題 目：Regularized Estimation for Ordinary Differential Equations:
An Alternative View on Penalty and beyond
主講人：Prof. Naisyin Wang (University of Michigan, USA)
時 間：101年4月30日(星期一)下午13:30-14:20
地 點：交大綜合一館427室
Abstract
Dynamic modeling through solving ordinary differential equations has ample
applications in the fields of physics, engineering, economics and biological
sciences. The recently proposed parameter-cascades estimation procedure with
a penalized estimation component (Ramsay et al., 2007) combines the strengths
of basis-function approximation, profile-based estimation and computation
feasibility. Consequently, it has become a very popular estimation procedure.
In this manuscript, we take an alternative view through variance/stability
evaluation on the penalized estimation component within the parameter-
cascades procedure. We found, through some theoretical evaluation and
numerical experiments, that the penalty term in the profile component could
increase estimation variation. Further, contrary to the traditional belief
established from the penalized spline literature, this penalty term in the
ordinary differential equations setup also makes the procedure more sensitive
to the number of basis functions. By taking the penalty parameter to its
limit, we eliminate this problem. We observe this phenomenon in a numerical
study even when the underlying ordinary differential equations model is
mis-specified. This recognition enables us to address the goodness of fit
problems by considering regularization procedure with a more flexible
parameter structures across a long period of study time, and by using an
alternative penalty structure. In this talk, we will illustrate our findings
on both theoretical and numerical aspects. This is joint work with Yun Li
and Ji Zhu of University of Michigan.
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