Related papers: A Jammed Parisi Ansatz
Random $k$-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
A single McCulloch-Pitts neuron, that is, the simple perceptron is studied, with focus on the region beyond storage capacity. It is shown that Parisi's hierarchical ansatz for the overlap matrix of the synaptic couplings with so called…
We study constrained selection sets of random closed sets defined on a non-atomic probability space. Given a random interval $Y=[y_L,y_U]$ and scalar constraints on the expectation or the median of admissible selections, we characterize the…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
The Random Satisfiability problem has been intensively studied for decades. For a number of reasons the focus of this study has mostly been on the model, in which instances are sampled uniformly at random from a set of formulas satisfying…
Over the last two decades, propositional satisfiability (SAT) has become one of the most successful and widely applied techniques for the solution of NP-complete problems. The aim of this paper is to investigate theoretically how Sat can be…
Statistical performance bounds for reinforcement learning (RL) algorithms can be critical for high-stakes applications like healthcare. This paper introduces a new framework for theoretically measuring the performance of such algorithms…
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…
Jalali and Poor introduced an asymptotic framework for compressed sensing of stochastic processes, demonstrating that any rate strictly greater than the mean information dimension serves as an upper bound on the number of random linear…
In this paper we determine the complexity of a broad class of problems that extends the temporal constraint satisfaction problems. To be more precise we study the problems Poset-SAT($\Phi$), where $\Phi$ is a given set of quantifier-free…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
We study the constrained variant of the \emph{multi-armed bandit} (MAB) problem, in which the learner aims not only at minimizing the total loss incurred during the learning dynamic, but also at controlling the violation of multiple…
The so-called algebraic approach to the constraint satisfaction problem (CSP) has been a prevalent method of the study of complexity of these problems since early 2000's. The core of this approach is the notion of polymorphisms which…
We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in…
This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…
We study the random binary symmetric perceptron problem, focusing on the behavior of rare high-margin solutions. While most solutions are isolated, we demonstrate that these rare solutions are part of clusters of extensive entropy,…
Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating…
The solution-space structure of the 3-Satisfiability Problem (3-SAT) is studied as a function of the control parameter alpha (ratio of number of clauses to the number of variables) using numerical simulations. For this purpose, one has to…