Related papers: Approximate Counting, the Lovasz Local Lemma and I…
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
We study the sequential general online regression, known also as the sequential probability assignments, under logarithmic loss when compared against a broad class of experts. We focus on obtaining tight, often matching, lower and upper…
This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…
Recurrent Neural Networks and in particular Long Short-Term Memory (LSTM) networks have demonstrated state-of-the-art accuracy in several emerging Artificial Intelligence tasks. However, the models are becoming increasingly demanding in…
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,…
Covering arrays are generalizations of orthogonal arrays that have been widely studied and are used in software testing. The probabilistic method has been employed to derive upper bounds on the sizes of minimum covering arrays and give…
In this paper, we give the first constant approximation algorithm for the lower bounded facility location (LBFL) problem with general lower bounds. Prior to our work, such algorithms were only known for the special case where all facilities…
We call an $\alpha \in \mathbb{R}$ regainingly approximable if there exists a computable nondecreasing sequence $(a_n)_n$ of rational numbers converging to $\alpha$ with $\alpha - a_n < 2^{-n}$ for infinitely many $n \in \mathbb{N}$. We…
Over the last decade, approximating functions in infinite dimensions from samples has gained increasing attention in computational science and engineering, especially in computational uncertainty quantification. This is primarily due to the…
The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
It has been established that when the gradient coding problem is distributed among $n$ servers, the computation load (number of stored data partitions) of each worker is at least $s+1$ in order to resists $s$ stragglers. This scheme incurs…
This paper proves that a wide class of local search algorithms extend as is to the fully dynamic setting with an adaptive adversary, achieving an amortized $\tilde{O}(1)$ number of local-search steps per update. A breakthrough by Moser…
We consider the task of designing Local Computation Algorithms (LCA) for applications of the Lov\'{a}sz Local Lemma (LLL). LCA is a class of sublinear algorithms proposed by Rubinfeld et al.~\cite{Ronitt} that have received a lot of…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
This paper establishes an approximation theorem for randomized neural networks (RaNNs) whose hidden-layer parameters are uniformly sampled from a prescribed bounded domain. Our analysis shows that, for RaNNs of the form $\mathop{\sum}_i W_i…
A solution for Smale's 17th problem, for the case of systems with bounded degree was recently given. This solution, an algorithm computing approximate zeros of complex polynomial systems in average polynomial time, assumed infinite…
Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the…
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$.…
We study sampling problems associated with non-convex potentials that meanwhile lack smoothness. In particular, we consider target distributions that satisfy either logarithmic-Sobolev inequality or Poincar\'e inequality. Rather than…