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This paper resolves a common complexity issue in the Bethe approximation of statistical physics and the Belief Propagation (BP) algorithm of artificial intelligence. The Bethe approximation and the BP algorithm are heuristic methods for…
The traditional Multilayer Perceptron (MLP) using McCulloch-Pitts neuron model is inherently limited to a set of neuronal activities, i.e., linear weighted sum followed by nonlinear thresholding step. Previously, Generalized Operational…
Constrained machine learning enables fairness-aware training, physics-informed neural networks, and integration of symbolic domain knowledge into statistical models. Despite its practical importance, no general method exists for the…
We investigate online kernel algorithms which simultaneously process multiple classification tasks while a fixed constraint is imposed on the size of their active sets. We focus in particular on the design of algorithms that can efficiently…
The sum-product or belief propagation (BP) algorithm is a widely-used message-passing algorithm for computing marginal distributions in graphical models with discrete variables. At the core of the BP message updates, when applied to a…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
Signal detection in environments with unknown signal bandwidth and time intervals is a fundamental problem in adversarial and spectrum-sharing scenarios. This paper addresses the problem of detecting signals occupying unknown degrees of…
This paper presents a novel spectral algorithm with additive clustering designed to identify overlapping communities in networks. The algorithm is based on geometric properties of the spectrum of the expected adjacency matrix in a random…
The binary symmetric stochastic block model deals with a random graph of $n$ vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability $p$ within clusters and $q$ across…
Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…
This paper considers the parameter estimation problem in Mixed Membership Stochastic Block Model (MMSB), which is a quite general instance of random graph model allowing for overlapping community structure. We present the new algorithm…
The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of…
Quantum computers can solve semidefinite programs (SDPs) using resources that scale better than state-of-the-art classical methods as a function of the problem dimension. At the same time, the known quantum algorithms scale very unfavorably…
It has recently been observed that certain extremely simple feature encoding techniques are able to achieve state of the art performance on several standard image classification benchmarks including deep belief networks, convolutional nets,…
Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…
We analyze the performance of the greedy algorithm, and also a discrete semi-gradient based algorithm, for maximizing the sum of a suBmodular and suPermodular (BP) function (both of which are non-negative monotone non-decreasing) under two…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
The backpropagation (BP) algorithm is often thought to be biologically implausible in the brain. One of the main reasons is that BP requires symmetric weight matrices in the feedforward and feedback pathways. To address this "weight…