Related papers: Slepian-Bangs formula and Cramer Rao bound for cir…
The stochastic blockmodel (SBM) models the connectivity within and between disjoint subsets of nodes in networks. Prior work demonstrated that the rows of an SBM's adjacency spectral embedding (ASE) and Laplacian spectral embedding (LSE)…
We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…
A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…
The least squares (LS) estimate is the archetypical solution of linear regression problems. The asymptotic Gaussianity of the scaled LS error is often used to construct approximate confidence ellipsoids around the LS estimate, however, for…
We consider the problem of estimating the joint distribution $P$ of $n$ independent random variables within the Bayes paradigm from a non-asymptotic point of view. Assuming that $P$ admits some density $s$ with respect to a given reference…
This paper generalizes stochastic collocation methods to handle correlated non-Gaussian random parameters. The key challenge is to perform a multivariate numerical integration in a correlated parameter space when computing the coefficient…
We propose a localized consensus-based method for sampling from non-Gaussian distributions. This method arises from an alternative derivation of consensus-based sampling (CBS). Starting from ensemble-preconditioned Langevin dynamics, we…
The vertical distribution of suspended sediment concentration (SSC) remains a subject of active research given its relevance to a plethora of problems in hydraulics, hydrology, ecology, and water quality control. Much of the classical…
Distributed optimization methods are often applied to solving huge-scale problems like training neural networks with millions and even billions of parameters. In such applications, communicating full vectors, e.g., (stochastic) gradients,…
The segment distribution around the center of gravity is derived for unperturbed ring polymers. We show that, although a small difference is observed, the exact distribution can be well approximated by the Gaussian probability distribution…
A new analysis of the CMB, using WMAP data, supports earlier indications of non-Gaussian features of concentric circles of low temperature variance. Conformal cyclic cosmology (CCC) predicts such features from supermassive black-hole…
Score-based generative models have recently attracted significant attention for their ability to generate high-fidelity data by learning maps from simple Gaussian priors to complex data distributions. A natural generalization of this idea…
Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) A new version of the \v{C}erven\'y equations for the…
A new functional for the entropy that is asymptotically correct both in the high and low density limits is proposed. The new form is [ S=S^{(id)}+S^{(ln)}+S^{(r)}+S^{(c)} ] where the new term S^{(c)} depends on the p-bodies density…
Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel…
We consider the classical problem of missing-mass estimation, which deals with estimating the total probability of unseen elements in a sample. The missing-mass estimation problem has various applications in machine learning, statistics,…
Belief Propagation (BP) is a powerful algorithm for distributed inference in probabilistic graphical models, however it quickly becomes infeasible for practical compute and memory budgets. Many efficient, non-parametric forms of BP have…
This paper considers a non-standard problem of generating samples from a low-temperature Gibbs distribution with \emph{constrained} support, when some of the coordinates of the mode lie on the boundary. These coordinates are referred to as…
In this contribution we derive an explicit formula for the boundary non-crossing probabilities for Slepian processes associated with the piecewise linear boundary function. This formula is used to develop an approximation formula to the…
Two classes of GRBs have been confidently identified thus far and are prescribed to different physical scenarios -- NS-NS or NS-BH mergers, and collapse of massive stars, for short and long GRBs, respectively. A third, intermediate in…