Related papers: Applied Measure Theory for Probabilistic Modeling
We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and…
Numeral systems and units of measurement are two conjoined topics in activities of human beings and have mutual effects with the languages expressing them. Currently, the evaluation of Large Language Models (LLMs) often involves…
Motivation: Estimating model parameters from experimental observations is one of the key challenges in systems biology and can be computationally very expensive. While the Julia programming language was recently developed as a high-level…
I consider two problems in machine learning and statistics: the problem of estimating the joint probability density of a collection of random variables, known as density estimation, and the problem of inferring model parameters when their…
Language modeling studies the probability distributions over strings of texts. It is one of the most fundamental tasks in natural language processing (NLP). It has been widely used in text generation, speech recognition, machine…
Julia has been heralded as a potential successor to Python for scientific machine learning and numerical computing, boasting ergonomic and performance improvements. Since Julia's inception in 2012 and declaration of language goals in 2017,…
We present an open source computational framework geared towards the efficient numerical investigation of open quantum systems written in the Julia programming language. Built exclusively in Julia and based on standard quantum optics…
As astronomical data grows in volume and complexity, the scalability of analysis software becomes increasingly important. At the same time, astrophysics analysis software relies heavily on open-source contributions, so languages and tools…
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
Classical methods to simulate quantum systems are not only a key element of the physicist's toolkit for studying many-body models but are also increasingly important for verifying and challenging upcoming quantum computers. Pauli…
Decision theory does not traditionally include uncertainty over utility functions. We argue that the a person's utility value for a given outcome can be treated as we treat other domain attributes: as a random variable with a density…
The impressive capabilities of large language models (LLMs) have sparked debate over whether these models genuinely generalize to unseen tasks or predominantly rely on memorizing vast amounts of pretraining data. To explore this issue, we…
Machine learning as a discipline has seen an incredible surge of interest in recent years due in large part to a perfect storm of new theory, superior tooling, renewed interest in its capabilities. We present in this paper a framework named…
In this paper we make a novel use of the Johnson-Lindenstrauss Lemma. The Lemma has an existential form saying that there exists a JL transformation $f$ of the data points into lower dimensional space such that all of them fall into…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
Causality is a central concept in a wide range of research areas, yet there is still no universally agreed axiomatisation of causality. We view causality both as an extension of probability theory and as a study of \textit{what happens when…
This paper addresses the issues of conservativeness and computational complexity of probabilistic robustness analysis. We solve both issues by defining a new sampling strategy and robustness measure. The new measure is shown to be much less…
We begin our journey by recalling the fundamentals of Probability Theory that underlie one of its most significant applications to real-world problems: Parametric Estimation. Throughout the text, we systematically develop this theme by…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…