Related papers: Towards an agnostic algorithm for sampling empiric…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
We investigate the problem of density estimation on the unit circle and the unit sphere from a computational perspective. Our primary goal is to develop new density estimators that are both rate-optimal and computationally efficient for…
The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude…
We present a novel population-based Bayesian inference approach to model the average and population variance of spatial distribution of a set of observables from ensemble analysis of low signal-to-noise ratio measurements. The method…
The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…
There is a rich literature on Bayesian methods for density estimation, which characterize the unknown density as a mixture of kernels. Such methods have advantages in terms of providing uncertainty quantification in estimation, while being…
Neutron star matter spans a wide range of densities, from that of nuclei at the surface to exceeding several times normal nuclear matter density in the core. While terrestrial experiments, such as nuclear or heavy-ion collision experiments,…
We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior…
Earth's mass and internal structure have been primarily studied through gravitational and seismic methods. Neutrinos, however, offer an independent way to explore Earth's interior via matter effects in neutrino oscillations that depend on…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
Existing techniques for certifying the robustness of models for discrete data either work only for a small class of models or are general at the expense of efficiency or tightness. Moreover, they do not account for sparsity in the input…
Estimating the density of states of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers. Density of states estimation has also…
Despite their successes in the field of self-learning AI, Convolutional Neural Networks (CNNs) suffer from having too many trainable parameters, impacting computational performance. Several approaches have been proposed to reduce the number…
NASA's Juno mission provided exquisite measurements of Jupiter's gravity field that together with the Galileo entry probe atmospheric measurements constrains the interior structure of the giant planet. Inferring its interior structure range…
This study focuses on membrane-based systems for CO$_2$ separation, addressing the urgent need for efficient carbon capture solutions to mitigate climate change. Linear regression models, based on membrane equations, were utilized to…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…
Computer models are widely used across a range of scientific disciplines to describe various complex physical systems, however to perform full uncertainty quantification we often need to employ emulators. An emulator is a fast statistical…
Interior characterization traditionally relies on individual planetary properties, ignoring correlations between different planets of the same system. For multi-planetary systems, planetary data are generally correlated. This is because,…
The field of autonomous navigation for unmanned ground vehicles (UGVs) is in continuous growth and increasing levels of autonomy have been reached in the last few years. However, the task becomes more challenging when the focus is on the…