Related papers: Open Problem: Separating Geometric and Algorithmic…

We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries. This problem is a natural generalization of fundamental problems in combinatorial…

Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…

A fundamental challenge in developing general learning algorithms is their tendency to forget past knowledge when adapting to new data. Addressing this problem requires a principled understanding of forgetting; yet, despite decades of…

We develop a new collaborative filtering (CF) method that combines both previously known users' preferences, i.e. standard CF, as well as product/user attributes, i.e. classical function approximation, to predict a given user's interest in…

Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying…

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…

Compressing neural nets is an active research problem, given the large size of state-of-the-art nets for tasks such as object recognition, and the computational limits imposed by mobile devices. We give a general formulation of model…

In federated learning, communication cost is often a critical bottleneck to scale up distributed optimization algorithms to collaboratively learn a model from millions of devices with potentially unreliable or limited communication and…

This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather…

Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute.…

This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…

While deep learning is successful in a number of applications, it is not yet well understood theoretically. A satisfactory theoretical characterization of deep learning however, is beginning to emerge. It covers the following questions: 1)…

We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (\emph{Tiling for Binary Matrix Completion}), gives interpretable output in the…

Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…

In this comprehensive review, we describe a new mathematical problem in artificial intelligence (AI) from a mathematical modeling perspective, following the philosophy stated by Rudolf E. Kalman that "Once you get the physics right, the…

We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

This paper attempts to analyze the effectiveness of deep learning for tabular data processing. It is believed that decision trees and their ensembles is the leading method in this domain, and deep neural networks must be content with…

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…