Related papers: Boltzmann Machine Learning with a Parallel, Persis…
We present a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria utilizing adjoint-based a posteriori error analysis for differential equations. This is in contrast to classical…
The Boltzmann Machine (BM) is a neural network composed of stochastically firing neurons that can learn complex probability distributions by adapting the synaptic interactions between the neurons. BMs represent a very generic class of…
There is a lack of methodological results for continuous time change detection due to the challenges of noninformative prior specification and efficient posterior inference in this setting. Most methodologies to date assume data are…
We propose and show the efficacy of a new method to address generic inverse problems. Inverse modeling is the task whereby one seeks to determine the control parameters of a natural system that produce a given set of observed measurements.…
The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and…
Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data.…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
Efficient sampling from the Boltzmann distribution given its energy function is a key challenge for modeling complex physical systems such as molecules. Boltzmann Generators address this problem by leveraging continuous normalizing flows to…
We study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning…
Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling are finding widespread use in applied statistics and machine learning. These often lead to difficult computational problems, which are increasingly being solved on parallel and…
The problem of large scale multiple testing arises in many contexts, including testing for pairwise interaction among large numbers of neurons. With advances in technologies, it has become common to record from hundreds of neurons…
Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…
We consider a generic representation problem of internal coordinates (bond lengths, valence angles, and dihedral angles) and their transformation to 3-dimensional Cartesian coordinates of a biomolecule. We show that the…
Monte Carlo (MC) integration is the de facto method for approximating the predictive distribution of Bayesian neural networks (BNNs). But, even with many MC samples, Gaussian-based BNNs could still yield bad predictive performance due to…
Sequence-based protein homology detection has been extensively studied and so far the most sensitive method is based upon comparison of protein sequence profiles, which are derived from multiple sequence alignment (MSA) of sequence homologs…
We develop a modular approach to Markov chain Monte Carlo (MCMC) sampling for unnormalized target densities. In this approach, Markov chains are constructed in parallel, each constrained to a subset of the target space. The Monte Carlo…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of partial differential equations. In…
Adaptive Markov chain Monte Carlo (MCMC) algorithms, which automatically tune their parameters based on past samples, have proved extremely useful in practice. The self-tuning mechanism makes them `non-Markovian', which means that their…
In many hierarchical inverse problems, not only do we want to estimate high- or infinite-dimensional model parameters in the parameter-to-observable maps, but we also have to estimate hyperparameters that represent critical assumptions in…