218 research outputs found
Mean field variational bayes for elaborate distributions
We develop strategies for mean field variational Bayes approximate inference for Bayesian hierarchical models containing elaborate distributions. We loosely define elaborate distributions to be those having more complicated forms compared with common distributions such as those in the Normal and Gamma families. Examples are Asymmetric Laplace, Skew Normal and Generalized Extreme Value distributions. Such models suffer from the difficulty that the parameter updates do not admit closed form solutions. We circumvent this problem through a combination of (a) specially tailored auxiliary variables, (b) univariate quadrature schemes and (c) finite mixture approximations of troublesome density functions. An accuracy assessment is conducted and the new methodology is illustrated in an application. © 2011 International Society for Bayesian Analysis
A similarity-based Bayesian mixture-of-experts model
We present a new nonparametric mixture-of-experts model for multivariate
regression problems, inspired by the probabilistic -nearest neighbors
algorithm. Using a conditionally specified model, predictions for out-of-sample
inputs are based on similarities to each observed data point, yielding
predictive distributions represented by Gaussian mixtures. Posterior inference
is performed on the parameters of the mixture components as well as the
distance metric using a mean-field variational Bayes algorithm accompanied with
a stochastic gradient-based optimization procedure. The proposed method is
especially advantageous in settings where inputs are of relatively high
dimension in comparison to the data size, where input--output relationships are
complex, and where predictive distributions may be skewed or multimodal.
Computational studies on two synthetic datasets and one dataset comprising dose
statistics of radiation therapy treatment plans show that our
mixture-of-experts method performs similarly or better than a conditional
Dirichlet process mixture model both in terms of validation metrics and visual
inspection
Large-scale Heteroscedastic Regression via Gaussian Process
Heteroscedastic regression considering the varying noises among observations
has many applications in the fields like machine learning and statistics. Here
we focus on the heteroscedastic Gaussian process (HGP) regression which
integrates the latent function and the noise function together in a unified
non-parametric Bayesian framework. Though showing remarkable performance, HGP
suffers from the cubic time complexity, which strictly limits its application
to big data. To improve the scalability, we first develop a variational sparse
inference algorithm, named VSHGP, to handle large-scale datasets. Furthermore,
two variants are developed to improve the scalability and capability of VSHGP.
The first is stochastic VSHGP (SVSHGP) which derives a factorized evidence
lower bound, thus enhancing efficient stochastic variational inference. The
second is distributed VSHGP (DVSHGP) which (i) follows the Bayesian committee
machine formalism to distribute computations over multiple local VSHGP experts
with many inducing points; and (ii) adopts hybrid parameters for experts to
guard against over-fitting and capture local variety. The superiority of DVSHGP
and SVSHGP as compared to existing scalable heteroscedastic/homoscedastic GPs
is then extensively verified on various datasets.Comment: 14 pages, 15 figure
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Signal separation of musical instruments: simulation-based methods for musical signal decomposition and transcription
This thesis presents techniques for the modelling of musical signals, with particular regard to monophonic and polyphonic pitch estimation. Musical signals are modelled as a set of notes, each comprising of a set of harmonically-related sinusoids. An hierarchical model is presented that is very general and applicable to any signal that can be decomposed as the sum of basis functions. Parameter estimation is posed within a Bayesian framework, allowing for the incorporation of prior information about model parameters. The resulting posterior distribution is of variable dimension and so reversible jump MCMC simulation techniques are employed for the parameter estimation task. The extension of the model to time-varying signals with high posterior correlations between model parameters is described. The parameters and hyperparameters of several frames of data are estimated jointly to achieve a more robust detection. A general model for the description of time-varying homogeneous and heterogeneous multiple component signals is developed, and then applied to the analysis of musical signals. The importance of high level musical and perceptual psychological knowledge in the formulation of the model is highlighted, and attention is drawn to the limitation of pure signal processing techniques for dealing with musical signals. Gestalt psychological grouping principles motivate the hierarchical signal model, and component identifiability is considered in terms of perceptual streaming where each component establishes its own context. A major emphasis of this thesis is the practical application of MCMC techniques, which are generally deemed to be too slow for many applications. Through the design of efficient transition kernels highly optimised for harmonic models, and by careful choice of assumptions and approximations, implementations approaching the order of realtime are viable.Engineering and Physical Sciences Research Counci
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