1,041 research outputs found
Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures
In this article we propose novel Bayesian nonparametric methods using
Dirichlet Process Mixture (DPM) models for detecting pairwise dependence
between random variables while accounting for uncertainty in the form of the
underlying distributions. A key criteria is that the procedures should scale to
large data sets. In this regard we find that the formal calculation of the
Bayes factor for a dependent-vs.-independent DPM joint probability measure is
not feasible computationally. To address this we present Bayesian diagnostic
measures for characterising evidence against a "null model" of pairwise
independence. In simulation studies, as well as for a real data analysis, we
show that our approach provides a useful tool for the exploratory nonparametric
Bayesian analysis of large multivariate data sets
Encrypted statistical machine learning: new privacy preserving methods
We present two new statistical machine learning methods designed to learn on
fully homomorphic encrypted (FHE) data. The introduction of FHE schemes
following Gentry (2009) opens up the prospect of privacy preserving statistical
machine learning analysis and modelling of encrypted data without compromising
security constraints. We propose tailored algorithms for applying extremely
random forests, involving a new cryptographic stochastic fraction estimator,
and na\"{i}ve Bayes, involving a semi-parametric model for the class decision
boundary, and show how they can be used to learn and predict from encrypted
data. We demonstrate that these techniques perform competitively on a variety
of classification data sets and provide detailed information about the
computational practicalities of these and other FHE methods.Comment: 39 page
Two-sample Bayesian Nonparametric Hypothesis Testing
In this article we describe Bayesian nonparametric procedures for two-sample
hypothesis testing. Namely, given two sets of samples
\stackrel{\scriptscriptstyle{iid}}{\s
im} and \stackrel{\scriptscriptstyle{iid}}{\sim},
with unknown, we wish to
evaluate the evidence for the null hypothesis
versus the
alternative . Our
method is based upon a nonparametric P\'{o}lya tree prior centered either
subjectively or using an empirical procedure. We show that the P\'{o}lya tree
prior leads to an analytic expression for the marginal likelihood under the two
hypotheses and hence an explicit measure of the probability of the null
.Comment: Published at http://dx.doi.org/10.1214/14-BA914 in the Bayesian
Analysis (http://projecteuclid.org/euclid.ba) by the International Society of
Bayesian Analysis (http://bayesian.org/
Population-Based Reversible Jump Markov Chain Monte Carlo
In this paper we present an extension of population-based Markov chain Monte
Carlo (MCMC) to the trans-dimensional case. One of the main challenges in
MCMC-based inference is that of simulating from high and trans-dimensional
target measures. In such cases, MCMC methods may not adequately traverse the
support of the target; the simulation results will be unreliable. We develop
population methods to deal with such problems, and give a result proving the
uniform ergodicity of these population algorithms, under mild assumptions. This
result is used to demonstrate the superiority, in terms of convergence rate, of
a population transition kernel over a reversible jump sampler for a Bayesian
variable selection problem. We also give an example of a population algorithm
for a Bayesian multivariate mixture model with an unknown number of components.
This is applied to gene expression data of 1000 data points in six dimensions
and it is demonstrated that our algorithm out performs some competing Markov
chain samplers
Power-efficiency enhanced thermally tunable Bragg grating for silica-on-silicon photonics
A thermally tunable Bragg grating device has been fabricated in a silica-on-silicon integrated optical chip, incorporating a suspended microbeam improving power efficiency. A waveguide and Bragg grating are defined through the middle of the microbeam via direct ultraviolet writing. A tuning range of 0.4 nm (50 GHz) is demonstrated at the telecommunication wavelength of 1550 nm. Power consumption during wavelength tuning is measured at 45 pm/mW, which is a factor of 90 better than reported values for similar bulk thermally tuned silica-on-silicon planar devices. The response time to a step change in heating is longer by a similar factor, as expected for a highly power-efficient device. The fabrication procedure involves a deep micromilling process, as well as wet etching and metal deposition. With this response, the device would be suitable for trimming applications and wherever low modulation frequencies are acceptable. A four-point-probe-based temperature measurement was also done to ascertain the temperature reached during tuning and found an average volume temperature of 48 °C, corresponding to 0.4 nm of tuning. The role of stress-induced buckling in device fabrication is included
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