Related papers: Discrete minimax estimation with trees
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
We present a detailed analysis of the class of regression decision tree algorithms which employ a regulized piecewise-linear node-splitting criterion and have regularized linear models at the leaves. From a theoretic standpoint, based on…
This paper considers estimation of a univariate density from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known…
Conditional density estimation (CDE) goes beyond regression by modeling the full conditional distribution, providing a richer understanding of the data than just the conditional mean in regression. This makes CDE particularly useful in…
Random forests are one of the most popular machine learning methods due to their accuracy and variable importance assessment. However, random forests only provide variable importance in a global sense. There is an increasing need for such…
In the past several years a wide range of methods for the construction of regression trees and other estimators based on the recursive partitioning of samples have appeared in the statistics literature. Many applications involve data…
Itemset mining has been an active area of research due to its successful application in various data mining scenarios including finding association rules. Though most of the past work has been on finding frequent itemsets, infrequent…
We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…
The decomposition of a density function on a domain into a minimal sum of unimodal components is a fundamental problem in statistics, leading to the topological invariant of unimodal category of a density. This paper gives an efficient…
In this paper, we propose a unified energy minimization model for the segmentation of non-smooth image structures. The energy of piecewise linear patch reconstruction is considered as an objective measure of the quality of the segmentation…
This paper proposes a method for solving multivariate regression and classification problems using piecewise linear predictors over a polyhedral partition of the feature space. The resulting algorithm that we call PARC (Piecewise Affine…
A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…
While normalizing flows for continuous data have been extensively researched, flows for discrete data have only recently been explored. These prior models, however, suffer from limitations that are distinct from those of continuous flows.…
We study recovery of piecewise-constant signals on graphs by the estimator minimizing an $l_0$-edge-penalized objective. Although exact minimization of this objective may be computationally intractable, we show that the same statistical…
Partition-wise models offer a flexible approach for modeling complex and multidimensional data that are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with…
A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…
We study the problem of learning to choose from m discrete treatment options (e.g., news item or medical drug) the one with best causal effect for a particular instance (e.g., user or patient) where the training data consists of passive…
We present sparse tree-based and list-based density estimation methods for binary/categorical data. Our density estimation models are higher dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the…
Estimating a joint Highest Posterior Density credible set for a multivariate posterior density is challenging as dimension gets larger. Credible intervals for univariate marginals are usually presented for ease of computation and…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…