[Colloquium] TTIC Talks: Ronny Luss, UC Berkeley

[Liv Leader]

When:     Wednesday, April 18 @ 11 a.m.

Where:    TTIC, 6045 S. Kenwood Avenue, Room 526

Who:      Ronny Luss, UC Berkeley

Title:       Efficient Regularized Isotonic Regression via Partitioning and
L1 Penalization

Isotonic regression is a nonparametric approach for fitting monotonic
models to data that has been widely studied from both theoretical and
practical perspectives.  However, this approach encounters computational
and statistical overfitting issues in higher dimensions. To address both
concerns we present an algorithm, which we term Isotonic Recursive
Partitioning (IRP), for isotonic regression based on recursively
partitioning the covariate space through solution of progressively smaller
``best cut'' subproblems. This creates a regularized sequence of isotonic
models of increasing model complexity that converges to the global isotonic
regression solution. Models along this sequence are often more accurate
than the unregularized isotonic regression model because of the complexity
control they offer. We quantify this complexity control through estimation
of degrees of freedom along the path. Furthermore, we show that IRP for the
classic l2 isotonic regression can be generalized to convex differentiable
loss functions such as Huber's loss.  In another direction, we use the
Lasso framework to develop another isotonic path of solutions that is
computationally more expensive but offers even better complexity control.
Success of the regularized models in prediction and IRP's favorable
computational properties are demonstrated through a series of simulated and
real data experiments.

 This is joint work with Saharon Rosset and Moni Shahar.

Host: Nati Srebro, nati at ttic.edu

-- 
Liv Leader
Human Resources Coordinator

Toyota Technological Institute Chicago
6045 S Kenwood Ave
Chicago, IL 60637
Phone- (773) 702-5033
Fax-     (773) 834-9881
Email-  lleader at ttic.edu <jam at ttic.edu>
Web-   www.ttic.edu
<http://www.ttic.edu/>
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