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Within the framework of Gaussian graphical models, a prior distribution for the underlying graph is introduced to induce a block structure in the adjacency matrix of the graph and learning relationships between fixed groups of variables. A…

Weighted average sampling is more practical and numerically more stable than sampling at single points as in the classical Shannon sampling framework. Using the frame theory, one can completely reconstruct a bandlimited function from its…

The Bayesian inference is widely used in many scientific and engineering problems, especially in the linear inverse problems in infinite-dimensional setting where the unknowns are functions. In such problems, choosing an appropriate prior…

We present an implementation of range separated functionals utilizing the Slater-function on grids in real space in the projector augmented waves method. The screened Poisson equation is solved to evaluate the necessary screened exchange…

We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…

We consider optimization of composite objective functions, i.e., of the form $f(x)=g(h(x))$, where $h$ is a black-box derivative-free expensive-to-evaluate function with vector-valued outputs, and $g$ is a cheap-to-evaluate real-valued…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Consider observation of a phenomenon of interest subject to selective sampling due to a censoring mechanism regulated by some other variable. In this context, an extensive literature exists linked to the so-called Heckman selection model. A…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…

We introduce hybrid gausslet/Gaussian basis sets, where a standard Gaussian basis is added to a gausslet basis in order to increase accuracy near the nuclei while keeping the spacing of the grid of gausslets relatively large. The Gaussians…

Extended free energy Lagrangians are proposed for first principles molecular dynamics simulations at finite electronic temperatures for plane-wave pseudopotential and local orbital density matrix based calculations. Thanks to the extended…

This paper proposes a penalized composite likelihood method for model selection in colored graphical Gaussian models. The method provides a sparse and symmetry-constrained estimator of the precision matrix, and thus conducts model selection…

We consider deflation and augmentation techniques for accelerating the convergence of Krylov subspace methods for the solution of nonsingular linear algebraic systems. Despite some formal similarity, the two techniques are conceptually…

A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…

We propose an extension of the F-maximization principle to take into account the effects of non-superconformality. Guided by a four-dimensional analog, we formulate a modification of the free energy via the Lagrange multiplier technique. We…

The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals is available, but nearly all are based on the hierarchy of inputs commonly…

Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…

The expression of the free energy density of a classical crystalline system as a gradient expansion in terms of a set of order parameters is developed using classical density functional theory. The goal here is to extend and complete an…

Recently, the full version of the Eigenstate Thermalization Hypothesis (ETH) has been systematized using Free Probability. In this paper, we present a detailed discussion of the Free Cumulants approach to many-body dynamics within the…