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In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling…

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…

Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality. This paper proposes a joint dimensionality reduction and non-parametric density…

Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…

Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…

We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated…

A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

A powerful concept behind much of the recent progress in machine learning is the extraction of common features across data from heterogeneous sources or tasks. Intuitively, using all of one's data to learn a common representation function…

Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…

Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates…

The goal of supervised representation learning is to construct effective data representations for prediction. Among all the characteristics of an ideal nonparametric representation of high-dimensional complex data, sufficiency, low…

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…

We study the problem of learning classification functions from noiseless training samples, under the assumption that the decision boundary is of a certain regularity. We establish universal lower bounds for this estimation problem, for…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

Metric learning aims at finding a suitable distance metric over the input space, to improve the performance of distance-based learning algorithms. In high-dimensional settings, it can also serve as dimensionality reduction by imposing a…

Information theoretic quantities play a central role in machine learning. The recent surge in the complexity of data and models has increased the demand for accurate estimation of these quantities. However, as the dimension grows the…