# Brummer & Partners MathDataLab

Welcome to the home page of the Brummer & Partners MathDataLab. Here you can find information about the Lab and its activities.

## Upcoming events

### Seminar with Stephan Zhechev, IST Austria, May 22 (joint with combinatorics seminar)

Room 3418, Wednesday May 22, 11.15-12.15

**Title: **Embeddability is undecidable outside the meta-stable range

Abstract: We will prove that the following question is algorithmically undecidable for k+3 < d < 3(k+1)/2 , and k>4, which covers essentially everything outside the meta-stable range: Given a finite simplicial complex K of dimension k and an embedding f : L -> R^d of a subcomplex L of K, can f be extended to an embedding F : K -> R^d of the whole complex? Here, we assume that the given embedding f of the subcomplex L is linear (on each simplex of L) whereas the desired embedding F of the whole complex is allowed to be piecewise-linear (i.e., linear on an arbitrarily fine subdivision of K); moreover F is not required to be part of the output.

More generally, we prove that the question of deciding embeddability, which is the special case of the question above when we set L to be empty, is also undecidable for k+3 < d < 3(k+1)/2 , and k>4.

The strategy of our proof is to construct a reduction from Hilbert’s tenth problem to both the embeddability and extension of embeddings problems. More specifically, for particular types of systems of quadratic Diophantine equations, we will show how to construct corresponding instances of the two problems we consider, so that an embedding or extension exists if and only if the original system of equations has an integer solution. This is a joint work with Uli Wagner and Marek Filakovsky.

## Workshop on Mathematics for Complex Data, June 24-26, 2019

The purpose of this workshop is to bring together researchers interested in the mathematics of complex data. There will be talks on mathematical theory and methods related to data analysis and artificial intelligence.

### Speakers

Wojciech Chacholski, KTH

Henrik Hult, KTH

Johan Jonasson, Chalmers

Annika Lang, Chalmers

Joel Larsson, Warwick

Konstantin Mischaikow, Rutgers

Anna Persson, KTH

Daniel Persson, Chalmers

Thomas Schön, Uppsala

Martina Scolamiero, KTH

Natasa Sladoje, Uppsala

Tatyana Turova, Lund

Guo-Jhen Wu, Brown

### Registration

Please register here for the workshop (registration is free of charge).

### Location

KTH Campus, Valhallavägen, Stockholm.

## Past events

### Study group on Topological Data Analysis and Machine Learning

The aim of this study group is to explore and discuss links between these three topics through recent research papers. We will present state of the art techniques and focus on the approach of the TDA group at KTH. This study group will take place in room 3418 at the Mathematics department with the following schedule:

- Monday 28 January 10.00-12.00, talk by Martina Scolamiero, KTH
- Monday 4 February 10.00-12.00, talk by Steve Oudot, INRIA
- Monday 11 February 10.00-12.00, talk by Wojciech Chacholski, KTH
- Monday 18 February 10.00-12.00, talk by Oliver Gävfert, KTH.

### Workshop on Deep Learning and Inverse Problems, Jan 21-25, 2019

DLIP2019 is a one week workshop for researchers and practitioners working on deep learning techniques for inverse problems. The objective is to enable open discussions on both practical and theoretical aspects, and give researchers time to discuss these problems in depth.

The workshop will feature some invited talks, but we hope that most attendants will also contribute with their own knowledge.

*Invited Speakers*: Ozan Öktem (KTH), Andreas Hauptmann (UCL), Sebastian Lunz (Cambridge).

See the workshop webpage for more information.

### Seminar with Josef Teichmann, ETH Zurich, Jan 18

Room F11, Friday Jan 18, 14.15-15.15

**Title: **Machine Learning in Finance

Abstract: We show three instances of machine learning in finance: deep hedging, deep calibration and deep simulation. The first two applications are direct application of universal approximation theorems, in contrast to deep simulation where Johnson-Lindenstrauss random projection are used to obtain expressive but tractable sets of trajectories.

### Seminar with Per-Gunnar Martinsson, University of Texas, Nov 26

Room F11, Monday Oct 26, 15.15-16.15

**Title: **Fast Direct Solvers for Elliptic PDEs

Abstract: That the linear systems arising upon the discretization of elliptic PDEs can be solved very efficiently is well-known, and many successful iterative solvers with linear complexity have been constructed (multigrid, Krylov methods, etc). Interestingly, it has recently been demonstrated that it is often possible to directly compute an approximate inverse to the coefficient matrix in linear (or close to linear) time. The talk will survey some recent work in the field and will argue that direct solvers have several advantages, including improved stability and robustness, and dramatic improvements in speed in certain environments. Moreover, the direct solvers being proposed have low communication costs, and are very well suited to parallel implementations.

### Seminar with Phyllis Wan, Rotterdam University, Oct 22

Room F11, Monday Oct 22, 15.15-16.15

**Title: **Modeling social networks through linear preferential attachment

Abstract: Preferential attachment is an appealing mechanism for modeling power-law behavior of degree distributions in social networks. In this talk, we consider fitting a directed linear preferential attachment model to network data under three data scenarios: 1) When the full history of the network growth is given, MLE of the parameter vector and its asymptotic properties are derived. 2) When only a single-time snapshot of the network is available, an estimation method combining method of moments with an approximation to the likelihood is proposed. 3) When the data are believed to have come from a misspecified model or have been corrupted, a semi-parametric approach to model heavy-tailed features of the degree distributions is presented, using ideas from extreme value theory. We illustrate these estimation procedures and explore the usage of this model through simulated and real data examples. This is a joint work with Tiandong Wang (Cornell), Richard Davis (Columbia) and Sid Resnick (Cornell).

### Seminar with Jonas Peters, University of Copenhagen, Oct 15

Room F11, Monday Oct 15, 15.15-16.15

**Title: Causality and data**

Abstract: Causality enters data science in different ways. The goal of causal discovery is to learn causal structure from observational data, an important but difficult problem. Several methods rely on testing for conditional independence. We prove that, statistically, this is fundamentally harder than testing for unconditional independence; solving it requires carefully chosen assumptions on the data generating process. In many practical problems, the focus may lie on prediction, and it is not necessary to solve (full) causal discovery. It might still be beneficial, however, to apply causality related ideas. In particular, interpolating between causality and predictability enables us to infer models that yield more robust prediction with respect to changes in the test set. We illustrate this idea for ODE based systems considering artificial and real data sets. The talk does not require any prior knowledge in causal inference. It contains joint work with Stefan Bauer, Niklas Pfister, and Rajen Shah.

### Workshop on Mathematics for Complex Data, May 30-31, 2018

The purpose of this workshop is to bring together researchers interested in the mathematics of complex data. There will be talks on mathematical methods for data analysis as well as presentations of complex data in applications.

See here for details.

### Two lectures by Scott Baden, Lawrence Berkeley National Laboratory and University of California, San Diego, May 2-3, 2018

Lecture 1: Room F11, Wednesday, May 2, 11.15-12.00

Lecture 2: Room F11, Thursday, May 3, 11.15-12.00

**Title: Scalable memory machines**

Abstract: Distributed memory computers provide scalable memory and - hopefully - scalable performance. Over two lectures, I'll present the principles

and practice of applying scalable memory machines to solve scientific problems and describe my current research in addressing the challenges

entailed in highly scalable computing.

Bio: Prof. Baden received his M.S and PhD in Computer Science from UC Berkeley in 1982 and 1987. He is also Adjunct Professor in the Department of Computer Science and Engineering at UCSD, where he was a faculty member for 27 years. His research interests are in high performance and scientific computation: domain specific translation, abstraction mechanisms, run times, and irregular problems. He has taught parallel programming at both the graduate and undergraduate level at UCSD and at the PDC Summer School.

### Seminar with Jeffrey Herschel Giansiracusa

Room F11, Friday Feb 16, 9:00-10:00.

**Title: A tour of some applications of persistent homology**

Abstract: I will give an overview of persistent homology - how it is constructed and how we use it as a tool in data analysis. Originally it was popularised as a way of producing a description of the shape of a data set, but more recently it has taken on an alternative role as a component in functional data analysis pipelines where each element in a data set represents a complicated geometric object and persistent homology provides a way of comparing the topology and geometry of different elements, and potentially feeding the topology directly into statistical learning methods. I will describe how this works in some examples.

### Seminar with Caroline Uhler, MIT

Room F11, Wednesday Feb 7, 13.15-14.15

**Title: Your dreams may come true with MTP2**

Abstract: We study probability distributions that are multivariate totally positive of order two (MTP2). Such distributions appear in various applications from ferromagnetism to Brownian tree models used in phylogenetics. We first describe some of the intriguing properties of such distributions with respect to conditional independence and graphical models. In the Gaussian setting, these translate into new statements about M-matrices that may be of independent interest to algebraists. We then consider the problem of nonparametric density estimation under MTP2. This requires us to develop new results in geometric combinatorics. In particular, we introduce bimonotone subdivisions of polytopes and show that the maximum likelihood estimator under MTP2 is a piecewise linear function that induces bimonotone subdivisions. In summary, MTP2 distributions not only have broad applications for data analysis, but also leads to interesting new problems in combinatorics, geometry, and algebra.

Carolone Uhler joined the MIT faculty ni 2015 as the Henry L. and Grace Doherty assistant professor in EECS and IDSS. She is a member of the LIDS, the Center for Statistics, Machine Learning at MIT, and the ORC. She holds a PhD in statistics from UC Berkely. Her research focuses on mathematical statistics and computational biology, in particular on graphical models, causal inference and algebraic statistics, and on applications to learning gene regulatory networks and the development of geometric models for the organization of chromosomes. |

### Opening workshop on Nov 17, 2017.

For information, see