Related papers: The PSLQ Algorithm for Empirical Data
In spite of the large literature on reinforcement learning (RL) algorithms for partially observable Markov decision processes (POMDPs), a complete theoretical understanding is still lacking. In a partially observable setting, the history of…
Probabilistic record linkage (PRL) is the process of determining which records in two databases correspond to the same underlying entity in the absence of a unique identifier. Bayesian solutions to this problem provide a powerful mechanism…
A matrix algorithm runs superfast (aka at sublinear cost) if it involves much fewer flops and memory cells than an input matrix has entries. Big Data are frequently represented by matrices of immense sizes that cannot be handled directly…
We establish empirical risk minimization principles for active learning by deriving a family of upper bounds on the generalization error. Aligning with empirical observations, the bounds suggest that superior query algorithms can be…
The paper discusses properties of a DATALOG$^{\neg\neg}$-like query language 4QL, originally outlined in [MS10]. Negated literals in heads of rules naturally lead to inconsistencies. On the other hand, rules do not have to attach meaning to…
This paper explores semi-qualitative probabilistic networks (SQPNs) that combine numeric and qualitative information. We first show that exact inferences with SQPNs are NPPP-Complete. We then show that existing qualitative relations in…
This is a sequel of our previous paper where we described an algorithm to find a solution of differential equations for master integrals in the form of an $\epsilon$-expansion series with numerical coefficients. The algorithm is based on…
This paper studies the data-driven synthesis of linear quadratic integral (LQI) controllers for continuous-time systems. The objective is to achieve optimal state-feedback control with integral action for reference tracking using only…
Inductive logic programming (ILP) is a form of logical machine learning. The goal is to search a hypothesis space for a hypothesis that generalises training examples and background knowledge. We introduce an approach that 'shrinks' the…
While large language models (LLMs) have demonstrated remarkable abilities across various fields, hallucination remains a significant challenge. Recent studies have explored hallucinations through the lens of internal representations,…
High-stakes domains like cyber operations need responsible and trustworthy AI methods. While large language models (LLMs) are becoming increasingly popular in these domains, they still suffer from hallucinations. This research paper…
We consider the computation of the matrix logarithm by using numerical quadrature. The efficiency of numerical quadrature depends on the integrand and the choice of quadrature formula. The Gauss--Legendre quadrature has been conventionally…
Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…
This paper introduces a new technique for quantifying the approximation error of a broad class of probabilistic inference programs, including ones based on both variational and Monte Carlo approaches. The key idea is to derive a subjective…
We propose a numerical validation of a probabilistic approach applied to estimate the relative accuracy between two Lagrange finite elements $P_k$ and $P_m, (k<m)$. In particular, we show practical cases where finite element $P_{k}$ gives…
A gradient-based method is proposed for solving the linear quadratic regulator (LQR) problem for linear systems with nonlinear dependence on time-invariant probabilistic parametric uncertainties. The approach explicitly accounts for model…
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and…
Many machine learning applications require the ability to learn from and reason about noisy multi-relational data. To address this, several effective representations have been developed that provide both a language for expressing the…
Large language models (LLMs) have achieved a degree of success in generating coherent and contextually relevant text, yet they remain prone to a significant challenge known as hallucination: producing information that is not substantiated…
SQL/PGQ is a new standard that integrates graph querying into relational systems, allowing users to freely switch between graph patterns and SQL. Our experiments show performance gaps between these models, as queries written in both…