5 papers
Statistical Advantages of Oblique Randomized Decision Trees and Forests
Eliza O'Reilly
This work studies the statistical implications of using features comprised of general linear combinations of covariates to partition the data in randomized decision tree and forest…
TrIM: Transformed Iterative Mondrian Forests for Gradient-based Dimension Reduction and High-Dimensional Regression
Ricardo Baptista, Eliza O'Reilly, Yangxinyu Xie
We propose a computationally efficient algorithm for gradient-based linear dimension reduction and high-dimensional regression. The algorithm initially computes a Mondrian forest a…
Operatopes, Operanoids, and Noncommutative Zonoids
Eliza O'Reilly, Venkat Chandrasekaran
We study a class of convex bodies called operatopes that are obtained by taking Minkowski sums of affine images of an operator norm ball. This notion generalizes that of zonotopes…
Optimal Regularization Under Uncertainty: Distributional Robustness and Convexity Constraints
Oscar Leong, Eliza O'Reilly, Yong Sheng Soh
Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliabilit…
The Uniformly Rotated Mondrian Kernel
Calvin Osborne, Eliza O'Reilly
Random feature maps are used to decrease the computational cost of kernel machines in large-scale problems. The Mondrian kernel is one such example of a fast random feature approxi…