Csáji, Balázs Csanád (MTA SZTAKI)
Finite Sample System Identification: Exact, Distribution-Free Confidence Regions
(joint work with M.C. Campi and E. Weyer)
System Identification aims
at building mathematical models of dynamical systems from experimental data.
These (usually stochastic) models are widely used for prediction and control
purposes in engineering and economic applications. Standard approaches (such as
correlation-, prediction error-, maximum likelihood-, and instrumental variable
methods) provide point-estimates; nonetheless, in many applications involving
strict safety-, stability- or quality guarantees, additional confidence regions
are needed. The classical approach to get confidence regions is to use the
limiting distribution of the estimates, which results in asymptotic confidence sets,
typically ellipsoids. This however means that, for finite samples, such
confidence ellipsoids are only heuristics.
The recently developed
Sign-Perturbed Sums (SPS) method aims at overcoming this issue as it can construct
non-asymptotic confidence regions for parameters of (linear and nonlinear) dynamical
systems under mild statistical assumptions. One of its main features is that,
for any finite number of data points and any user-specified probability, the
constructed confidence region contains the true parameters with exactly the
given probability, i.e., it is non-conservative. Moreover, assuming linear regression
models, SPS confidence regions are star convex (with the nominal estimate as a
star center), strongly consistent and asymptotically coincide with the standard
asymptotic ellipsoids. The talk will overview SPS from its simplest
construction for linear regression models through more general systems, like ARX
(autoregressive exogenous) and Box-Jenkins models, to nonlinear variants, such
as an extension for GARCH (generalized autoregressive conditional
heteroskedasticity) models.
Date: Oct. 13, Tuesday 4:15pm
Place: BME, Building „Q”, Room QBF13