# Overview

This is a weakly reading group of Data-Centric Engineering (DCE) group in The Alan Turing Institute (ATI). The reading / talk topics are broad on statistical theory, methodology, and application (e.g. stocastic process, optimization, surrogate modelling, etc). Please see our schedule below to check the topics and times for upcoming weeks. This group is open to everyone. If you would like to join the group and the emailing list, please feel free to contact organizers.

# Schedule

## January (Invited Talks + Surrogate Modelling)

### 15th Wednesday 11:00 - 12:00 @ Lovelace Room at ATI

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In this paper we propose and study a family of continuous wavelets on general domains, and a corresponding stochastic discretization that we call Monte Carlo wavelets. First, using tools from the theory of reproducing kernel Hilbert spaces and associated integral operators, we define a family of continuous wavelets by spectral calculus. Then, we propose a stochastic discretization based on Monte Carlo estimates of integral operators. Using concentration of measure results, we establish the convergence of such a discretization and derive convergence rates under natural regularity assumptions.

TBA

TBA

## February (Invited Talks + Surrogate Modelling)

### 5th Wednesday 11:00 - 12:00 @ Mary Shelley Room at ATI

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With the incorporation of new data gathering methods in clinical research, it becomes fundamental for Survival Analysis techniques to be able to deal with high-dimensional or/and non-standard covariates. In this paper we introduce a general non-parametric independence test between right-censored survival times and covariates taking values on a general space $\mathcal{X}$. We show our test statistic has a dual intepretation, first in terms of the supremum of a potentially infinite collection of weight-indexed log-rank tests, with weight functions belonging to a Reproducing kernel Hilbert space of functions (RKHS), and second, as the norm of the difference of the embeddings of certain depencency" measures into the RKHS, similarly to the well-know HSIC test-statistic. We provide an easy-to-use test-statistic as well as an economic Wild-Bootstrap procedure and study asymptotic properties of the test, finding sufficient conditions to ensure our test is omnibus. We perform extensive simulations demonstrating that our testing procedure performs, in general, better than competing approaches.

TBA

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### 26th Wednesday 11:00 - 12:00 @ Mary Shelley Room at ATI

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Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely on iterated steepest descent steps with respect to a reproducing kernel Hilbert space norm. This construction leads to interacting particle systems, the mean-field limit of which is a gradient flow on the space of probability distributions equipped with a certain geometrical structure. We leverage this viewpoint to shed some light on the convergence properties of the algorithm, in particular addressing the problem of choosing a suitable positive definite kernel function. Our analysis leads us to considering certain nondifferentiable kernels with adjusted tails. We demonstrate significant performs gains of these in various numerical experiments.

TBA

# Contact

## Location

The Alan Turing Institute