Related papers: Bayesian statistical learning using density operat…
Characterizing statistical properties of solutions of inverse problems is essential for decision making. Bayesian inversion offers a tractable framework for this purpose, but current approaches are computationally unfeasible for most…
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…
In this work we explore the possibility of using sparse statistical modeling in condensed matter physics. The procedure is employed to two well known problems: elemental superconductors and heavy fermions, and was shown that in most cases…
We are studying the problem of estimating density in a wide range of metric spaces, including the Euclidean space, the sphere, the ball, and various Riemannian manifolds. Our framework involves a metric space with a doubling measure and a…
Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the…
In quantum mechanics, a norm squared wave function can be interpreted as the probability density that describes the likelihood of a particle to be measured in a given position or momentum. This statistical property is at the core of the…
State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…
Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…
We study the sample complexity of Bayesian recovery for solving inverse problems with general prior, forward operator and noise distributions. We consider posterior sampling according to an approximate prior $\mathcal{P}$, and establish…
Bayesian Optimization has become the reference method for the global optimization of black box, expensive and possibly noisy functions. Bayesian Op-timization learns a probabilistic model about the objective function, usually a Gaussian…
This expository article presents the approach to statistical machine learning based on reproducing kernel Hilbert spaces. The basic framework is introduced for scalar-valued learning and then extended to operator learning. Finally, learning…
Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without…
We present a principled Bayesian framework for signal reconstruction, in which the signal is modelled by basis functions whose number (and form, if required) is determined by the data themselves. This approach is based on a Bayesian…
This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
In this work, we propose new objective functions to train deep neural network based density ratio estimators and apply it to a change point detection problem. Existing methods use linear combinations of kernels to approximate the density…
In environmental studies, realistic simulations are essential for understanding complex systems. Statistical emulation with Gaussian processes (GPs) in functional data models have become a standard tool for this purpose. Traditional…
We propose a novel capsule network based variational encoder architecture, called Bayesian capsules (B-Caps), to modulate the mean and standard deviation of the sampling distribution in the latent space. We hypothesized that this approach…