Related papers: Automated Search for Conjectures on Mathematical C…

The problem of detecting anomalies in multiple processes is considered. We consider a composite hypothesis case, in which the measurements drawn when observing a process follow a common distribution with an unknown parameter (vector), whose…

In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large…

Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…

The scientific method relies on the iterated processes of inference and inquiry. The inference phase consists of selecting the most probable models based on the available data; whereas the inquiry phase consists of using what is known about…

Explainable boosting machines (EBMs) are popular "glass-box" models that learn a set of univariate functions using boosting trees. These achieve explainability through visualizations of each feature's effect. However, unlike linear model…

We introduce Symbolic Alternating Finite Automata (s-AFA) as an expressive, succinct, and decidable model for describing sets of finite sequences over arbitrary alphabets. Boolean operations over s-AFAs have linear complexity, which is in…

We present a novel probabilistic programming framework that couples directly to existing large-scale simulators through a cross-platform probabilistic execution protocol, which allows general-purpose inference engines to record and control…

In this paper we consider change-points in multiple sequences with the objective of minimizing the estimation error of a sequence by making use of information from other sequences. This is in contrast to recent interest on change-points in…

Probabilistic Programming Languages (PPLs) allow users to encode statistical inference problems and automatically apply an inference algorithm to solve them. Popular inference algorithms for PPLs, such as sequential Monte Carlo (SMC) and…

Due to the rapid development of science and technology, the importance of imprecise, noisy, and uncertain data is increasing at an exponential rate. Thus, mining patterns in uncertain databases have drawn the attention of researchers.…

Generative Large Language Models (LLMs) are widely utilized for their excellence in various tasks. However, their tendency to produce inaccurate or misleading outputs poses a potential risk, particularly in high-stakes environments.…

The application of physics formulas is a fundamental human capability in numerical reasoning. While existing datasets often rely on implicit mathematical knowledge, they rarely explicitate the underlying formulas. To address this, we…

Many questions in experimental mathematics are fundamentally inductive in nature. Here we demonstrate how Bayesian inference --the logic of partial beliefs-- can be used to quantify the evidence that finite data provide in favor of a…

A new algorithm named EXPected Similarity Estimation (EXPoSE) was recently proposed to solve the problem of large-scale anomaly detection. It is a non-parametric and distribution free kernel method based on the Hilbert space embedding of…

We give a quantum algorithm for evaluating formulas over an extended gate set, including all two- and three-bit binary gates (e.g., NAND, 3-majority). The algorithm is optimal on read-once formulas for which each gate's inputs are balanced…

Large language models often generate confident but incorrect answers rather than abstaining when uncertain. This problem is particularly acute for small language models (SLMs), where computational constraints and autonomous operation…

An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…

Linear recurrence equations with constant coefficients define the power series coefficients of rational functions. However, one usually prefers to have an explicit formula for the sequence of coefficients, provided that such a formula is…

Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the…

Large numbers of MS/MS peptide spectra generated in proteomics experiments require efficient, sensitive and specific algorithms for peptide identification. In the Open Mass Spectrometry Search Algorithm [OMSSA], specificity is calculated by…