Related papers: Improved Randomized Approximation of Hard Universa…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not…
We are concerned with learning models that generalize well to different \emph{unseen} domains. We consider a worst-case formulation over data distributions that are near the source domain in the feature space. Only using training data from…
This paper introduces a new algorithm for solving a sub-class of quantified constraint satisfaction problems (QCSP) where existential quantifiers precede universally quantified inequalities on continuous domains. This class of QCSPs has…
Sampling from multivariate normal distributions, subjected to a variety of restrictions, is a problem that is recurrent in statistics and computing. In the present work, we demonstrate a general framework to efficiently sample a…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
We study sampling problems associated with potentials that lack smoothness. The potentials can be either convex or non-convex. Departing from the standard smooth setting, the potentials are only assumed to be weakly smooth or non-smooth, or…
The computational equivalence between approximate counting and sampling is well established for polynomial-time algorithms. The most efficient general reduction from counting to sampling is achieved via simulated annealing, where the…
In this paper, we consider convex feasibility problems where the underlying sets are loosely coupled, and we propose several algorithms to solve such problems in a distributed manner. These algorithms are obtained by applying proximal…
The Laplace approximation provides a scalable and efficient means of quantifying weight-space uncertainty in deep neural networks, enabling the application of Bayesian tools such as predictive uncertainty and model selection via Occam's…
In this work we discuss the problem of selecting suitable approximators from families of parameterized elementary functions that are known to be dense in a Hilbert space of functions. We consider and analyze published procedures, both…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the…
We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…
Randomized approximation algorithms for many #P-complete problems (such as the partition function of a Gibbs distribution, the volume of a convex body, the permanent of a $\{0,1\}$-matrix, and many others) reduce to creating random…
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…
We consider approximation problems for a special space of d variate functions. We show that the problems have small number of active variables, as it has been postulated in the past using concentration of measure arguments. We also show…
We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification…
The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large literature on empirical approaches to…
Constraints over finite sequences of variables are ubiquitous in sequencing and timetabling. Moreover, the wide variety of such constraints in practical applications led to general modelling techniques and generic propagation algorithms,…