Related papers: Exact Expressions for the Log-likelihood's Hessian…

The selection of the most suitable evolutionary model to analyze the given molecular data is usually left to biologist's choice. In his famous book, J Felsenstein suggested that certain linear equations satisfied by the expected…

Generalized linear models play an essential role in a wide variety of statistical applications. This paper discusses an approximation of the likelihood in these models that can greatly facilitate computation. The basic idea is to replace a…

We study the problem of maximum likelihood estimation of densities that are log-concave and lie in the graphical model corresponding to a given undirected graph $G$. We show that the maximum likelihood estimate (MLE) is the product of the…

Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn latent representations in modern multivariate data sets with complex dependency structures. Among…

We investigate the optimization landscape of maximum likelihood estimation (MLE) for the Cavender-Farris-Neyman (CFN) model, a two-state latent tree model fundamental to statistical phylogenetics and the ferromagnetic Ising model. Although…

Many application domains such as ecology or genomics have to deal with multivariate non Gaussian observations. A typical example is the joint observation of the respective abundances of a set of species in a series of sites, aiming to…

In this article we consider the development of unbiased estimators of the Hessian, of the log-likelihood function with respect to parameters, for partially observed diffusion processes. These processes arise in numerous applications, where…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree is modelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to…

We present a kernel-independent method that applies hierarchical matrices to the problem of maximum likelihood estimation for Gaussian processes. The proposed approximation provides natural and scalable stochastic estimators for its…

Multivariate Gaussian (MVG) distributions are central to modeling correlated continuous variables in probabilistic forecasting. Neural forecasting models typically parameterize the mean vector and covariance matrix of the distribution using…

Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…

Time series of observables measured from complex systems do often exhibit non-normal statistics, their statistical distributions (PDF's) are not gaussian and often skewed, with roughly exponential tails. Departure from gaussianity is…

We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…

Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the…

We introduce a novel matrix-variate extension of the Heckman selection model to accommodate multiple outcomes, providing a flexible and natural generalization of classical selection models for matrix-valued data. By relying on the matrix…

Gaussian distributions are widely used in Bayesian variational inference to approximate intractable posterior densities, but the ability to accommodate skewness can improve approximation accuracy significantly, when data or prior…

More than ever, today we are left with the abundance of molecular data outpaced by the advancements of the phylogenomic methods. Especially in the case of presence of many genes over a set of species under the phylogeny question, more…

We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…

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…