent fine tuning, known as an Abstract Deep Network (ADN). New features are built…
This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined…
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…
Paraphrase generation is an important and challenging natural language processing (NLP) task. In this work, we propose a deep generative model to generate paraphrase with diversity. Our model is based on an encoder-decoder architecture. An…
Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic. Thus, we propose to augment mechanistic cognitive models with a temporal dimension…
We present the Deep Convolutional Gaussian Mixture Model (DCGMM), a new probabilistic approach for image modeling capable of density estimation, sampling and tractable inference. DCGMM instances exhibit a CNN-like layered structure, in…
Diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. From a theoretical standpoint, a number of recent works have studied the iteration…
A basic, and still largely unanswered, question in the context of Generative Adversarial Networks (GANs) is whether they are truly able to capture all the fundamental characteristics of the distributions they are trained on. In particular,…
Generative adversarial networks (GANs) are a machine learning framework comprising a generative model for sampling from a target distribution and a discriminative model for evaluating the proximity of a sample to the target distribution.…
Self-supervised learning is one of the most promising approaches to acquiring knowledge from limited labeled data. Despite the substantial advancements made in recent years, self-supervised models have posed a challenge to practitioners, as…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
Distributional ambiguity sets provide quantifiable ways to characterize the uncertainty about the true probability distribution of random variables of interest. This makes them a key element in data-driven robust optimization by exploiting…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
Traditional deep neural networks (NNs) have significantly contributed to the state-of-the-art performance in the task of classification under various application domains. However, NNs have not considered inherent uncertainty in data…