Related papers: Reparameterizing the Birkhoff Polytope for Variati…
We consider the problem of approximating numerically the moments and the supports of measures which are invariant with respect to the dynamics of continuous- and discrete-time polynomial systems, under semialgebraic set constraints. First,…
We give a method for computing asymptotic formulas and approximations for the volumes of spectrahedra, based on the maximum-entropy principle from statistical physics. The method gives an approximate volume formula based on a single convex…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
An important problem in shape analysis is to match configurations of points in space filtering out some geometrical transformation. In this paper we introduce hierarchical models for such tasks, in which the points in the configurations are…
In this thesis, I explore the possibilities of conducting Bayesian optimization techniques in high dimensional domains. Although high dimensional domains can be defined to be between hundreds and thousands of dimensions, we will primarily…
The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…
We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…
We introduce a Bayesian model for inferring mixtures of subspaces of different dimensions. The key challenge in such a mixture model is specification of prior distributions over subspaces of different dimensions. We address this challenge…
In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
The normalizing constant plays an important role in Bayesian computation, and there is a large literature on methods for computing or approximating normalizing constants that cannot be evaluated in closed form. When the normalizing constant…
Let $\mathbb{K}$ be a field of characteristic zero and $\mathbb{K}[x_1, \dots, x_n]$ the corresponding multivariate polynomial ring. Given a sequence of $s$ polynomials $\mathbf{f} = (f_1, \dots, f_s)$ and a polynomial $\phi$, all in…
The set of nonnegative integer lattice points in a polytope, also known as the fiber of a linear map, makes an appearance in several applications including optimization and statistics. We address the problem of sampling from this set using…
The estimation of large covariance matrices has a high dimensional bias. Correcting for this bias can be reformulated via the tool of Free Probability Theory as a free deconvolution. The goal of this work is a computational and statistical…
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…
We study a linear observation model with an unknown permutation called \textit{permuted/shuffled linear regression}, where responses and covariates are mismatched and the permutation forms a discrete, factorial-size parameter. The…
The invariant polytope algorithm was a breakthrough in the joint spectral radius computation, allowing to find the exact value of the joint spectral radius for most matrix families~\cite{GP2013,GP2016}. This algorithm found many…
Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…
Conventional approximations to Bayesian inference rely on either approximations by statistics such as mean and covariance or by point particles. Recent advances such as the ensemble Gaussian mixture filter have generalized these notions to…
We give a geometrically exact treatment of percolation through voids around assemblies of randomly placed impermeable barrier particles, introducing a computationally inexpensive approach to finding critical barrier density thresholds…
Approximate Bayesian Computation (ABC) methods have become essential tools for performing inference when likelihood functions are intractable or computationally prohibitive. However, their scalability remains a major challenge in…