Construction of nonparametric Bayesian models from parametric Bayes equations

We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in non-parametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.

Robust estimation of local genetic ancestry in admixed populations using a nonparametric Bayesian approach.

We present a new haplotype-based approach for inferring local genetic ancestry of individuals in an admixed population. Most existing approaches for local ancestry estimation ignore the latent genetic relatedness between ancestral populations and treat them as independent. In this article, we exploit such information by building an inheritance model that describes both the ancestral populations and the admixed population jointly in a unified framework. Based on an assumption that the common hypothetical founder haplotypes give rise to both the ancestral and the admixed population haplotypes, we employ an infinite hidden Markov model to characterize each ancestral population and further extend it to generate the admixed population. Through an effective utilization of the population structural information under a principled nonparametric Bayesian framework, the resulting model is significantly less sensitive to the choice and the amount of training data for ancestral populations than state-of-the-art algorithms. We also improve the robustness under deviation from common modeling assumptions by incorporating population-specific scale parameters that allow variable recombination rates in different populations. Our method is applicable to an admixed population from an arbitrary number of ancestral populations and also performs competitively in terms of spurious ancestry proportions under a general multiway admixture assumption. We validate the proposed method by simulation under various admixing scenarios and present empirical analysis results from a worldwide-distributed dataset from the Human Genome Diversity Project.

Bayesian inference for multidimensional NMR image reconstruction

Reconstruction of an image from a set of projections has been adapted to generate multidimensional nuclear magnetic resonance (NMR) spectra, which have discrete features that are relatively sparsely distributed in space. For this reason, a reliable reconstruction can be made from a small number of projections. This new concept is called Projection Reconstruction NMR (PR-NMR). In this paper, multidimensional NMR spectra are reconstructed by Reversible Jump Markov Chain Monte Carlo (RJMCMC). This statistical method generates samples under the assumption that each peak consists of a small number of parameters: position of peak centres, peak amplitude, and peak width. In order to find the number of peaks and shape, RJMCMC has several moves: birth, death, merge, split, and invariant updating. The reconstruction schemes are tested on a set of six projections derived from the three-dimensional 700 MHz HNCO spectrum of a protein HasA.

Bayesian interpolation in a dynamic sinusoidal model with application to packet-loss concealment

In this paper, we consider Bayesian interpolation and parameter estimation in a dynamic sinusoidal model. This model is more flexible than the static sinusoidal model since it enables the amplitudes and phases of the sinusoids to be time-varying. For the dynamic sinusoidal model, we derive a Bayesian inference scheme for the missing observations, hidden states and model parameters of the dynamic model. The inference scheme is based on a Markov chain Monte Carlo method known as Gibbs sampler. We illustrate the performance of the inference scheme to the application of packet-loss concealment of lost audio and speech packets. © EURASIP, 2010.

Automated Computation of the Fundamental Matrix for Vision-Based Construction Site Applications

Estimating the fundamental matrix (F), to determine the epipolar geometry between a pair of images or video frames, is a basic step for a wide variety of vision-based functions used in construction operations, such as camera-pair calibration, automatic progress monitoring, and 3D reconstruction. Currently, robust methods (e.g., SIFT + normalized eight-point algorithm + RANSAC) are widely used in the construction community for this purpose. Although they can provide acceptable accuracy, the significant amount of required computational time impedes their adoption in real-time applications, especially video data analysis with many frames per second. Aiming to overcome this limitation, this paper presents and evaluates the accuracy of a solution to find F by combining the use of two speedy and consistent methods: SURF for the selection of a robust set of point correspondences and the normalized eight-point algorithm. This solution is tested extensively on construction site image pairs including changes in viewpoint, scale, illumination, rotation, and moving objects. The results demonstrate that this method can be used for real-time applications (5 image pairs per second with the resolution of 640 × 480) involving scenes of the built environment.

Bayesian correlated clustering to integrate multiple datasets.

MOTIVATION: The integration of multiple datasets remains a key challenge in systems biology and genomic medicine. Modern high-throughput technologies generate a broad array of different data types, providing distinct-but often complementary-information. We present a Bayesian method for the unsupervised integrative modelling of multiple datasets, which we refer to as MDI (Multiple Dataset Integration). MDI can integrate information from a wide range of different datasets and data types simultaneously (including the ability to model time series data explicitly using Gaussian processes). Each dataset is modelled using a Dirichlet-multinomial allocation (DMA) mixture model, with dependencies between these models captured through parameters that describe the agreement among the datasets. RESULTS: Using a set of six artificially constructed time series datasets, we show that MDI is able to integrate a significant number of datasets simultaneously, and that it successfully captures the underlying structural similarity between the datasets. We also analyse a variety of real Saccharomyces cerevisiae datasets. In the two-dataset case, we show that MDI's performance is comparable with the present state-of-the-art. We then move beyond the capabilities of current approaches and integrate gene expression, chromatin immunoprecipitation-chip and protein-protein interaction data, to identify a set of protein complexes for which genes are co-regulated during the cell cycle. Comparisons to other unsupervised data integration techniques-as well as to non-integrative approaches-demonstrate that MDI is competitive, while also providing information that would be difficult or impossible to extract using other methods.

Monte Carlo-Based Bayesian group object tracking and causal reasoning

We present algorithms for tracking and reasoning of local traits in the subsystem level based on the observed emergent behavior of multiple coordinated groups in potentially cluttered environments. Our proposed Bayesian inference schemes, which are primarily based on (Markov chain) Monte Carlo sequential methods, include: 1) an evolving network-based multiple object tracking algorithm that is capable of categorizing objects into groups, 2) a multiple cluster tracking algorithm for dealing with prohibitively large number of objects, and 3) a causality inference framework for identifying dominant agents based exclusively on their observed trajectories.We use these as building blocks for developing a unified tracking and behavioral reasoning paradigm. Both synthetic and realistic examples are provided for demonstrating the derived concepts. © 2013 Springer-Verlag Berlin Heidelberg.

Linear gaussian computations for near-exact Bayesian Monte Carlo inference in skewed alpha-stable time series models

In this paper we study parameter estimation for time series with asymmetric α-stable innovations. The proposed methods use a Poisson sum series representation (PSSR) for the asymmetric α-stable noise to express the process in a conditionally Gaussian framework. That allows us to implement Bayesian parameter estimation using Markov chain Monte Carlo (MCMC) methods. We further enhance the series representation by introducing a novel approximation of the series residual terms in which we are able to characterise the mean and variance of the approximation. Simulations illustrate the proposed framework applied to linear time series, estimating the model parameter values and model order P for an autoregressive (AR(P)) model driven by asymmetric α-stable innovations. © 2012 IEEE.

Bayesian non-parametrics and the probabilistic approach to modelling.

Modelling is fundamental to many fields of science and engineering. A model can be thought of as a representation of possible data one could predict from a system. The probabilistic approach to modelling uses probability theory to express all aspects of uncertainty in the model. The probabilistic approach is synonymous with Bayesian modelling, which simply uses the rules of probability theory in order to make predictions, compare alternative models, and learn model parameters and structure from data. This simple and elegant framework is most powerful when coupled with flexible probabilistic models. Flexibility is achieved through the use of Bayesian non-parametrics. This article provides an overview of probabilistic modelling and an accessible survey of some of the main tools in Bayesian non-parametrics. The survey covers the use of Bayesian non-parametrics for modelling unknown functions, density estimation, clustering, time-series modelling, and representing sparsity, hierarchies, and covariance structure. More specifically, it gives brief non-technical overviews of Gaussian processes, Dirichlet processes, infinite hidden Markov models, Indian buffet processes, Kingman's coalescent, Dirichlet diffusion trees and Wishart processes.

Probabilistic computation in human perception under variability in encoding precision.

A key function of the brain is to interpret noisy sensory information. To do so optimally, observers must, in many tasks, take into account knowledge of the precision with which stimuli are encoded. In an orientation change detection task, we find that encoding precision does not only depend on an experimentally controlled reliability parameter (shape), but also exhibits additional variability. In spite of variability in precision, human subjects seem to take into account precision near-optimally on a trial-to-trial and item-to-item basis. Our results offer a new conceptualization of the encoding of sensory information and highlight the brain's remarkable ability to incorporate knowledge of uncertainty during complex perceptual decision-making.