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SUMMARY:Title: Theory of Adaptive Oblique Regression Trees
DTSTART:20231206T161500
DTEND:20231206T171500
DTSTAMP:20260922T014003Z
UID:b71c7c847226438bae567d5e7121de6953ad2a5c4cdfa1507178f6f2
CATEGORIES:Conferences - Seminars
DESCRIPTION:Rajita Chandak  - Princeton University           \
 nPresentation in Mathematics\nI will introduce a theoretical framework for
  the analysis of oblique decision trees\, where the splits at each decisio
 n node occur at linear combinations of the covariates (as opposed to conve
 ntional tree constructions that force axis-aligned splits involving only a
  single covariate). While this methodology has garnered significant attent
 ion from the computer science and optimization communities since the mid-8
 0s\, the advantages they offer over their axis-aligned counterparts remain
  only empirically justified\, and explanations for their success are large
 ly based on heuristics. Filling this long-standing gap between theory and 
 practice\, I will show that oblique regression trees (constructed by recur
 sively minimizing squared error) satisfy a type of oracle inequality and c
 an adapt to a rich library of regression models consisting of linear combi
 nations of ridge functions. This provides a quantitative baseline to compa
 re and contrast decision trees with other less interpretable methods\, suc
 h as projection pursuit regression and neural networks\, which target simi
 lar model forms. As a result of this theory and contrary to popular belief
 \, one need not always trade-off interpretability with accuracy. Specifica
 lly\, I will show that\, under suitable conditions\, oblique decision tree
 s achieve similar predictive accuracy as shallow neural networks for the s
 ame library of regression models. To address the combinatorial complexity 
 of finding the optimal splitting hyperplane at each decision node\, the pr
 oposed theoretical framework can accommodate many existing computational m
 ethods in the literature. The results rely on (arguably surprising) connec
 tions between recursive adaptive partitioning and sequential greedy approx
 imation algorithms for convex optimization problems (e.g.\, orthogonal gre
 edy algorithms)\, which may be of independent theoretical interest. This t
 alk will be based on the results established in a recent paper (arXiv:2210
 .14429).\n 
LOCATION:https://epfl.zoom.us/j/66872951844
STATUS:CONFIRMED
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