Related papers: An introduction to Bent Jorgensen's ideas

Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its complexity. One way to do so is through compositional…

We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The…

In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…

Mapping data from and/or onto a known family of distributions has become an important topic in machine learning and data analysis. Deep generative models (e.g., generative adversarial networks ) have been used effectively to match known and…

The measurement of dispersion is one of the most fundamental and ubiquitous statistical concepts, in both applied and theoretical contexts. For dispersion measures, such as the standard deviation, to effectively capture the variability of a…

We consider the problem of estimating the joint distribution of $n$ independent random variables. Our approach is based on a family of candidate probabilities that we shall call a model and which is chosen to either contain the true…

We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a…

We show that a language model's ability to predict text is tightly linked to the breadth of its embedding space: models that spread their contextual representations more widely tend to achieve lower perplexity. Concretely, we find that…

Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…

Imputation of missing values is a strategy for handling non-responses in surveys or data loss in measurement processes, which may be more effective than ignoring them. When the variable represents a count, the literature dealing with this…

A general class of models is proposed that is able to estimate the whole predictive distribution of a dependent variable $Y$ given a vector of explanatory variables $\xb$. The models exploit that the strength of explanatory variables to…

Recently much attention has been paid to deep generative models, since they have been used to great success for variational inference, generation of complex data types, and more. In most all of these settings, the goal has been to find a…

Exponential dispersion model is a useful framework in machine learning and statistics. Primarily, thanks to the additive structure of the model, it can be achieved without difficulty to estimate parameters including mean. However, tight…

Diffusion models are powerful generative models that produce high-quality samples from complex data. While their infinite-data behavior is well understood, their generalization with finite data remains less clear. Classical learning theory…

Although diffusion models now occupy a central place in generative modeling, introductory treatments commonly assume Euclidean data and seldom clarify their connection to discrete-state analogues. This article is a self-contained primer on…

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…

The Boltzmann-Gibbs probability distribution, seen as a statistical model, belongs to the exponential family. Recently, the latter concept has been generalized. The q-exponential family has been shown to be relevant for the statistical…

As one of the most popular and sought-after generative models in the recent years, diffusion models have sparked the interests of many researchers and steadily shown excellent advantage in various generative tasks such as image synthesis,…

In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed, where the defining convex function has an exponential nature. These estimators avoid the necessity of using an intermediate kernel…

Diffusion models have become a powerful family of deep generative models, with record-breaking performance in many applications. This paper first gives an overview and derivation of the basic theory of diffusion models, then reviews the…