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01.06.2022 12:15 Jack Kuipers (ETH Zürich):
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

01.06.2022 13:00 Mark Peletier:
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.

09.06.2022 16:15 Angelo Lucia (Universidad Complutense de Madrid):
Thermalization of 2D quantum memoriesMI 03.04.011 (Boltzmannstr. 3, 85748 Garching)

The aim of a quantum memory is to protect an encoded quantum state against errors for long periods of time. Quantum double models are a class of 2D quantum memories proposed by Kitaev, in which the protection from noise is due to the topological properties of the ground state degeneracy. Heuristic arguments have long pointed to a weakness of these models against thermal noise processes. In this talk I will present a rigorous estimate on the lifetime of these memories under a noise process modelled by Davies generators which confirms these findings. This estimate is obtained by proving that the spectral gap of the generator is lower bounded by a positive constant uniformly in the system size.

10.06.2022 10:00 Jonas Latz (Heriot-Watt University):
Stochastic gradient descent in continuous time: discrete and continuous dataMI 03.10.011 (Boltzmannstr. 3, 85748 Garching)

Optimisation problems with discrete and continuous data appear in statistical estimation, machine learning, functional data science, robust optimal control, and variational inference. The 'full' target function in such an optimisation problem is given by the integral over a family of parameterised target functions with respect to a discrete or continuous probability measure. Such problems can often be solved by stochastic optimisation methods: performing optimisation steps with respect to the parameterised target function with randomly switched parameter values. In this talk, we discuss a continuous-time variant of the stochastic gradient descent algorithm. This so-called stochastic gradient process couples a gradient flow minimising a parameterised target function and a continuous-time 'index' process which determines the parameter.

We first briefly introduce the stochastic gradient processes for finite, discrete data which uses pure jump index processes. Then, we move on to continuous data. Here, we allow for very general index processes: reflected diffusions, pure jump processes, as well as other Lévy processes on compact spaces. Thus, we study multiple sampling patterns for the continuous data space. We show that the stochastic gradient process can approximate the gradient flow minimising the full target function at any accuracy. Moreover, we give convexity assumptions under which the stochastic gradient process with constant learning rate is geometrically ergodic. In the same setting, we also obtain ergodicity and convergence to the minimiser of the full target function when the learning rate decreases over time sufficiently slowly.

15.06.2022 12:15 Harry Joe (University of British Columbia, CAN):
Comparison of dependence graphs based on different functions of correlation matricesOnline: attendBC1 2.01.10 (Parkring 11, 85748 Garching)

A dependence graph for a set of variables has rules for which pairs of variables are connected. In the literature on dependence graphs for gene expression measurements, there have been several rules for connecting pairs of variables based on a correlation matrix: (a) absolute correlation of the pair exceed a threshold; (b) absolute partial correlation of the pair given the rest exceed a threshold; (c) first-order conditional independence rule of Magwene and Kim (2004).

These three methods will be compared with the dependence graph from a truncated partial correlation vine with thresholding. The comparisons are made for correlation matrices that are derived from (a) factor dependence structures, (b) Markov tree structure, and (c) variables that form groups with strong within group dependence and weaker between group dependence. If there are latent variables, the graphs are compared with and without them. The goal is to show that more parsimonious and interpretable graphs can be obtained with inclusion of latent variables.

15.06.2022 13:00 Gergely Röst, University of Szeged:
The COVID-19 Modelling and Epidemiology Task Force in HungaryOnline: attend (Passcode 101816)MI 03.04.011 (Boltzmannstr. 3, 85748 Garching)

The Hungarian COVID-19 Mathematical Modelling and Epidemiological Analysis Task Force (also known as the “epimath team”) was assembled in the early phase of the pandemic in March 2020, to provide in-depth epidemiological situation reports, forecasting, and scenario analysis to support evidence informed decision making during the COVID-19 pandemic. It is a multidisciplinary team of specialists from many institutions across the country, including mathematicians, medical doctors, epidemiologists, statisticians, network scientists, system biologists, public health experts, computer scientists and mathematical social scientists. Our aim was to integrate a wide range of competencies to tackle the complex public health, economical and societal challenges posed by the pandemic. This was an innovative initiative in Hungary, and in this talk we summarize how this team has worked and what has been achieved in the past two years, regarding policy advisory and scientific research. Several specific examples will be highlighted from the past pandemic waves to illustrate how the task force contributed to the fight against SARS-COV-2.

Link and Passcode: Code 101816

20.06.2022 15:00 Alexander Robinson:
Mapping the stability of dynamic Earth system componentsvia ZOOM (Boltzmannstr. 3, 85748 Garching)

Several components of the Earth system have been identified as tipping elements - systems that are subject to positive feedbacks that have the potential for abrupt transitions of state. These include the Greenland ice sheet, the Antarctic ice sheet and the Atlantic Meridional Overturning Circulation, among many others. It is often instructive to map the stability of these systems under equilibrium conditions using state of the art models, which are often highly computationally intensive. Here I present a new numerical method based on control theory to balance the needs of computational efficiency and accuracy in identifying tipping points in these nonlinear systems.

22.06.2022 12:15 Han Li (University of Melbourne, AUS):
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.

22.06.2022 13:00 Simon Strübbe, Klinikum rechts der Isar:
Computer linguistics project to simplify German sentences corresponding to the rules of simple languageOnline: attend (Passcode 101816)MI 03.04.011 (Boltzmannstr. 3, 85748 Garching)

Normal written German text, in news papers for example, is too complicated for patients with cerebral palsy or non-native speaker. To simplify and rearrange sentences automatically by a computer requires a recognition of the sentence structure, hence a parsing of the sentence. It exists up to date two widely used parsing technics, namely the generative grammar of Chomsky and the newer dependency parsing. None of them is suitable for this task. I present a new parsing technic, which relies on both, a new way to construct a semantic for an arbitrary sentence and the German grammar. Whereas the German grammar alone is not capable to give every word in a sentence a specific function, the new semantics does it. The semantics takes nouns as expanded entities and uses second order logics to describe them.

Link and Passcode: Code 101816

22.06.2022 13:15 Hans Manner (University of Graz, AT):
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.

22.06.2022 14:15 Josef Teichmann, ETH Zürich:
Four proofs supporting randomized signatures A027 (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.

22.06.2022 15:15 Christa Cuchiero, Universität Wien:
TBAA027 (Theresienstraße 39, 80333 Mathematisches Institut, LMU)

23.06.2022 15:45 Prof. Dr. Adriana Garroni (Sapienza, University of Rome / TUM):
Derivation of surface tension of grain boundaries in polycystalsMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

Inspired by a recent result of Lauteri and Luckhaus, with derive, via Gamma convergence, a surface tension model for polycrystals in dimension two. The starting point is a semi-discrete model accounting for the possibility of having crystal defects. The presence of defects is modelled by incompatible strain fields with quantised curl. In the limit as the lattice spacing tends to zero we obtain an energy for grain boundaries that depends on the relative angle of the orientations of the two neighbouring grains. The energy density is defined through an asymptotic cell problem formula. By means of the bounds obtained by Lauteri and Luckhaus we also show that the energy density exhibits a logarithmic behaviour for small angle grain boundaries in agreement with the classical Shockley Read formula. The talk is based on a paper in preparation in collaboration with Emanuele Spadaro.

23.06.2022 17:15 Prof. Dr. Lukas Gonon (LMU / Imperial):
Deep neural network expressivity and random features for non-local Kolmogorov equationsMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

27.06.2022 15:00 Iacopo Longo:
A path towards classifying rate-induced tipping as a nonautonomous bifurcationMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

Critical transitions are sudden changes in the dynamics of complex systems, often with catastrophic consequences. There are several mechanisms leading to a critical transition and we focus on those caused by the rate of a time-dependent drift of parameters (which are usually fixed or at most varied “adiabatically”), so-called rate-induced tipping. Particularly, in the case of a rate-induced tipping, a system evolves in time into another with possibly same topological properties of stability. However, depending on the rate at which such “transition” takes place, a local attractor of the past system can fail to track the “corresponding” local attractor of the future system. This encompasses various real scenarios for example in ecology, climate, biology and quantum mechanics. I will review some of the results on rate-induced tipping obtained with several collaborators in the past three years. The aim is to show that while the autonomous bifurcation theory can not explain the occurrence of rate-induced tipping, the nonautonomous one is the most adequate framework to do so. The results in this presentation stem from collaborations with Christian Kuehn, Technical University Munich, Carmen Nunez, University of Valladolid, Rafael Obaya, University of Valladolid, Martin Rasmussen, Imperial College London,