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Explicit finite-sample statistical guarantees on model performance are an important ingredient in responsible machine learning. Previous work has focused mainly on bounding either the expected loss of a predictor or the probability that an…
Knowing if a model will generalize to data 'in the wild' is crucial for safe deployment. To this end, we study model disagreement notions that consider the full predictive distribution - specifically disagreement based on Hellinger…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
In this paper, we study the problem of learning the skill distribution of a population of agents from observations of pairwise games in a tournament. These games are played among randomly drawn agents from the population. The agents in our…
We analyze the time series of soccer matches in a model-free way using data for the German soccer league (Bundesliga). We argue that the goal difference is a better measure for the overall fitness of a team than the number of points. It is…
Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce…
In this research, we examine the capabilities of different mathematical models to accurately predict various levels of the English football pyramid. Existing work has largely focused on top-level play in European leagues; however, our work…
Expected goals (xG) models estimate the probability that a shot results in a goal from its context (e.g., location, pressure), but they operate only on observed shots. We propose xG+, a possession-level framework that first estimates the…
Sports organizations often want to estimate athlete strengths. For games with scored outcomes, a common approach is to assume observed game scores follow a normal distribution conditional on athletes' latent abilities, which may change over…
The denoising diffusion model has recently emerged as a powerful generative technique, capable of transforming noise into meaningful data. While theoretical convergence guarantees for diffusion models are well established when the target…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
Regression methods dominate the practice of biostatistical analysis, but biostatistical training emphasises the details of regression models and methods ahead of the purposes for which such modelling might be useful. More broadly,…
Skewness is a common occurrence in statistical applications. In recent years, various distribution families have been proposed to model skewed data by introducing unequal scales based on the median or mode. However, we argue that the point…
We propose utilizing match-level suspense and surprise - which capture the entertainment utility created by competitive balance and outcome uncertainty for sports spectators - as alternative policy targets for league organizers and…
Binomial distributions capture the probabilities of `heads' outcomes when a (biased) coin is tossed multiple times. The coin may be identified with a distribution on the two-element set {0,1}, where the 1 outcome corresponds to `head'. One…
This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this…
A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…
Football is a very result-driven industry, with goals being rarer than in most sports, so having further parameters to judge the performance of teams and individuals is key. Expected Goals (xG) allow further insight than just a scoreline.…
There is growing evidence that converting targets to soft targets in supervised learning can provide considerable gains in performance. Much of this work has considered classification, converting hard zero-one values to soft labels---such…
Many data sets cannot be accurately described by standard probability distributions due to the excess number of zero values present. For example, zero-inflation is prevalent in microbiome data and single-cell RNA sequencing data, which…