Related papers: Great expectations: Unifying Statistical Theory an…

Large language models (LLMs) have shown promise in synthetic tabular data generation, yet existing methods struggle to preserve complex feature dependencies, particularly among categorical variables. This work introduces a…

The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…

This paper investigates the ability of large language models (LLMs) to solve statistical tasks, as well as their capacity to assess the quality of reasoning. While state-of-the-art LLMs have demonstrated remarkable performance in a range of…

The Mat\'ern model has been a cornerstone of spatial statistics for more than half a century. More recently, the Mat\'ern model has been central to disciplines as diverse as numerical analysis, approximation theory, computational…

We present a new game semantics for Martin-L\"of type theory (MLTT), our aim is to give a mathematical and intensional explanation of MLTT. Specifically, we propose a category with families of a novel variant of games, which induces a…

In an increasingly data-driven world, facility with statistics is more important than ever for our students. At institutions without a statistician, it often falls to the mathematics faculty to teach statistics courses. This paper presents…

Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…

Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…

Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…

R. A. Fisher founded modern statistical inference in 1922 and identified its fundamental problems to be: specification, estimation and distribution. Since then the problem of statistical model specification has received scant attention in…

Key to structured prediction is exploiting the problem structure to simplify the learning process. A major challenge arises when data exhibit a local structure (e.g., are made by "parts") that can be leveraged to better approximate the…

The field of computability and complexity was, where computer science sprung from. Turing, Church, and Kleene all developed formalisms that demonstrated what they held "intuitively computable". The times change however and today's…

These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…

The incorporation of unlabeled data in regression and classification analysis is an increasing focus of the applied statistics and machine learning literatures, with a number of recent examples demonstrating the potential for unlabeled data…

The crafting of machine learning (ML) based systems requires statistical control throughout its life cycle. Careful quantification of business requirements and identification of key factors that impact the business requirements reduces the…

In recent years, the field of statistics has experienced a surge in interest and application, largely due to significant advances in computer technology. This progress has led to remarkable developments in statistics methods and algorithms,…

This extended abstract presents a logic, called Lp, that is capable of representing and reasoning with a wide variety of both qualitative and quantitative statistical information. The advantage of this logical formalism is that it offers a…

This paper tries to tell the story of the general linear model, which saw the light of day 200 years ago, and the assumptions underlying it. We distinguish three principal stages (ignoring earlier more isolated instances). The model was…

Despite the considerable interest in new dependent type theories, simple type theory (which dates from 1940) is sufficient to formalise serious topics in mathematics. This point is seen by examining formal proofs of a theorem about…

Prediction is a complex notion, and different predictors (such as people, computer programs, and probabilistic theories) can pursue very different goals. In this paper I will review some popular kinds of prediction and argue that the theory…