Related papers: The PSLQ Algorithm for Empirical Data
The PSLQ algorithm computes integer relations for real numbers and Gaussian integer relations for complex numbers. We endeavour to extend PSLQ to find integer relations consisting of algebraic integers from some quadratic extension fields…
The PSLQ algorithm is one of the most popular algorithm for finding nontrivial integer relations for several real numbers. In the present work, we present an incremental version of PSLQ. For some applications needing to call PSLQ many…
In this vision paper, we explore the challenges and opportunities of a form of computation that employs an empirical (rather than a formal) approach, where the solution of a computational problem is returned as empirically most likely…
We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…
This paper studies a continuous-time stochastic linear-quadratic (SLQ) optimal control problem on infinite-horizon. A data-driven policy iteration algorithm is proposed to solve the SLQ problem. Without knowing three system coefficient…
In this paper, we address Linear Quadratic Regulator (LQR) problems through a novel iterative algorithm named EXtremum-seeking Policy iteration LQR (EXP-LQR). The peculiarity of EXP-LQR is that it only needs access to a truncated…
Probabilistic Structured Queries (PSQ) is a cross-language information retrieval (CLIR) method that uses translation probabilities statistically derived from aligned corpora. PSQ is a strong baseline for efficient CLIR using sparse…
Probabilistic extensions of logic programming languages, such as ProbLog, integrate logical reasoning with probabilistic inference to evaluate probabilities of output relations; however, prior work does not account for potential statistical…
The probabilistic threshold query is one of the most common queries in uncertain databases, where a result satisfying the query must be also with probability meeting the threshold requirement. In this paper, we investigate probabilistic…
Algorithms for exact and approximate inference in stochastic logic programs (SLPs) are presented, based respectively, on variable elimination and importance sampling. We then show how SLPs can be used to represent prior distributions for…
The handling of probabilities in the form of uncertainty or partial information is an essential task for LLMs in many settings and applications. A common approach to evaluate an LLM's probabilistic reasoning capabilities is to assess its…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these…
Machin-like arctangent relations are classical tools for computing $\pi$, with efficiency quantified by the Lehmer measure ($\lambda$). We present a framework for discovering low-measure relations by coupling the PSLQ integer-relation…
In this note, I present a simple PSLQ code for finding null linear combinations, with the best rational coefficients, of mathematical constants, within some prescribed precision. As an example, I explore approximate expressions for the…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
Let $\{x_1, x_2, ..., x_n\}$ be a vector of real numbers. An integer relation algorithm is a computational scheme to find the $n$ integers $a_k$, if they exist, such that $a_1 x_1 + a_2 x_2 + ... + a_n x_n= 0$. In the past few years,…
Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and…
Matrices with low numerical rank are omnipresent in many signal processing and data analysis applications. The pivoted QLP (p-QLP) algorithm constructs a highly accurate approximation to an input low-rank matrix. However, it is…
We present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of…
Nowadays, the importance of software with natural-language user interfaces cannot be underestimated. In particular, in Question Answering (QA) systems, generating a SPARQL query for a given natural-language question (often named Query…