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Efficient sampling for Bayesian networks and benchmarking their structure learning Online: attendBC1 2.01.10 (Parkring 11, 85748 Garching)

Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high-dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed acyclic graph (DAG) is highly challenging mainly due to the vast number of possible networks in combination with the acyclicity constraint, and a wide plethora of algorithms have been developed for this task. Efforts have focused on two fronts: constraint-based methods that perform conditional independence tests to exclude edges and score and search approaches which explore the DAG space with greedy or MCMC schemes. We synthesize these two fields in a novel hybrid method which reduces the complexity of Bayesian MCMC approaches to that of a constraint-based method. This enables full Bayesian model averaging for much larger Bayesian networks, and offers significant improvements in structure learning. To facilitate the benchmarking of different methods, we further present a novel automated workflow for producing scalable, reproducible, and platform-independent benchmarks of structure learning algorithms. It is interfaced via a simple config file, which makes it accessible for all users, while the code is designed in a fully modular fashion to enable researchers to contribute additional methodologies. We demonstrate the applicability of this workflow for learning Bayesian networks in typical data scenarios.

References: doi:10.1080/10618600.2021.2020127 and arXiv:2107.03863

How GENERIC arises from upscaling a Hamiltonian systemOnline: attend (Passcode 101816)MI 03.04.011 (Boltzmannstr. 3, 85748 Garching)

In this talk, on joint work with Alexander Mielke and Johannes Zimmer, I want to explain our recent insights in how irreversibility arises out of coarse-graining reversible systems. In this context, 'irreversibility' means a system in GENERIC form, and 'reversible system' is a Hamiltonian system. The big question is how and why entropy and the Onsager operator appear.

The mathematical version of this question consists of taking a Hamiltonian system, doing some 'coarse-graining' (I will explain this) and then proving that, miraculously, the irreversible parts of GENERIC appear. We study a particular example, in which many calculations can be done by hand, and in which one can trace the origins of entropy and the Onsager operator back to the Hamiltonian system. This talk will be informal, because many of the steps have not been made rigorous yet, and there still is much to be learned. But I hope it will at least be interesting.

"Analytic Geometry" Online: attend (Meeting-ID: 913-2473-4411; Password: StatsCol22)A 027 (Theresienstr. 39, 80333 München)

Comparison of dependence graphs based on different functions of correlation matricesOnline: attendBC1 2.01.10 (Parkring 11, 85748 Garching)

t.b.a.

Joint Extremes in Temperature and Mortality: A Bivariate POT ApproachOnline: attendBC1 2.01.10 (Parkring 11, 85748 Garching)

This research project contributes to insurance risk management by modeling extreme climate risk and extreme mortality risk in an integrated manner via extreme value theory (EVT). We conduct an empirical study using monthly temperature and death data and find that the joint extremes in cold weather and old-age death counts exhibit the strongest level of dependence. Based on the estimated bivariate generalized Pareto distribution, we quantify the extremal dependence between death counts and temperature indexes. Methodologically, we employ the bivariate peaks over threshold (POT) approach, which is readily applicable to a wide range of topics in extreme risk management.

Testing the equality of changepoints (joint with Siegfried Hörmann, TU Graz)Online: attendBC1 2.01.10 (Parkring 11, 85748 Garching)

Testing for the presence of changepoints and determining their location is a common problem in time series analysis. Applying changepoint procedures to multivariate data results in higher power and more precise location estimates, both in online and offline detection. However, this requires that all changepoints occur at the same time. We study the problem of testing the equality of changepoint locations. One approach is to treat common breaks as a common feature and test, whether an appropriate linear combination of the data can cancel the breaks. We propose how to determine such a linear combination and derive the asymptotic distribution resulting CUSUM and MOSUM statistics. We also study the power of the test under local alternatives and provide simulation results of its nite sample performance. Finally, we suggest a clustering algorithm to group variables into clusters that are co-breaking.

Four proofs supporting randomized signatures B349 (Theresienstraße 39, 80333 Mathematisches Institut, LMU)

Signature transforms, as advocated by Terry Lyons et al., provide a universal feature extraction scheme on path spaces for the purposes of machine learning. Randomized Signatures, based on intuition from Reservoir Computing, have been introduced to reduce computational complexity when dealing with signature transforms. We provide four different proofs shedding light on the construction of randomized signature based on Johnson-Lindenstrauss random projections, a representation theory of free algebras, on arguments from Malliavin calculus and on arguments from kernel based random feature selection.

Joint works with Christa Cuchiero, Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega.

"Test positiv - trotzdem gesund? Wie man Bayesianisches Denken fördern kann" Online: attend (Meeting-ID: 913-2473-4411; Password: StatsCol22)A 027 (Theresienstr. 39, 80333 München)