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Related papers: Probabilistic Model Counting with Short XORs

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Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…

Numerical Analysis · Mathematics 2018-09-05 Hermann G. Matthies

The XOR-satisfiability (XORSAT) problem deals with a system of $n$ Boolean variables and $m$ clauses. Each clause is a linear Boolean equation (XOR) of a subset of the variables. A $K$-clause is a clause involving $K$ distinct variables. In…

Disordered Systems and Neural Networks · Physics 2013-03-05 S. Hamed Hassani , Nicolas Macris , Rudiger Urbanke

Standard count models such as the Poisson and Negative Binomial models often fail to capture the large proportion of zero claims commonly observed in insurance data. To address such issue of excessive zeros, zero-inflated and hurdle models…

Applications · Statistics 2026-02-03 Hyemin Lee , Dohee Kim , Banghee So , Jae Youn Ahn

We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier's verdict is a function of the XOR of the two bits received. We show that, when the provers are allowed to…

Quantum Physics · Physics 2008-04-11 Richard Cleve , William Slofstra , Falk Unger , Sarvagya Upadhyay

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

Machine Learning · Statistics 2020-02-27 Tim Pearce , Felix Leibfried , Alexandra Brintrup , Mohamed Zaki , Andy Neely

Recently there has been sustained interest in modifying prediction algorithms to satisfy fairness constraints. These constraints are typically complex nonlinear functionals of the observed data distribution. Focusing on the path-specific…

Machine Learning · Statistics 2022-04-15 Razieh Nabi , Daniel Malinsky , Ilya Shpitser

Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…

Machine Learning · Computer Science 2017-08-08 Paul M. B. Vitanyi , Nick Chater

Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…

Methodology · Statistics 2026-05-12 Michael C. Sachs , Erin E. Gabriel , Robin J. Evans , Arvid Sjölander

This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…

Optimization and Control · Mathematics 2025-01-17 Jiaqi Lei , Sanjay Mehrotra

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…

Artificial Intelligence · Computer Science 2022-04-06 Carlos Ansótegui , Jordi Levy

Given complex numbers $w_1, \ldots, w_n$, we define the weight $w(X)$ of a set $X$ of 0-1 vectors as the sum of $w_1^{x_1} \cdots w_n^{x_n}$ over all vectors $(x_1, \ldots, x_n)$ in $X$. We present an algorithm, which for a set $X$ defined…

Combinatorics · Mathematics 2019-08-15 Alexander Barvinok , Guus Regts

In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…

Computational Complexity · Computer Science 2007-05-23 Asa Ben-Hur , Joshua Feinberg , Shmuel Fishman , Hava T. Siegelmann

We study the symmetric weighted first-order model counting task and present ApproxWFOMC, a novel anytime method for efficiently bounding the weighted first-order model count in the presence of an unweighted first-order model counting…

Artificial Intelligence · Computer Science 2020-01-16 Timothy van Bremen , Ondrej Kuzelka

In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint…

Computation and Language · Computer Science 2007-05-23 Stefan Riezler

The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of…

Logic · Mathematics 2018-04-09 A Mani

We consider random systems of linear equations over GF(2) in which every equation binds k variables. We obtain a precise description of the clustering of solutions in such systems. In particular, we prove that with probability that tends to…

Data Structures and Algorithms · Computer Science 2015-10-12 Dimitris Achlioptas , Michael Molloy

We present characterisations of "exact" gap-definable classes, in terms of indeterministic models of computation which slightly modify the standard model of quantum computation. This follows on work of Aaronson [arXiv:quant-ph/0412187], who…

Computational Complexity · Computer Science 2015-09-28 Niel de Beaudrap

We introduce a new protocol for a lossy data compression algorithm which is based on constraint satisfaction gates. We show that the theoretical capacity of algorithms built from standard parity-check gates converges exponentially fast to…

Disordered Systems and Neural Networks · Physics 2009-11-11 S. Ciliberti , M. Mezard , R. Zecchina

Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…

Optimization and Control · Mathematics 2018-05-22 Mark Cannon

We study a new class of NP search problems, those which can be proved total using standard combinatorial reasoning based on approximate counting. Our model for this kind of reasoning is the bounded arithmetic theory $\mathrm{APC}_2$ of…

Logic · Mathematics 2021-11-29 Leszek Aleksander Kołodziejczyk , Neil Thapen