[ibayesclub.beta] International Bayes Club, this Friday

[Andrade Serra, P.J. de]

Dear subscribers,


This coming Friday the 25th, 15:00-17:00, there is a meeting of the International Bayes Club. The speakers are Sara Wade (University of Edinburgh), and Rob Scheichl (Heidelberg University). You can find the respective titles and abstracts below.

You can join the meeting via zoom: 
https://vu-live.zoom.us/j/93507541253?pwd=VWtibnVSbHc2Y1B4cWl2T2dLajVTZz09 
(Meeting ID: 935 0754 1253, Passcode: 299396)

As always, up to date information can be found at the Bayes Club website:
https://www.math.vu.nl/thebayesclub/
In particular, the following meeting will be on the 21st of April, 15:00.


Best wishes,
Paulo

PS: sorry for any cross-posting.


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Sara Wade (University of Edinburgh) 
Title: Non-stationary Gaussian process discriminant analysis with variable selection for high-dimensional functional data
Abstract:
High-dimensional classification and feature selection tasks are ubiquitous with the recent advancement in data acquisition technology. In several application areas such as biology, genomics and proteomics, the data are often functional in their nature and exhibit a degree of roughness and non-stationarity. These structures pose additional challenges to commonly used methods that rely mainly on a two-stage approach performing variable selection and classification separately. We propose in this work a novel Gaussian process discriminant analysis (GPDA) that combines these steps in a unified framework. Our model is a two-layer non-stationary Gaussian process coupled with an Ising prior to identify differentially-distributed locations. Scalable inference is achieved via developing a variational scheme that exploits advances in the use of sparse inverse covariance matrices. We demonstrate the performance of our methodology on simulated datasets and two proteomics datasets: breast cancer and SARS-CoV-2. Our approach distinguishes itself by offering explainability as well as uncertainty quantification in addition to low computational cost, which are crucial to increase trust and social acceptance of data-driven tools.

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Rob Scheichl (Heidelberg University, DE) 
Title: Efficient Importance Sampling in High Dimensions using Low-Rank Tensor Approximations
Abstract:
Estimation of event probability is a famous statistical task. Headline applications include risk assessment of waste repositories, the certification of aircraft wings or the analysis of surges in infectious diseases. In most problems, neither the random variable defining the event nor its distribution are available explicitly. Instead, the event is parametrized by a high-dimensional random vector, and the unknown probability needs to be computed as a multivariate integral of a complicated and numerically expensive function (e.g. a PDE solution). Standard Monte Carlo approaches require numbers of samples inversely proportional to the product of the squared error and the event probability, which can exceed billions in the case of a rare event. In this paper, building on deep compositions of Rosenblatt transport maps, induced by a set of probability densities bridging from a tractable measure to the optimal biasing distribution, a computationally efficient method to approximate a biasing distribution is developed. Each map is computed using a low-rank tensor approximation in the tensor train format of the pullback of the bridging density by the previously computed map. Bridging densities are obtained by varying the width of the sigmoid approximation of the indicator function of the event. More importantly, the approach immediately extends also to intractable (e.g. posterior) densities using in addition tempering to obtain bridging densities. Numerical experiments with ODE- and PDE-constrained Bayesian inverse problems show little to no increase in the computational complexity with the failure probability going to zero, and allow to compute hitherto unattainable estimates of rare event probabilities for complex, high-dimensional posterior densities. This is joint work with Tiangang Cui (Monash) and Sergey Dolgov (Bath).

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