Related papers: Automatic differentiation for error analysis
This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error…
Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…
In this paper, we present a method for the accurate estimation of the derivative (aka.~sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression. The…
This paper proposes Monte Carlo Action Programming, a programming language framework for autonomous systems that act in large probabilistic state spaces with high branching factors. It comprises formal syntax and semantics of a…
Random variables and their distributions are a central part in many areas of statistical methods. The Distributions.jl package provides Julia users and developers tools for working with probability distributions, leveraging Julia features…
Automatic differentiation is everywhere, but there exists only minimal documentation of how it works in complex arithmetic beyond stating "derivatives in $\mathbb{C}^d$" $\cong$ "derivatives in $\mathbb{R}^{2d}$" and, at best, shallow…
In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlations detection - classical and modified rescaled range analyses. A focus is put on an effect of different distributional…
We explore the use of multiple deep learning models for detecting flaws in software programs. Current, standard approaches for flaw detection rely on a single representation of a software program (e.g., source code or a program binary). We…
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…
A procedure for unfolding the true distribution from experimental data is presented. Machine learning methods are applied for simultaneous identification of an apparatus function and solving of an inverse problem. A priori information about…
We introduce Gradus.jl, an open-source and publicly available general relativistic ray-tracing toolkit for spectral modelling in arbitrary spacetimes. Our software is written in the Julia programming language, making use of forward-mode…
We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift-diffusion-Poisson system with non-zero recombination rate. The a-posteriori error is estimated to enable goal-oriented adaptive mesh refinement for the…
Machine learning (ML) now pervades the field of Automated Program Repair (APR). Algorithms deploy neural machine translation and large language models (LLMs) to generate software patches, among other tasks. But, there are important…
Identification of nonlinear systems is a challenging problem. Physical knowledge of the system can be used in the identification process to significantly improve the predictive performance by restricting the space of possible mappings from…
With software maintenance accounting for 50% of the cost of developing software, enhancing code quality and reliability has become more critical than ever. In response to this challenge, this doctoral research proposal aims to explore…
The behavior of a Lattice Monte Carlo algorithm (if it is designed correctly) must approach that of the continuum system that it is designed to simulate as the time step and the mesh step tend to zero. However, we show for an algorithm for…
Verification of numerical accuracy properties in modern software remains an important and challenging task. This paper describes an original framework combining different solutions for numerical accuracy. First, we extend an existing…
Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…
Checking software application suitability using automated software tools has become a vital element for most organisations irrespective of whether they produce in-house software or simply customise off-the-shelf software applications for…
Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded…