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We introduce a class of auto-encoder neural networks tailored to data from the natural exponential family (e.g., count data). The architectures are inspired by the problem of learning the filters in a convolutional generative model with…
Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
In their fundamental paper on cubic variance functions, Letac and Mora (The Annals of Statistics,1990) presented a systematic, rigorous and comprehensive study of natural exponential families on the real line, their characterization through…
Continual learning is the ability to sequentially learn over time by accommodating knowledge while retaining previously learned experiences. Neural networks can learn multiple tasks when trained on them jointly, but cannot maintain…
We present a margin-free finite mixture model which allows us to simultaneously classify objects into known classes and to identify possible new object types using a set of continuous attributes. This application is motivated by the needs…
A new family of integer-valued Cauchy-type distributions is introduced, the {\it Cauchy-Cacoullos family}. The characteristic function is evaluated, showing some interesting distributional properties, similar to the ordinary (continuous)…
Transductive inference is widely used in few-shot learning, as it leverages the statistics of the unlabeled query set of a few-shot task, typically yielding substantially better performances than its inductive counterpart. The current…
We present a nonparametric Bayesian joint model for multivariate continuous and categorical variables, with the intention of developing a flexible engine for multiple imputation of missing values. The model fuses Dirichlet process mixtures…
Statistical models of real world data typically involve continuous probability distributions such as normal, Laplace, or exponential distributions. Such distributions are supported by many probabilistic modelling formalisms, including…
We construct a new distribution for the simplex using the Kumaraswamy distribution and an ordered stick-breaking process. We explore and develop the theoretical properties of this new distribution and prove that it exhibits symmetry under…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs…
Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…
Diffusion models have quickly become the go-to paradigm for generative modelling of perceptual signals (such as images and sound) through iterative refinement. Their success hinges on the fact that the underlying physical phenomena are…
The Dirichlet Belief Network~(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. In this work, we leverage its interpretable modelling architecture and propose a deep…
The $\lambda$-exponential family generalizes the standard exponential family via a generalized convex duality motivated by optimal transport. It is the constant-curvature analogue of the exponential family from the information-geometric…
We consider three new classes of exponential dispersion models of discrete probability distributions which are defined by specifying their variance functions in their mean value parameterization. In a previous paper (Bar-Lev and Ridder,…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
In selective classification (SC), a classifier abstains from making predictions that are likely to be wrong to avoid excessive errors. To deploy imperfect classifiers -- either due to intrinsic statistical noise of data or for robustness…