Technion, IEM faculty - Operations Research seminar
 
Speaker: Saharon Rosset, Tel Aviv University
 
Title: Isotonic Modeling - Methodology and Applications
 
Date: 05/11/2012
 
Time: 12:30
 
Place: Bloomfield-527
 
Abstract:  <http://ie.technion.ac.il/seminar_files/1351956188_Isotonic_abstract.pdf>
 
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Or see an approximation of the abstract here below:
 
In isotonic modeling, non parametric predictive models ˆy = ˆ f(x) are fitted to data,
requiring
only that ˆ f(x) is isotonic, i.e., monotone in all explanatory variables. The monotonicity
assumption on the underlying data generation process is appropriate in many applications,
for example in modeling gene-gene interactions in genetics. However, isotonic modeling
has enjoyed limited interest as a tool for modern data modeling due to a combination
of statistical (overrfitting) difficulties and computational difficulties. I will first
describe
our Isotonic Recursive Partitioning (IRP) algorithm, which overcomes both difficulties in
fitting isotonic regression (i.e, isotonic modeling with squared loss) to large data. IRP
recursively partitions the covariate space to an increasing number of regions and at every
iteration fits the best isotonic model to the current partition. At each iteration a linear
program is solved, and the whole algorithm can be practically applied to datasets with
tens of thousands of observations. Surprisingly, this greedy algorithm provably converges
to the global isotonic regression solution, and we view the recursive partitioning process as
a regularization path which allows overfitting control.
As time permits, I will discuss further methodological topics. First, generalization
of IRP to non-squared loss situations, like Poisson regression, or using robust Huber’s
loss. Second, development of other practically useful and theoretically sound regularization
approaches for isotonic modeling. In this context, we propose to use the range of model
predictions as a regularization functional. This problem can be formulated as a lasso
problem in the very high dimensional basis of upper-sets in the covariate space. We show
how this problem can be solved by a generalization of the LARS algorithm, and the results
of applying this algorithm to data.
Finally, I will review some “modern” applications of isotonic modeling, including isotonic
stacking and modeling of gene-gene interactions in human disease.
This is joint work with Ronny Luss of UC Berkeley and INRIA, Paris.
 
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