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Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
The expected improvement algorithm (or efficient global optimization) aims for global continuous optimization with a limited budget of black-box function evaluations. It is based on a statistical model of the function learned from previous…
This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…
We study the variational inference problem of minimizing a regularized R\'enyi divergence over an exponential family. We propose to solve this problem with a Bregman proximal gradient algorithm. We propose a sampling-based algorithm to…
Analyzing probabilistic programs and randomized algorithms are classical problems in computer science. The first basic problem in the analysis of stochastic processes is to consider the expectation or mean, and another basic problem is to…
Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search…
We generalize the notion of the stopping redundancy in order to study the smallest size of a trapping set in Tanner graphs of linear block codes. In this context, we introduce the notion of the trapping redundancy of a code, which…
EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in deep neural networks. Our…
We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency…
The nascent field of Rate-Distortion-Perception (RDP) theory is seeing a surge of research interest due to the application of machine learning techniques in the area of lossy compression. The information RDP function characterizes the…
Lattice reduction is a popular preprocessing strategy in multiple-input multiple-output (MIMO) detection. In a quest for developing a low-complexity reduction algorithm for large-scale problems, this paper investigates a new framework…
Many iterative algorithms in optimization, computational geometry, computer algebra, and other areas of computer science require repeated computation of some algebraic expression whose input changes slightly from one iteration to the next.…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…
There are many tasks within video compression which require fast bit rate estimation. As an example, rate-control algorithms are only feasible because it is possible to estimate the required bit rate without needing to encode the entire…
A fundamental problem in adversarial machine learning is to quantify how much training data is needed in the presence of evasion attacks. In this paper we address this issue within the framework of PAC learning, focusing on the class of…
In this paper, we focus on computational aspects of the Wasserstein barycenter problem. We propose two algorithms to compute Wasserstein barycenters of $m$ discrete measures of size $n$ with accuracy $\e$. The first algorithm, based on…
Many large-scale optimization problems decompose into a master problem and scenario subproblems, a structure that can be exploited by Benders decomposition. In Benders decomposition, each iteration may generate many cuts from scenario…
There have been several recent articles studying homology of various types of random simplicial complexes. Several theorems have concerned thresholds for vanishing of homology, and in some cases expectations of the Betti numbers. However…
A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed. Upper and lower bounds on the minimum $\rho$-th moment of the number of performed…
This paper presents new lower and upper bounds for the optimal compression of binary prefix codes in terms of the most probable input symbol, where compression efficiency is determined by the nonlinear codeword length objective of…