Related papers: Fast Gibbs Sampling on Bayesian Hidden Markov Mode…
Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling Bayesian inference to large datasets under an assumption of i.i.d data. We instead develop an SG-MCMC algorithm to learn the parameters of hidden Markov models…
Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient…
Gaussian Mixture models (GMMs) are a powerful tool for clustering, classification and density estimation when clustering structures are embedded in the data. The presence of missing values can largely impact the GMMs estimation process,…
Hidden Markov Models (HMMs) are powerful tools for modeling sequential data, where the underlying states evolve in a stochastic manner and are only indirectly observable. Traditional HMM approaches are well-established for linear sequences,…
We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the…
Standard practice in Hidden Markov Model (HMM) selection favors the candidate with the highest full-sequence likelihood, although this is equivalent to making a decision based on a single realization. We introduce a \emph{fragment-based}…
The Partially Collapsed Gibbs (PCG) sampler offers a new strategy for improving the convergence of a Gibbs sampler. PCG achieves faster convergence by reducing the conditioning in some of the draws of its parent Gibbs sampler. Although this…
This paper considers the quickest detection problem for hidden Markov models (HMMs) in a Bayesian setting. We construct an augmented HMM representation of the problem that allows the application of a dynamic programming approach to prove…
We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…
The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we…
Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted to a discrete and uniform time grid. They are thus not well suited to explain often irregularly spaced discrete event data from continuous-time phenomena. We show…
We consider Bayesian linear regression with sparsity-inducing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically…
Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…
The curse of dimensionality presents a pervasive challenge in optimization problems, with exponential expansion of the search space rapidly causing traditional algorithms to become inefficient or infeasible. An adaptive sampling strategy is…
Analysis of multivariate healthcare time series data is inherently challenging: irregular sampling, noisy and missing values, and heterogeneous patient groups with different dynamics violating exchangeability. In addition, interpretability…
Developing efficient Bayesian computation algorithms for imaging inverse problems is challenging due to the dimensionality involved and because Bayesian imaging models are often not smooth. Current state-of-the-art methods often address…
For large scale on-line inference problems the update strategy is critical for performance. We derive an adaptive scan Gibbs sampler that optimizes the update frequency by selecting an optimum mini-batch size. We demonstrate performance of…
Wearable devices including accelerometers are increasingly being used to collect high-frequency human activity data in situ. There is tremendous potential to use such data to inform medical decision making and public health policies.…
In this work we propose a Bayesian framework for data fusion of multivariate signals which arises in imaging systems. More specifically, we consider the case where we have observed two images of the same object through two different imaging…
Sequential algorithms such as sequential importance sampling (SIS) and sequential Monte Carlo (SMC) have proven fundamental in Bayesian inference for models not admitting a readily available likelihood function. For approximate Bayesian…