Aalto University, 18 Dec 2019
is a traditional workshop that brings together researchers and students working on probability, statistics, and their applications. The workshop will be held on Wed 18 December 2019.
- Tom Claeys (UCLouvain): Random growth, interacting particles, and Riemann-Hilbert problems: from KPZ to KdV
- Vesa Julin (U Jyväskylä): The Gaussian isoperimetric problem for symmetric sets
- Kaie Kubjas (Aalto U): Exact solutions in log-concave maximum likelihood estimation
- Teemu Pennanen (King's College London): Convex duality in nonlinear optimal transport
- Jaron Sanders (TU Eindhoven): Markov chains for error accumulation in quantum circuits
- Joni Virta (U Turku): Fast tensorial independent component analysis
All talks take place at Hall M1, Aalto University, Otakaari 1 Espoo. The lecture hall is equipped with a blackboard, beamer, and a computer.
||Social program (Sauna @ Radisson Blu Espoo)
||Dinner (self-organized @ Fat Lizard Otaniemi)
The social program includes a sauna (@ Hotel Radisson Blu, Otaranta 2, Espoo). Separate saunas will be reserved for male and female participants.
There is no participation fee, but registration is mandatory. Please fill in the registration form.
Random growth, interacting particles, and Riemann-Hilbert problems: from KPZ to KdV
Tom Claeys (UCLouvain)
The Kardar-Parisi-Zhang (KPZ) equation is a stochastic PDE which allows to model various types of interface growth, including coffee stains, burning paper, and bacterial growth. Amir, Corwin, and Quastel established a remarkable connection between this equation and the Airy point process, which describes the largest eigenvalues of random matrices, and also the liquid-to-solid transition in random tilings. I will explain how this connection can be used to analyze the tails of the distribution of the narrow wedge solution to KPZ using Riemann-Hilbert methods. This approach also yields an intriguing connection between the KPZ equation and the KdV equation.
The Gaussian isoperimetric problem for symmetric sets
Vesa Julin (University of Jyväskylä)
The Gaussian isoperimetric inequality states that among all sets with given Gaussian measure the half-space has the smallest Gaussian surface area. Since the half-space is not symmetric with respect to the origin, a natural question is to restrict the problem among symmetric sets. This problem turns out to be surprisingly difficult. In my talk I will discuss how it is related to probability and to the study of singularities of the mean curvature flow, and present our recent result which partially solves the problem. This is a joint work with Marco Barchiesi.
Exact solutions in log-concave maximum likelihood estimation
Kaie Kubjas (Aalto University)
In this talk, we consider log-concave density functions, i.e. density functions whose logarithm is concave. It has been shown that the logarithm of the maximum likelihood estimate is a piecewise linear function. We explore properties of exact solutions to log-concave maximum likelihood estimation in special cases. This is joint work with Alexandros Grosdos, Alexander Heaton, Olga Kuznetsova, Georgy Scholten and Miruna-Stefana Sorea.
Convex duality in nonlinear optimal transpor
Teemu Pennanen (King's College London)
We study problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows for generalizations of the classical problem formulations. General results on convex duality yield dual problems and optimality conditions for these problems. When the objective takes the form of a convex integral functional, we obtain more explicit optimality conditions and establish the existence of solutions for a relaxed formulation of the problem. This covers, in particular, the mass transportation problem and its nonlinear generalizations. The work is joint with Ari-Pekka Perkkiö.
Markov chains for error accumulation in quantum circuits
Jaron Sanders (TU Eindhoven)
Joint work between: Long Ma (TU Delft), Jaron Sanders (TU/e) Abstract: We study a model for the accumulation of errors in multi-qubit quantum computations, as well as a model describing continuous errors accumulating in a single qubit. By modeling the error process in a quantum computation using two coupled Markov chains, we are able to capture a weak form of time-dependency between errors in the past and future. By subsequently using techniques from the field of discrete probability theory, we calculate the probability that error measures such as the fidelity and trace distance exceed a threshold analytically. The formulae cover fairly generic error distributions, cover multi-qubit scenarios, and are applicable to e.g. the randomized benchmarking protocol. To combat the numerical challenge that may occur when evaluating our expressions, we additionally provide an analytical bound on the error probabilities that is of lower numerical complexity, and we also discuss a state space reduction that occurs for stabilizer circuits. Finally, taking inspiration from the field of operations research, we illustrate how our expressions can be used to e.g. decide how many gates one can apply before too many errors accumulate with high probability, and how one can lower the rate of error accumulation in existing circuits through simulated annealing. A preprint is available on arXiv:1909.04432.
Fast tensorial independent component analysis
Joni Virta (University of Turku)
A novel method of tensorial independent component analysis is proposed based on TJADE and k-JADE, two recently proposed generalizations of the classical JADE algorithm. The new method achieves consistency and the limiting distribution of TJADE under mild assumptions, and at the same time offers notable improvement in computational speed. A trade-off between computational speed and assumptions is controlled by a tuning parameter which has a natural interpretation as the maximal kurtosis multiplicity. Simulations and timing comparisons demonstrate the method's gain in speed and show that the desired efficiency is obtained approximately also for finite samples. The method is applied successfully to large-scale video data, for which neither TJADE nor k-JADE is feasible. Finally, an experimental procedure is proposed to select the values of a set of tuning parameters. Joint work with Niko Lietzén, Pauliina Ilmonen, and Klaus Nordhausen.
The workshop is hosted by the Department of Mathematics and Systems Analysis, Aalto University and organized by
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