Institute of Computing (CI) Seminar
Decanato - Facoltà di scienze informatiche
Data: 18 Ottobre 2021 / 12:30 - 13:30
USI Campus EST, room D0.03, Sector D // online on MS Teams
The talks are part of the public seminar series organized by the Institute of Computing (CI).
You can join here.
Talk 1: Gaussian likelihoods for ’intractable’ situations
Heikki Haario, LUT University, Finland
Various modelling situations – including chaotic dynamics, synchronization, stochastic differential equations, random patterns such as produced by the Turing reaction-diffusion systems, or the Cahn-Hilliard equation – share the analogy that a fixed model parameter corresponds to a family of solutions rather than a fixed deterministic one. This may be due to extreme sensitivity with respect to the initial values, randomized or unknown initial values, or the explicit stochasticity of the system. As a result, standard methods based on directly measuring the distance between model output and data are no more available. We discuss an approach that allows a unified construction of likelihoods for such ‘intractable’ situations. The starting point is the Donsker theorem stating that the cumulative distribution function of i.i.d. scalar samples tends to a Gaussian distribution. But the approach can be extended also to weakly dependent, and vector-valued data. Several cases from the above list are presented as examples.
Heikki Eino Tapani Haario is Applied Mathematics professor and director of Mathematics and Physics Department at Lappeenranta University of Technology. Haario received his doctorate in Philosophy from the University of Helsinki in 1979. Haario worked as an assistant at the University of Helsinki from 1978–1991 and as a researcher at the Academy of Finland in 1984–1986. In 1992, Haario founded a mathematical consulting company, ProfMath Oy, which he worked full-time for ten years. Haario specializes in industrial process modeling and inversion problems, as well as model reliability analysis.
Talk 2: On recently developed non-Gaussian priors and sampling methods with application to industrial tomography
Lassi Roininen, LUT University, Finland
We consider two sets of new priors for Bayesian inversion and machine learning: The first one is based on mixture of experts models with Gaussian processes. The target is to estimate the number of experts and their parameters, and to make state estimation. For sampling, we use SMC^2. For non-Gaussian priors, we continue the discussion on Cauchy priors and the generalisation to high-order Cauchy fields and further generalisation to alpha-stable fields. For sampling, we use a selection of modern MCMC tools. Finally, we apply some of the methods and models to an industrial tomography problem on estimating log internal structure, measured at sawmills, based on X-ray, RGB camera and laser scanning.
Lassi Roininen holds the position of Associate Professor in Applied Mathematics in LUT University, Finland. He develops rigorous numerical and computational tools for inverse problems with applications in near-space remote sensing, subsurface imaging, and X-ray tomography.
Host: Prof. Ernst Wit