Driving Markov chain Monte Carlo with a dependent random stream

Markov chain Monte Carlo is a widely-used technique for generating a dependent sequence of samples from complex distributions. Conventionally, these methods require a source of independent random variates. Most implementations use pseudo-random numbers instead because generating true independent variates with a physical system is not straightforward. In this paper we show how to modify some commonly used Markov chains to use a dependent stream of random numbers in place of independent uniform variates. The resulting Markov chains have the correct invariant distribution without requiring detailed knowledge of the stream's dependencies or even its marginal distribution. As a side-effect, sometimes far fewer random numbers are required to obtain accurate results.Comment: 16 pages, 4 figure

Blind deconvolution of sparse pulse sequences under a minimum distance constraint: a partially collapsed Gibbs sampler method

For blind deconvolution of an unknown sparse sequence convolved with an unknown pulse, a powerful Bayesian method employs the Gibbs sampler in combination with a Bernoulli–Gaussian prior modeling sparsity. In this paper, we extend this method by introducing a minimum distance constraint for the pulses in the sequence. This is physically relevant in applications including layer detection, medical imaging, seismology, and multipath parameter estimation. We propose a Bayesian method for blind deconvolution that is based on a modified Bernoulli–Gaussian prior including a minimum distance constraint factor. The core of our method is a partially collapsed Gibbs sampler (PCGS) that tolerates and even exploits the strong local dependencies introduced by the minimum distance constraint. Simulation results demonstrate significant performance gains compared to a recently proposed PCGS. The main advantages of the minimum distance constraint are a substantial reduction of computational complexity and of the number of spurious components in the deconvolution result

Elliptical slice sampling

Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with multivariate Gaussian priors. Its key properties are: 1) it has simple, generic code applicable to many models, 2) it has no free parameters, 3) it works well for a variety of Gaussian process based models. These properties make our method ideal for use while model building, removing the need to spend time deriving and tuning updates for more complex algorithms.Comment: 8 pages, 6 figures, appearing in AISTATS 2010 (JMLR: W&CP volume 6). Differences from first submission: some minor edits in response to feedback

Probabilistic Graphical Model Representation in Phylogenetics

Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to statistical model representation and software development. Clear communication and representation of the chosen model is crucial for: (1) reproducibility of an analysis, (2) model development and (3) software design. Moreover, a unified, clear and understandable framework for model representation lowers the barrier for beginners and non-specialists to grasp complex phylogenetic models, including their assumptions and parameter/variable dependencies. Graphical modeling is a unifying framework that has gained in popularity in the statistical literature in recent years. The core idea is to break complex models into conditionally independent distributions. The strength lies in the comprehensibility, flexibility, and adaptability of this formalism, and the large body of computational work based on it. Graphical models are well-suited to teach statistical models, to facilitate communication among phylogeneticists and in the development of generic software for simulation and statistical inference. Here, we provide an introduction to graphical models for phylogeneticists and extend the standard graphical model representation to the realm of phylogenetics. We introduce a new graphical model component, tree plates, to capture the changing structure of the subgraph corresponding to a phylogenetic tree. We describe a range of phylogenetic models using the graphical model framework and introduce modules to simplify the representation of standard components in large and complex models. Phylogenetic model graphs can be readily used in simulation, maximum likelihood inference, and Bayesian inference using, for example, Metropolis-Hastings or Gibbs sampling of the posterior distribution

Scalable Population Synthesis with Deep Generative Modeling

Population synthesis is concerned with the generation of synthetic yet realistic representations of populations. It is a fundamental problem in the modeling of transport where the synthetic populations of micro-agents represent a key input to most agent-based models. In this paper, a new methodological framework for how to 'grow' pools of micro-agents is presented. The model framework adopts a deep generative modeling approach from machine learning based on a Variational Autoencoder (VAE). Compared to the previous population synthesis approaches, including Iterative Proportional Fitting (IPF), Gibbs sampling and traditional generative models such as Bayesian Networks or Hidden Markov Models, the proposed method allows fitting the full joint distribution for high dimensions. The proposed methodology is compared with a conventional Gibbs sampler and a Bayesian Network by using a large-scale Danish trip diary. It is shown that, while these two methods outperform the VAE in the low-dimensional case, they both suffer from scalability issues when the number of modeled attributes increases. It is also shown that the Gibbs sampler essentially replicates the agents from the original sample when the required conditional distributions are estimated as frequency tables. In contrast, the VAE allows addressing the problem of sampling zeros by generating agents that are virtually different from those in the original data but have similar statistical properties. The presented approach can support agent-based modeling at all levels by enabling richer synthetic populations with smaller zones and more detailed individual characteristics.Comment: 27 pages, 15 figures, 4 table

A hierarchy of recurrent networks for speech recognition

Generative models for sequential data based on directed graphs of Restricted Boltzmann Machines (RBMs) are able to accurately model high dimensional sequences as recently shown. In these models, temporal dependencies in the input are discovered by either buffering previous visible variables or by recurrent connections of the hidden variables. Here we propose a modification of these models, the Temporal Reservoir Machine (TRM). It utilizes a recurrent artificial neural network (ANN) for integrating information from the input over time. This information is then fed into a RBM at each time step. To avoid difficulties of recurrent network learning, the ANN remains untrained and hence can be thought of as a random feature extractor. Using the architecture of multi-layer RBMs (Deep Belief Networks), the TRMs can be used as a building block for complex hierarchical models. This approach unifies RBM-based approaches for sequential data modeling and the Echo State Network, a powerful approach for black-box system identification. The TRM is tested on a spoken digits task under noisy conditions, and competitive performances compared to previous models are observed