Related papers: Variational Characterizations of Local Entropy and…

Tensor-based discrete density estimation requires flexible modeling and proper divergence criteria to enable effective learning; however, traditional approaches using $\alpha$-divergence face analytical challenges due to the $\alpha$-power…

In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…

We revisit two fundamental decentralized optimization methods, Decentralized Gradient Tracking (DGT) and Decentralized Gradient Descent (DGD), with multiple local updates. We consider two settings and demonstrate that incorporating local…

We consider machine learning, particularly regression, using locally-differentially private datasets. The Wasserstein distance is used to define an ambiguity set centered at the empirical distribution of the dataset corrupted by local…

Certifiable local robustness, which rigorously precludes small-norm adversarial examples, has received significant attention as a means of addressing security concerns in deep learning. However, for some classification problems, local…

The training process of ranking models involves two key data selection decisions: a sampling strategy, and a labeling strategy. Modern ranking systems, especially those for performing semantic search, typically use a ``hard negative''…

Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…

Effective uncertainty quantification is important for training modern predictive models with limited data, enhancing both accuracy and robustness. While Bayesian methods are effective for this purpose, they can be challenging to scale. When…

We present a novel class of Physics-Informed Neural Networks that is formulated based on the principles of Evidential Deep Learning, where the model incorporates uncertainty quantification by learning parameters of a higher-order…

While modern convolutional neural networks achieve outstanding accuracy on many image classification tasks, they are, compared to humans, much more sensitive to image degradation. Here, we describe a variant of Batch Normalization,…

Doubly stochastic learning algorithms are scalable kernel methods that perform very well in practice. However, their generalization properties are not well understood and their analysis is challenging since the corresponding learning…

Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL)…

There is a family of label modification approaches including self and non-self label correction (LC), and output regularisation. They are widely used for training robust deep neural networks (DNNs), but have not been mathematically and…

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…

This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…

In recent years, the Deep Learning Alternating Minimization (DLAM), which is actually the alternating minimization applied to the penalty form of the deep neutral networks training, has been developed as an alternative algorithm to overcome…

Clustering analysis by nonnegative low-rank approximations has achieved remarkable progress in the past decade. However, most approximation approaches in this direction are still restricted to matrix factorization. We propose a new low-rank…

This paper addresses a new interpretation of the traditional optimization method in reinforcement learning (RL) as optimization problems using reverse Kullback-Leibler (KL) divergence, and derives a new optimization method using forward KL…

Many two-sample problems call for a comparison of two distributions from an exponential family. Density ratio estimation methods provide ways to solve such problems through direct estimation of the differences in natural parameters. The…

We present an algorithm for the calibration of local volatility from market option prices through deep self-consistent learning, by approximating both market option prices and local volatility using deep neural networks. Our method uses the…