Related papers: Approximate Model Counting, Sparse XOR Constraints…
Span programs are a model of computation that have been used to design quantum algorithms, mainly in the query model. For any decision problem, there exists a span program that leads to an algorithm with optimal quantum query complexity,…
We have focused on Answer Set Programming (ASP), more specifically, answer set counting, exploring both exact and approximate methodologies. We developed an exact ASP counter, sharpASP, which utilizes a compact encoding for propositional…
Model counting is a fundamental problem which has been influential in many applications, from artificial intelligence to formal verification. Due to the intrinsic hardness of model counting, approximate techniques have been developed to…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
We describe a method of model checking called Computing Range Reduction (CRR). The CRR method is based on derivation of clauses that reduce the set of traces of reachable states in such a way that at least one counterexample remains (if…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
The approximation of a high-dimensional vector by a small combination of column vectors selected from a fixed matrix has been actively debated in several different disciplines. In this paper, a sampling approach based on the Monte Carlo…
For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
Recent universal-hashing based approaches to sampling and counting crucially depend on the runtime performance of SAT solvers on formulas expressed as the conjunction of both CNF constraints and variable-width XOR constraints (known as…
Representing some problems with XOR clauses (parity constraints) can allow to apply more efficient reasoning techniques. In this paper, we present a gadget for translating SAT clauses into Max2XOR constraints, i.e., XOR clauses of at most 2…
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…
Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions.…
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…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
Satisfiability Modulo Theory (SMT) solvers have advanced automated reasoning, solving complex formulas across discrete and continuous domains. Recent progress in propositional model counting motivates extending SMT capabilities toward model…
We prove a query complexity lower bound for $\mathsf{QMA}$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $\mathsf{SBP}^A \not\subset…
Given an $n*n$ sparse symmetric matrix with $m$ nonzero entries, performing Gaussian elimination may turn some zeroes into nonzero values. To maintain the matrix sparse, we would like to minimize the number $k$ of these changes, hence…
This paper tackles the task of storing a large collection of vectors, such as visual descriptors, and of searching in it. To this end, we propose to approximate database vectors by constrained sparse coding, where possible atom weights are…