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Genealogical networks, also known as family trees or population pedigrees, are commonly studied by genealogists wanting to know about their ancestry, but they also provide a valuable resource for disciplines such as digital demography,…
We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone…
Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…
We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a…
We show that the forward and backward propagation can be formulated as a solution of lower and upper triangular systems of equations. For standard feedforward (FNNs) and recurrent neural networks (RNNs) the triangular systems are always…
Many aspects of the historical relationships between populations in a species are reflected in genetic data. Inferring these relationships from genetic data, however, remains a challenging task. In this paper, we present a statistical model…
Polynomial ensembles are determinantal point processes associated with (non necessarily orthogonal) projections onto polynomial subspaces. The aim of this survey article is to put forward the use of recurrence coefficients to obtain the…
In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…
To understand biological diversification, it is important to account for large-scale processes that affect the evolutionary history of groups of co-distributed populations of organisms. Such events predict temporally clustered divergences…
We study ancestral structures for the two-type Moran model with mutation and frequency-dependent selection under the nonlinear dominance or fittest-type-wins scheme. Under appropriate conditions, both lead, in distribution, to the same…
Likelihood-based generative models are the backbones of lossless compression due to the guaranteed existence of codes with lengths close to negative log likelihood. However, there is no guaranteed existence of computationally efficient…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees. Substitutions in sequences are modelled through a continuous-time Markov process, characterised by an instantaneous rate matrix, which standard…
We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. A general…
Optimising probabilistic models is a well-studied field in statistics. However, its connection with the training of generative models remains largely under-explored. In this paper, we show that the evolution of time-varying generative…
Inferring the phylogenetic relationships among a sample of organisms is a fundamental problem in modern biology. While distance-based hierarchical clustering algorithms achieved early success on this task, these have been supplanted by…
The deterministic selection-recombination equation describes the evolution of the genetic type composition of a population under selection and recombination in a law of large numbers regime. So far, an explicit solution has seemed out of…
Importance sampling is a popular technique in Bayesian inference: by reweighting samples drawn from a proposal distribution we are able to obtain samples and moment estimates from a Bayesian posterior over latent variables. Recent work,…
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
The Forward-Forward algorithm has evolved in machine learning research, tackling more complex tasks that mimic real-life applications. In the last years, it has been improved by several techniques to perform better than its original…
We give an outline of a formalism for the solution of the evolution equations for off-forward parton distributions in leading and next-to-leading orders based on partial conformal wave expansion and orthogonal polynomials reconstruction.