相关论文: Error analysis of Abate--Whitt methods for Inverse…

We reexamine Smale's alpha theory as a way to certify a numerical solution to an analytic system. For a given point and a system, Smale's alpha theory determines whether Newton's method applied to this point shows the quadratic convergence…

Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization…

Approximate probabilistic inference algorithms are central to many fields. Examples include sequential Monte Carlo inference in robotics, variational inference in machine learning, and Markov chain Monte Carlo inference in statistics. A key…

We present a novel application of the recently developed AAA algorithm to the solution of Laplace 2D problems; an application to conformal mapping is also shown as a particular case. These classes of problems have also been addressed by…

The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…

Two-phase sampling is a simple and cost-effective estimation strategy in survey sampling and is widely used in practice. Because the phase-2 sampling probability typically depends on low-cost variables collected at phase 1, naive estimation…

We investigate several approaches to address the inverse problem that arises in the limited inverse Fourier transform (L-IDFT) of quasi-distributions. The methods explored include Tikhonov regularization, the Backus-Gilbert method, the…

The quantum $\tau_2$-model with generic site-dependent inhomogeneity and arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix are given in terms of an…

While Quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT)) is highly constrained by the requirement of high-precision…

We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…

While recent advances in machine learning have equipped Weather Foundation Models (WFMs) with substantial generalization capabilities across diverse downstream tasks, the escalating computational requirements associated with their expanding…

The Bethe ansatz represents an analytical method enabling the exact solution of numerous models in condensed matter physics and statistical mechanics. When a global symmetry is present, the trial wavefunctions of the Bethe ansatz consist of…

We introduce innovative inference procedures for analyzing time series data. Our methodology enables density approximation and composite hypothesis testing based on Whittle's estimator, a widely applied M-estimator in the frequency domain.…

Quantization-aware training (QAT) is a leading technique for improving the accuracy of quantized neural networks. Previous work has shown that decomposing training into a full-precision (FP) phase followed by a QAT phase yields superior…

We present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are…

Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization…

The Wright-Fisher (W-F) diffusion model serves as a foundational framework for interpreting population evolution through allele frequency dynamics over time. Despite the known transition probability between consecutive generations, an exact…

A novel method is proposed to infer Bayesian predictions of computationally expensive models. The method is based on the construction of quadrature rules, which are well-suited for approximating the weighted integrals occurring in Bayesian…

This study explores the quantisation-aware training (QAT) on time series Transformer models. We propose a novel adaptive quantisation scheme that dynamically selects between symmetric and asymmetric schemes during the QAT phase. Our…

We investigate the theoretical foundations of the simulated tempering method and use our findings to design efficient algorithms. Employing a large deviation argument first used for replica exchange molecular dynamics [Plattner et al., J.…