Research Group "Stochastic Algorithms and Nonparametric Statistics"

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Seminar "Modern Methods in Applied Stochastics and Nonparametric Statistics" Summer Semester 2023

18.04.2023 Wilfried Kenmoe Nzali (WIAS Berlin)
Optimal control problem in energy finance (hybrid talk)
25.04.2023 Dr. Sven Wang (Massachusetts Institute of Technology)
On polynomial-time mixing of MCMC for high-dimensional posterior distributions (online talk)
We consider the problem of generating random samples from high-dimensional posterior distributions. We will discuss both (i) conditions under which diffusion-based MCMC algorithms mix in polynomial-time (based on https://arxiv.org/pdf/2009.05298.pdf) as well as (ii) situations in which MCMC suffers from an exponentially long mixing time (based on https://arxiv.org/pdf/2209.02001.pdf). We will focus on the setting of non-linear inverse regression models. Our positive results on polynomial-time mixing are derived under local `gradient stability' assumptions on the forward map, which can be verified for a range of well-known non-linear inverse problems involving elliptic PDE, as well as under the assumption that a good initializer is available. Our negative results on exponentially long mixing times hold for `cold-start' MCMC. We show that there exist non-linear regression models in which the posterior distribution is unimodal, but there exists a so-called `free entropy barrier', which local Markov chains take an exponentially long time to traverse.
02.05.2023 N.N.

09.05.2023 N.N.

16.05.2023 Dr. Christian Bayer (WIAS Berlin)
An introduction to Hawkes processes (hybrid talk)
Hawkes processes are a prototypical example of self-exciting point processes. They are one of the most useful processes in science, engineering, and finance. Introduced as a model for time and magnitude of earthquakes, they have also been used as models for epidemics, crimes, traffic accidents, and so on. In finance, they are often used as models for order flow, for instance in order to solve the optimal execution problem, or to analyse market activity. We give a short introduction into Hawkes processes, including motivation, definitions and basic properties, and simulation.
23.05.2023 Prof. Dr. Daniel Walter (HU Berlin)
Nonsmooth minimization in infinite dimensional spaces meets sparse dictionary learning (hybrid talk)
We propose a novel method for problems involving nonsmooth but convex regularization terms over infinite dimensional function spaces . It resembles a dictionary learning algorithm which switches between the update of a dictionary $\mathcal{A}_k$ of extremal points of the unit ball of the regularizer and of a sparse represenation of the iterate $u_k$ in its conic hull by solving a finite dimensional~$\ell_1$-regularized problem. Imposing additional assumptions on the involved dual variables , its asymptotic linear convergence is shown. The theoretical results are accompanied by numerical experiments involving challenging regularizers such as the Benamou-Brenier energy as well as the BV-seminorm, highlighting both, the sharpeness of our results as well as the practical applicability of the method.
30.05.2023 N.N.

06.06.2023 Simon Breneis (WIAS Berlin)
American options under rough Heston (hybrid talk)
The rough Heston model is a popular option pricing model in mathematical finance. However, due to the non-semimartingale and non-Markovian characteristics of its volatility process, simulations can be prohibitively expensive in practice. Building on previous works, we approximate the volatility process with an N-dimensional diffusion, yielding a Markovian approximation of the rough Heston model. Then, we introduce a weak discretization scheme to simulate paths of these Markovian approximations. Our numerical experiments show that these approximations converge at a second-order rate as the number of time steps approaches infinity. We leverage these approximations to price American options under the rough Heston model.
13.06.2023 Dr. Oleg Butkovsky (WIAS Berlin)
Stochastic sewing for weak uniqueness of SDEs and SPDEs (hybrid talk)
I would like to report about very early steps of a new project. It has been thought for a while that stochastic sewing is relevant only for obtaining strong unqiueness and strong rate of convergence of numerical methods. I will try to convince you that stochastic sewing combined with the Scheutzow-Kulik generalized coupling technique allows to achieve weak uniqueness of SDEs and weak rate of convergence of Euler scheme. Work in progress with Leonid Mytnik.
20.06.2023 Dr. Leon Bungert (TU Berlin)
Polarized consensus based particle dynamics (hybrid talk)
In this talk I will speak about a novel polarized consensus based method for optimization and sampling which relies on a kernelized weighted mean and covariance. This way the method allows for finding several global minima of non-convex functions and for multi-modal sampling. I will present numerical examples and first theoretical results on this novel method. This talk is based on recent joint work together with Tim Roith and Philipp Wacker.
27.06.2023 Prof. Dr. Vladimir Spokoiny (WIAS/HU Berlin)
Sharp deviation bounds and concentration phenomenon for sub-gaussian quadratic forms (hybrid talk)
Under a mild assumption of linearity on the log-likelihood function, the tools of empirical processes are not necessary, the analysis of a general MLE can be reduced to a deviation bound for a quadratic form. This paper explains how the recent advances in Laplace approximation from [Spokoiny, 2022, 2023] can be used for obtaining sharp Gaussian-like finite sample bounds and for stating the prominent concentration phenomenon for the squared norm of a sub-gaussian vector. Some extensions and open problems will be discussed as well.
04.07.2023 Dr. John Schoenmakers (WIAS Berlin)
Primal-dual regression approach for Markov decision processes with infinite state and action spaces (hybrid talk)
11.07.2023 Prof. Dr. Fanny Yang (ETH Zürich)
Surprising failures of standard practices in ML when the sample size is small (hybrid talk)
In this talk, we discuss two failure cases of common practices that are typically believed to improve on vanilla methods: (i) adversarial training can lead to worse robust accuracy than standard training (ii) active learning can lead to a worse classifier than a model trained using uniform samples. In particular, we can prove both mathematically and empirically, that such failures can happen in the small-sample regime. We discuss high-level explanations derived from the theory, that shed light on the causes of these phenomena in practice.
18.07.2023 PhD Daniel J. Mankowitz (Google Deepmind)
AlphaDev: Faster sorting algorithms discovered using deep reinforcement learning (hybrid talk)
Fundamental algorithms such as sorting or hashing are used trillions of times on any given day. As demand for computation grows, it has become critical for these algorithms to be as performant as possible. Whereas remarkable progress has been achieved in the past, making further improvements on the efficiency of these routines has proved challenging for both human scientists and computational approaches. Here we show how artificial intelligence can go beyond the current state of the art by discovering hitherto unknown routines. To realize this, we formulated the task of finding a better sorting routine as a single-player game. We then trained a new deep reinforcement learning agent, AlphaDev, to play this game. AlphaDev discovered small sorting algorithms from scratch that outperformed previously known human benchmarks. These algorithms have been integrated into the LLVM standard C++ sort library3. This change to this part of the sort library represents the replacement of a component with an algorithm that has been automatically discovered using reinforcement learning. We also present results in extra domains, showcasing the generality of the approach.
25.07.2023 No Seminar

01.08.2023 No Seminar

08.08.2023 No Seminar

15.08.2023 Egor Gladin (HU Berlin)
Accuracy certificates for convex minimization with inexact oracle (hybrid talk)
A notion of certificates for convex minimization problems allows to verify the accuracy of approximate solutions and provides a theoretically valid stopping criterion. When the dual optimization problem is solved, certificates produce a simple way to recover primal solution. In the talk, the notion of certificates is generalized to take into account the error in a first-order oracle. A recipe for computation of certificates for a large class of cutting plane methods is presented. As a by-product, we show that considered methods that were originally designed to be equipped with an exact oracle can also be efficiently used with a noisy oracle.


last reviewed: August 13, 2023 by Christine Schneider