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A spatially distributed system contains a large amount of agents with limited sensing, data processing, and communication capabilities. Recent technological advances have opened up possibilities to deploy spatially distributed systems for…
Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from…
Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…
Bayesian inference is useful to obtain a predictive distribution with a small generalization error. However, since posterior distributions are rarely evaluated analytically, we employ the variational Bayesian inference or sampling method to…
We propose a linear-complexity method for sampling from truncated multivariate normal (TMVN) distributions with high fidelity by applying nearest-neighbor approximations to a product-of-conditionals decomposition of the TMVN density. To…
In the mixture models problem it is assumed that there are $K$ distributions $\theta_{1},\ldots,\theta_{K}$ and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances…
We study Thompson sampling (TS) in online decision making, where the uncertain environment is sampled from a mixture distribution. This is relevant in multi-task learning, where a learning agent faces different classes of problems. We…
We propose a new global optimization method ({\em Simulated Tempering}) for simulating effectively a system with a rough free energy landscape (i.e. many coexisting states) at finite non-zero temperature. This method is related to simulated…
We report a novel Monte Carlo scheme that greatly enhances the power of parallel-tempering simulations. In this method, we boost the accumulation of statistical averages by including information about all potential parallel tempering trial…
In this paper, we propose Neural Spectrum Decomposition, a generic decomposition framework for dataset distillation. Unlike previous methods, we consider the entire dataset as a high-dimensional observation that is low-rank across all…
There has been a recent surge of interest in coupling methods for Markov chain Monte Carlo algorithms: they facilitate convergence quantification and unbiased estimation, while exploiting embarrassingly parallel computing capabilities.…
Bayesian inference for factorial hidden Markov models is challenging due to the exponentially sized latent variable space. Standard Monte Carlo samplers can have difficulties effectively exploring the posterior landscape and are often…
Langevin diffusion (LD) is one of the main workhorses for sampling problems. However, its convergence rate can be significantly reduced if the target distribution is a mixture of multiple densities, especially when each component…
We introduce a Markov Chain Monte Carlo (MCMC) method that is designed to sample from target distributions with irregular geometry using an adaptive scheme. In cases where targets exhibit non-Gaussian behaviour, we propose that adaption…
We study convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (Andrieu and Roberts [Ann. Statist. 37 (2009) 697-725]). We find that the asymptotic variance of the pseudo-marginal algorithm is always at least as…
We propose a framework to model the distribution of sequential data coming from a set of entities connected in a graph with a known topology. The method is based on a mixture of shared hidden Markov models (HMMs), which are jointly trained…
Hamiltonian Monte Carlo (HMC) has become routinely used for sampling from posterior distributions. Its extension Riemann manifold HMC (RMHMC) modifies the proposal kernel through distortion of local distances by a Riemannian metric. The…
In this paper, a distributed stochastic gradient (SG) algorithm is proposed where the estimators are aimed to collectively estimate an unknown time-invariant parameter from a set of noisy measurements obtained by distributed sensors. The…
The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…
Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant…