Related papers: A Jammed Parisi Ansatz
We introduce and study the random "locked" constraint satisfaction problems. When increasing the density of constraints, they display a broad "clustered" phase in which the space of solutions is divided into many isolated points. While the…
Phase retrieval (PR), also sometimes referred to as quadratic sensing, is a problem that occurs in numerous signal and image acquisition domains ranging from optics, X-ray crystallography, Fourier ptychography, sub-diffraction imaging, and…
Compressed Sensing (CS) is an effective approach to reduce the required number of samples for reconstructing a sparse signal in an a priori basis, but may suffer severely from the issue of basis mismatch. In this paper we study the problem…
The solution space of a K-satisfiability (K-SAT) formula is a collection of solution clusters, each of which contains all the solutions that are mutually reachable through a sequence of single-spin flips. Knowledge of the statistical…
This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…
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…
Answer Set Programming (ASP) is a popular framework for modeling combinatorial problems. However, ASP cannot easily be used for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
In the constraint satisfaction problem (CSP) corresponding to a constraint language (i.e., a set of relations) $\Gamma$, the goal is to find an assignment of values to variables so that a given set of constraints specified by relations from…
We introduce a highly structured family of hard satisfiable 3-SAT formulas corresponding to an ordered spin-glass model from statistical physics. This model has provably "glassy" behavior; that is, it has many local optima with large energy…
Given a predicate $P: \{-1, 1\}^k \to \{-1, 1\}$, let $CSP(P)$ be the set of constraint satisfaction problems whose constraints are of the form $P$. We say that $P$ is approximable if given a nearly satisfiable instance of $CSP(P)$, there…
In Verification and in (optimal) AI Planning, a successful method is to formulate the application as boolean satisfiability (SAT), and solve it with state-of-the-art DPLL-based procedures. There is a lack of understanding of why this works…
This paper provides an extension of compressed sensing which bridges a substantial gap between existing theory and its current use in real-world applications. It introduces a mathematical framework that generalizes the three standard…
Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…
This article describes a novel approach to chance-constrained programming based on the sample average approximation (SAA) method. Recent work focuses on heuristic approximations to the SAA problem and we introduce a novel approach which…
Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
Let $P:\{0,1\}^k \to \{0,1\}$ be a nontrivial $k$-ary predicate. Consider a random instance of the constraint satisfaction problem $\mathrm{CSP}(P)$ on $n$ variables with $\Delta n$ constraints, each being $P$ applied to $k$ randomly chosen…
In the Potts spin glass model, inspired by the symmetry argument in [arXiv:2310.06745] for the constrained free energy, we study the free energy with self-overlap correction. Similarly, we simplify the Parisi-type formula, originally an…
Recent work has made substantial progress in understanding the transitions of random constraint satisfaction problems. In particular, for several of these models, the exact satisfiability threshold has been rigorously determined, confirming…