Research Seminars

PCA in an asymmetric norm

Speaker(s): 
Petra Burdejova (HU Berlin)
Date: 
Wednesday, May 17, 2017 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of high-dimensional data. However, in many applications such as risk quantification in finance or climatology, one is interested in capturing the tail variations rather than variation around the mean. In this paper, we develop Principal Expectile Analysis (PEC), which generalizes PCA for expectiles. It can be seen as a dimension reduction tool for extreme value theory, where one approximates fluctuations in the \tau-expectile level of the data by a low dimensional subspace.

A review of regularized optimal transport and applications to Wasserstein barycenters

Speaker(s): 
Marco Cuturi (ENSAE / CREST)
Date: 
Wednesday, May 10, 2017 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Robust Utility Maximization with Lévy Processes

Speaker(s): 
Ariel Neufeld (ETH Zürich)
Date: 
Thursday, May 4, 2017 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We present a tractable framework for Knightian uncertainty, the so-called nonlinear Lévy processes, and use it to formulate and solve problems of robust utility maximization for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible Lévy triplets; that is, possible instantaneous drift, volatility and jump characteristics of the price process. Thus, our setup describes uncertainty about drift, volatility and jumps over a class of fairly general models. We show that an optimal investment strategy exists and compute it in semi-closed form.

Local asymptotic equivalence for quantum models

Speaker(s): 
Cristina Butucea (Université Marne-la-Vallée)
Date: 
Wednesday, May 3, 2017 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Quantum statistics is concerned with inference for physical systems described by quantum mechanics. After an introduction to the main notions of quantum statistics: quantum states, measurements, channels, we describe nonparametric quantum models. We prove the local asymptotic equivalence (LAE) of i.i.d. quantum pure states and a quantum Gaussian state, in the sense of Le Cam theory. As an application, we show the optimal rates for the estimation of pure states, for the estimation of some quadratic functionals and for the testing of pure states.

Optimal rates of estimation for the multi-reference alignment problem

Speaker(s): 
Jonathan Weed (MIT)
Date: 
Wednesday, April 26, 2017 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

How should one estimate a signal, given only access to noisy versions of the signal corrupted by unknown circular shifts? This simple problem has surprisingly broad applications, in fields from structural biology to aircraft radar imaging. We describe how this model can be viewed as a multivariate Gaussian mixture model whose centers belong to an orbit of a group of orthogonal transformations. This enables us to derive matching lower and upper bounds for the optimal rate of statistical estimation for the underlying signal.

Optimal Portfolio Choice with Benchmarks

Speaker(s): 
Carole Bernard (Grenoble Ecole de Management)
Date: 
Thursday, February 16, 2017 - 5:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

We construct an algorithm that allows to numerically obtain an investor's optimal portfolio under general preferences. In particular, the objective function and risks constraints may be driven by benchmarks (reflecting state-dependent preferences). We apply the algorithm to various classic optimal portfolio problems for which explicit solutions are available and show that our numerical solutions are compatible with them.

Duality for American options in non-dominated discrete-time models

Speaker(s): 
Xiaolu Tan (Université Paris Dauphine)
Date: 
Thursday, February 16, 2017 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

The classical pricing-hedging duality for American options with semi-static hedging does not hold in general in the simple formulation inherited from European option set-up. We propose two approaches to recover the duality result. The first approach consists in considering a bigger class of models and rendering an American option a European one. The second way is to relax the static trading and by allowing dynamic trading in the set of vanilla options.

The role of machine learning in the nonparametric prediction of time

Speaker(s): 
László Györfi (Budapest University)
Date: 
Wednesday, February 15, 2017 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

The main purpose of this paper is to consider the prediction of stationary time series for various losses: squared loss (regression problem), $0, 1$ loss (pattern recognition) and log utility (growth optimal portfolio selection). We are interested in universal prediction rules, which are consistent for all possible stationary and ergodic processes. Such rules can be constructed using aggregation techniques of machine learning by combining elementary rules (experts) in data dependent way.

Multiscale scanning in inverse problems - With applications to nanobiophotonics

Speaker(s): 
Katharina Proksch (Universität Göttingen)
Date: 
Wednesday, February 8, 2017 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

We propose a multiscale scanning method to determine active components of a quantity $f$ w.r.t. a dictionary $\mathcal U$ from observations $Y$ in an inverse regression model $Y = Tf + \xi$ with operator $T$ and general random error $\xi$. To this end, we provide uniform confidence statements for the coefficients $(\varphi, f),\varphi\in\mathcal U$, under the assumption that $(T^{\star})^{-1}(\mathcal U)$ is of wavelet-type. Based on this we obtain a decision rule that allows to identify the active components of $\mathcal U$, i.e.

A randomisation approach for the probabilistic representation and approximation of HJB equations

Speaker(s): 
Idris Kharroubi (CEREMADE - Universitè Paris)
Date: 
Thursday, February 2, 2017 - 5:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

We propose a new probabilistic numerical scheme for fully nonlinear equation of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem, which is based on the Feynman-Kac representation by means of control randomization and backward stochastic differential equation with nonpositive jumps. We study a discrete time approximation for the minimal solution to this class of BSDE when the time step goes to zero, which provides both an approximation for the value function and for an optimal control in feedback form.

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