Related papers: A Numerical Example on the Principles of Stochasti…

We introduce data structures for solving robust regression through stochastic gradient descent (SGD) by sampling gradients with probability proportional to their norm, i.e., importance sampling. Although SGD is widely used for large scale…

Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…

LSTD is a popular algorithm for value function approximation. Whenever the number of features is larger than the number of samples, it must be paired with some form of regularization. In particular, L1-regularization methods tend to perform…

In this article, we present a new method to study uniqueness of form extensions in a rather general setting. The method is based on the theory of ordered Hilbert spaces and the concept of domination of semigroups. Our main abstract result…

The covariate shift is a challenging problem in supervised learning that results from the discrepancy between the training and test distributions. An effective approach which recently drew a considerable attention in the research community…

This work addresses the challenge of providing consistent explanations for predictive models in the presence of model indeterminacy, which arises due to the existence of multiple (nearly) equally well-performing models for a given dataset…

Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by…

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…

In the present paper, we studied a Dynamic Stochastic Block Model (DSBM) under the assumptions that the connection probabilities, as functions of time, are smooth and that at most $s$ nodes can switch their class memberships between two…

Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model (SBM) for…

Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…

This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the…

Machine learning has made tremendous progress in recent years, with models matching or even surpassing humans on a series of specialized tasks. One key element behind the progress of machine learning in recent years has been the ability to…

We prove a general criterion providing sufficient conditions under which a time-discretiziation of a given Stochastic Differential Equation (SDE) is a uniform in time approximation of the SDE. The criterion is also, to a certain extent,…

The stochastic mirror descent (SMD) algorithm is a general class of training algorithms, which includes the celebrated stochastic gradient descent (SGD), as a special case. It utilizes a mirror potential to influence the implicit bias of…

We provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper.The…

Stochastic convex optimization is one of the most well-studied models for learning in modern machine learning. Nevertheless, a central fundamental question in this setup remained unresolved: "How many data points must be observed so that…

Sketching and stochastic gradient methods are arguably the most common techniques to derive efficient large scale learning algorithms. In this paper, we investigate their application in the context of nonparametric statistical learning.…

We develop a principled methodology to infer assortative communities in networks based on a nonparametric Bayesian formulation of the planted partition model. We show that this approach succeeds in finding statistically significant…

In this paper we introduce a unified analysis of a large family of variants of proximal stochastic gradient descent ({\tt SGD}) which so far have required different intuitions, convergence analyses, have different applications, and which…