Related papers: Solving #SAT and Bayesian Inference with Backtrack…
Constrained learning is prevalent in many statistical tasks. Recent work proposes distance-to-set penalties to derive estimators under general constraints that can be specified as sets, but focuses on obtaining point estimates that do not…
The problem of model counting, also known as #SAT, is to compute the number of models or satisfying assignments of a given Boolean formula $F$. Model counting is a fundamental problem in computer science with a wide range of applications.…
Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…
The workflow satisfiability problem (WSP) asks whether there exists an assignment of authorised users to the steps in a workflow specification, subject to certain constraints on the assignment. (Such an assignment is called valid.) The…
Belief updating in Bayes nets, a well known computationally hard problem, has recently been approximated by several deterministic algorithms, and by various randomized approximation algorithms. Deterministic algorithms usually provide…
Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…
Model-based sequential approaches to discrete "black-box" optimization, including Bayesian optimization techniques, often access the same points multiple times for a given objective function in interest, resulting in many steps to find the…
The challenge in the widely applicable online matching problem lies in making irrevocable assignments while there is uncertainty about future inputs. Most theoretically-grounded policies are myopic or greedy in nature. In real-world…
In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists…
The classical satisfiability problem (SAT) is used as a natural and general tool to express and solve combinatorial problems that are in NP. We postulate that provability for implicational intuitionistic propositional logic (IIPC) can serve…
We consider Bayesian optimization of the output of a network of functions, where each function takes as input the output of its parent nodes, and where the network takes significant time to evaluate. Such problems arise, for example, in…
A strong backdoor in a formula $\phi$ of propositional logic to a tractable class $\mathcal{C}$ of formulas is a set $B$ of variables of $\phi$ such that every assignment of the variables in $B$ results in a formula from $\mathcal{C}$.…
We propose a recursive algorithm for identifying all finite sequences of positive integers whose product equals their sum. Our method uses solutions of strictly shorter length that are iteratively extended in pursuit of a valid solution.…
Previous studies have demonstrated that encoding a Bayesian network into a SAT formula and then performing weighted model counting using a backtracking search algorithm can be an effective method for exact inference. In this paper, we…
We study a broad class of algorithmic problems with an "additive flavor" such as computing sumsets, 3SUM, Subset Sum and geometric pattern matching. Our starting point is that these problems can often be solved efficiently for integers,…
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these…
We design a new myopic strategy for a wide class of sequential design of experiment (DOE) problems, where the goal is to collect data in order to to fulfil a certain problem specific goal. Our approach, Myopic Posterior Sampling (MPS), is…
Variable selection remains a fundamental challenge in statistics, especially in nonparametric settings where model complexity can obscure interpretability. Bayesian tree ensembles, particularly the popular Bayesian additive regression trees…
The most common method to auto-grade a student's submission in a CS1 or a CS2 course is to run it against a pre-defined test suite and compare the results against reference results. However, this technique cannot be used if the correctness…
The subset sum problem, also referred as SSP, is a NP-Hard computational problem. SSP has its applications in broad domains like cryptography, number theory, operation research and complexity theory. The most famous algorithm for solving…