GRAF uses global partitioning to improve ensemble classifier performance.
problem Improving ensemble classifier performance.
method GRAF extends oblique decision trees to global partitioning.
result GRAF reduces generalization error and improves performance on benchmark datasets.
Random Tessellation Process improves multi-dimensional data analysis.
problem Axis-aligned cuts limit flexibility in space partitioning methods.
method Proposes Random Tessellation Process (RTP) for non-axis aligned cuts.
result Improved accuracies in gene expression data analysis.
SBT model uses randomized sharding and sub-models to improve Bayesian Additive Regression Trees.
problem Improving efficiency and accuracy of Bayesian Additive Regression Trees.
method Randomized sharding, sub-models, intersection tree structure, optimal design.
result Theoretical optimal weights and worst-case complexity of SBT model.
Partition Tree estimates conditional densities for mixed continuous and categorical variables.
problem Estimating conditional densities for mixed data types.
method Tree-based framework modeling conditional distributions as piecewise-constant densities on adaptive partitions, minimizing conditional negative log-likelihood.
result Improved probabilistic prediction compared to CART-style trees and state-of-the-art methods.
Improved Random Forests detect pure interactions better.
problem Random Forests struggle with certain pure interactions.
method Alternative partitioning schemes during tree construction.
result Improved Random Forests enhance fitting ability in scenarios with pure interactions.
The paper challenges the use of decision trees for pointwise inference due to slow convergence rates.
problem The slow convergence rates of decision trees in uniform norm, especially with non-vanishing probability.
method Demonstrates the limitations of adaptive recursive partitioning and shows how random forests can improve performance.
result Decision trees can fail to achieve polynomial rates of convergence in uniform norm, even with pruning.
flexBART improves BART for categorical predictors by creating flexible tree partitions.
problem Limitation of BART in handling categorical predictors with one-hot encoding.
method flexBART re-implements BART with regression trees that can assign multiple levels to both branches of a decision tree node, and proposes a new decision rule prior for spatial data.
result flexBART often yields improved predictive performance and scales better to larger datasets than existing BART implementations.
Recent theory work has found that a special type of spatial partition tree - called a random projection tree - is adaptive to the intrinsic dimension of the data from which it is built. Here we examine this same question, with a combination of theory and experiments, for a broader class of trees that includes k-d trees…
New algorithm PART improves EP-MCMC for large data sets.
problem Expensive MCMC for large data sets.
method Random partition trees for combining subset posterior draws.
result PART algorithm provides distribution-free, easy-to-resample, and scalable posterior approximations.
Oblique BART improves tree-based predictions.
problem Axis-aligned decision rules in BART can be suboptimal.
method Developed an oblique version of BART using data-adaptive hyperplane partitions.
result Oblique BART outperformed axis-aligned BART and other tree methods on benchmarks.
DTE uses tree leaf means to embed data, balancing accuracy and speed.
problem High variance in decision tree splits and computational inefficiency of ensembles.
method DTE constructs an interpretable feature representation using leaf means of a trained tree.
result DTE strikes a balance between accuracy and computational efficiency, outperforming ensembles.
We present the first tree-based regressor whose convergence rate depends only on the intrinsic dimension of the data, namely its Assouad dimension. The regressor uses the RPtree partitioning procedure, a simple randomized variant of k-d trees.
Enhances random forests by smoothing predictions for better performance.
problem Suboptimal performance due to piecewise constant predictions in random forests.
method Kernel-based smoothing mechanism to introduce local regularity.
result Smoothed random forest model consistently improves predictive performance.
Undirected graphical models encode in a graph G the dependency structure of a random vector Y. In many applications, it is of interest to model Y given another random vector X as input. We refer to the problem of estimating the graph G(x) of Y conditioned on X=x as ``graph-valued regression.'' In this pap…
A new algorithm, Regular Tree Search, tackles non-convex simulation optimization problems.
problem Non-convex objective functions in simulation optimization.
method Integrates adaptive sampling with recursive partitioning of the search space.
result Proves global convergence and reliably identifies the global optimum.
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an individual sequence manner. We use a tree notion in order to partition the space of regr…
Enhances multi-class classification using neural networks and decision trees.
problem Improving multi-class classification accuracy.
method Combines neural networks, decision trees, and random vector functional link networks with oblique decision surfaces.
result Superior performance on multi-class datasets compared to state-of-the-art classifiers.
Estimates sample size for subgroup analysis in randomized experiments.
problem Determining sample size for accurate subgroup analysis.
method Turns inference problem into simultaneous inference, calculates sample size based on confidence level and margin of error.
result Allows inversion of sample size to feasible number of treatment arms or partition complexity.
Causal trees struggle with accuracy in estimating treatment effects.
problem Estimating heterogeneous causal treatment effects using recursive decision trees.
method Adaptive recursive partitioning with and without sample splitting.
result Causal tree estimators can have uniform-norm errors decreasing more slowly than any power of the sample size.
New tree and forest methods use oblique splits for better risk bounds.
problem Improving risk bounds for regression algorithms.
method Randomized decision trees and forests with oblique splits.
result Oblique splits lead to better risk bounds for multi-index models.
Develops a new method to recover large latent tree models efficiently.
problem Inference of large latent tree structures from terminal node observations.
method Spectral Top-Down Recovery (STDR) using Fiedler vector partitioning.
result Proves statistical consistency and sample complexity for accurate tree recovery.
Survey of Bayesian nonparametric space partition models and their applications.
problem Partitioning high-dimensional spaces into homogeneous regions.
method Various strategies for generating partitions in a D-dimensional space.
result Review of current progress in BNSP research.
DiFF-RF detects point-wise and collective anomalies using random partitioning trees.
problem Detecting anomalies in data, especially collective anomalies.
method Random partitioning binary trees with distance-based leaves and semi-supervised learning.
result DiFF-RF significantly outperforms isolation forest and one-class SVM.
This paper studies Mondrian Forests, proving they achieve optimal rates in arbitrary dimensions.
problem Understanding optimal rates for Mondrian Forests in arbitrary dimensions.
method Theoretical study based on new results about Mondrian partitions.
result Mondrian Forests achieve minimax optimal rates for s-Hölder functions in arbitrary dimensions. We analyze the consistency of decision trees and random forests in regression.
problem Consistency of decision trees and random forests in regression.
method Elementary proofs following classical arguments for smoothing methods.
result Establish weak and almost sure convergence of honest trees and forest averages to the true regression function.
New methods improve prediction performance and reduce computation time in boosting and random forest models.
problem Improving prediction performance and reducing computation time in boosting and random forest models.
method Random tree depth injection approach for Boosting and Random Forests.
result The new methods can improve prediction performance and reduce computation time by up to 40%.
Automatically tunes hyperparameters for faster approximate nearest neighbor search.
problem Tuning hyperparameters for efficient approximate nearest neighbor search is slow and impractical.
method Proposes an algorithm using randomized space-partitioning trees to automatically tune hyperparameters.
result Significantly faster than existing approaches and competitive in query time.
New methods improve variance estimation in random forests using IJ.
problem Estimating prediction variance in random forests.
method Simulation experiments with different resampling and base learner methods.
result CI trees and subsampling lead to more accurate variance estimation.
Proposes a new BSP-Tree process for flexible space partition modeling.
problem Limited modelling flexibility of axis-aligned partitions in Mondrian process.
method Introduces a self-consistent Binary Space Partitioning (BSP)-Tree process with oblique cuts.
result Clear inferential improvements over standard Mondrian process and related methods.
Develops RKHS framework for analyzing tree ensembles.
problem Analyzing the theoretical properties of tree ensembles.
method Reproducing Kernel Hilbert Spaces (RKHS) for tree ensembles.
result Characterizes Random Forest predictor as minimizer of a penalized empirical risk functional in RKHS.
We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of particles (representing the objects) diffusing in some continuous space, analogou…
We present a method for incorporating missing data in non-parametric statistical learning without the need for imputation. We focus on a tree-based method, Bayesian Additive Regression Trees (BART), enhanced with "Missingness Incorporated in Attributes," an approach recently proposed incorporating missingness into deci…
RLF uses Riemann-Lebesgue cutting for better regression.
problem Improving regression accuracy through novel tree splitting.
method Develops Riemann-Lebesgue Tree (RLT) for partitioning response intervals.
result RLF achieves larger variance reduction compared to CART.
We propose a multiresolution Gaussian process to capture long-range, non-Markovian dependencies while allowing for abrupt changes. The multiresolution GP hierarchically couples a collection of smooth GPs, each defined over an element of a random nested partition. Long-range dependencies are captured by the top-level GP…
Proposes LIME-SUP for interpreting complex SML models.
problem Complexity of SML models makes them hard to interpret.
method Fits trees to the fitted response and its derivatives.
result Advantages over KLIME in simulation and real data.
This research designs a data-driven partition to test independence between continuous variables.
problem Testing independence between continuous random variables.
method Empirical log-likelihood statistic and data-driven tree-structured partition.
result Strongly consistent test of independence over probability families.
New method handles metric space data for regression.
problem Handling heterogeneous data like curves, images, and shapes.
method Fréchet trees and Fréchet random forests for metric space valued regression.
result Random forests can now handle complex data types.
The Random Projection Tree structures proposed in [Freund-Dasgupta STOC08] are space partitioning data structures that automatically adapt to various notions of intrinsic dimensionality of data. We prove new results for both the RPTreeMax and the RPTreeMean data structures. Our result for RPTreeMax gives a near-optimal…
Study improves Morse-Smale regression for actuarial science using various machine learning algorithms.
problem Dealing with subgroups in actuarial science through piecewise regression.
method Extends Morse-Smale regression to machine learning algorithms like random forest, conditional inference trees, and neural networks.
result New algorithms improve performance and provide insights into predictor relationships.
We introduce a new class of lower bounds on the log partition function of a Markov random field which makes use of a reversed Jensen's inequality. In particular, our method approximates the intractable distribution using a linear combination of spanning trees with negative weights. This technique is a lower-bound count…
Data-driven label space division outperforms random partitioning in multi-label classification.
problem Improving multi-label classification performance through better label space division.
method Community detection algorithms applied to label co-occurence graphs to partition the label space.
result Community detection methods on label co-occurence graphs outperform random partitioning in most evaluation measures.
TBRF improves large-scale regression with two-stage random forest.
problem Large-scale regression problems with boundary discontinuities.
method Two-stage best-scored random forest approach.
result TBRF achieves high prediction accuracy and computational efficiency.
New method creates adaptive prediction intervals for regression models.
problem Need to quantify uncertainty in regression model predictions.
method Regression trees and Random Forests trained on conformity scores.
result Superior scalability and performance compared to baselines.
Online BSP-Forest improves space partitioning for large-scale classification and regression.
problem Efficient space partitioning for large-scale classification and regression problems.
method Developed an online BSP-Forest framework that expands space coverage and refines partition structure in real-time.
result Guaranteed universal consistency for both classification and regression problems.
The paper develops a theory for random forests, separating variance components and providing methods for estimating prediction intervals.
problem Understanding the variance and uncertainty in random forest predictions.
method Design-based theory, Monte Carlo averaging, PASR resampling.
result The floor of prediction uncertainty is positive and persists even without observation overlap, providing conservative prediction intervals.
A new hybrid MCMC method guides MCMC with tree-based clustering for faster and more efficient inference.
problem Slow convergence of MCMC methods in posterior inference for NRM mixture models.
method Tree-guided MCMC (tgMCMC) that combines MCMC's convergence guarantees with IBHC's efficiency.
result tgMCMC provides faster convergence and better performance compared to MCMC and IBHC alone.
We introduce a method for creating a special type of tree, called a tree position, from a weighted graph. Leaves of the tree correspond to vertices of the original graph, and the tree edges contain information which can be used to partition these vertices. By repeatedly applying reducing operations to the tree position…
A method combining multiple random projection trees for fast k-NN search.
problem Efficient nearest neighbor search in high-dimensional spaces.
method Combining multiple random projection trees with a novel voting scheme.
result Significantly faster than existing methods on high accuracy levels.