EESS talk on "Bayesian Parameter Inference of Nonlinear Stochastic Differential Equation Models"
Event details
| Date | 01.03.2016 |
| Hour | 12:15 › 13:15 |
| Speaker | Dr Albert CARLO, Head of Mathematical Methods in Env. Research, Dept of Systems Analysis, Integrated Assessment and Modelling, EAWAG, CH |
| Location | |
| Category | Conferences - Seminars |
Abstract:
Parameter inference is a fundamental problem in data-driven modeling. Given observed data, which is believed to be a realization of some parameterized model the aim is to find parameter values that are able to explain the observed data. If the model is to make reliable predictions it must contain the dominant sources of uncertainty, which naturally leads us to stochastic models. Stochastic models render parameter inference much harder, as its aim is to find the whole distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution expresses the probability of a given parameter to be the "true" one, and can be used to make probabilistic predictions.
For truly stochastic models this posterior distribution is typically extremely expensive to evaluate. There is a number of sampling techniques, for Bayesian parameter inference, that avoid repeated evaluation of the posterior. Sequential filtering methods (Kalman filters, particle filters) form a class of powerful methods. Approximate Bayesian computation (ABC) methods are of particular importance if the data is rare or expensive.
In my talk, I propose a novel, exact and very efficient, approach for generating posterior parameter distributions, for stochastic differential equation models calibrated to measured time-series. The algorithm is inspired by re-interpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, whose dynamics is confined by both the model and the measurements. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for 1D problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.
Short biography:
Carlo Albert was born in Valais, Switzerland. He studied mathematics at ETHZ and did his PhD in Theoretical Physics with Prof. Jürg Fröhlich. After a short Post Doc at the mathematics department of the University of Geneva he moved to Eawag, the aquatic research institute of the ETH domain. Since autumn 2012 he holds a tenure track position and builds up a group for mathematical methods in the environmental sciences.
Parameter inference is a fundamental problem in data-driven modeling. Given observed data, which is believed to be a realization of some parameterized model the aim is to find parameter values that are able to explain the observed data. If the model is to make reliable predictions it must contain the dominant sources of uncertainty, which naturally leads us to stochastic models. Stochastic models render parameter inference much harder, as its aim is to find the whole distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution expresses the probability of a given parameter to be the "true" one, and can be used to make probabilistic predictions.
For truly stochastic models this posterior distribution is typically extremely expensive to evaluate. There is a number of sampling techniques, for Bayesian parameter inference, that avoid repeated evaluation of the posterior. Sequential filtering methods (Kalman filters, particle filters) form a class of powerful methods. Approximate Bayesian computation (ABC) methods are of particular importance if the data is rare or expensive.
In my talk, I propose a novel, exact and very efficient, approach for generating posterior parameter distributions, for stochastic differential equation models calibrated to measured time-series. The algorithm is inspired by re-interpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, whose dynamics is confined by both the model and the measurements. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for 1D problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.
Short biography:
Carlo Albert was born in Valais, Switzerland. He studied mathematics at ETHZ and did his PhD in Theoretical Physics with Prof. Jürg Fröhlich. After a short Post Doc at the mathematics department of the University of Geneva he moved to Eawag, the aquatic research institute of the ETH domain. Since autumn 2012 he holds a tenure track position and builds up a group for mathematical methods in the environmental sciences.
Practical information
- General public
- Free
- This event is internal
Organizer
- EESS - IIE