New tree splitting criteria improve probabilistic predictions.
problem Improving tree-based nonparametric predictive distributions.
method Using proper scoring rules for tree splitting criteria.
result Trees with new splitting criteria produce better predictive distributions.
Adversarial online nonparametric regression achieves optimal rates with locally adaptive learning.
problem Adversarial online nonparametric regression with general convex losses.
method Parameter-free learning algorithm leveraging chaining trees to compete against H{ö}lder functions, dynamically tracking and adapting to local smoothness variations.
result First computationally efficient algorithm with locally adaptive optimal rates for online regression in an adversarial setting.
Decision stumps accurately screen variables in nonparametric models.
problem Challenges in theoretical properties of tree-based variable importance measures.
method Derive performance guarantees for variable selection using a single-level CART decision tree (decision stump).
result Decision stumps can perform consistent model selection despite being inaccurate for estimation.
Bayesian test assesses conditional independence between variables.
problem Quantifying dependence or independence between variables given a third.
method Uses Polya tree priors on conditional probability densities.
result Provides a Bayesian measure of conditional dependence or independence.
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.
We present the nested Chinese restaurant process (nCRP), a stochastic process which assigns probability distributions to infinitely-deep, infinitely-branching trees. We show how this stochastic process can be used as a prior distribution in a Bayesian nonparametric model of document collections. Specifically, we presen…
A new nonparametric test measures dependence between variables using decision trees.
problem Measuring statistical dependence between two variables robustly and efficiently.
method An ensemble of decision trees discriminates between observed and permuted samples without generating the latter.
result The method effectively detects complex relationships from noisy data.
Bayesian nonparametric machine learning improves instrumental variable inference.
problem Estimating causal effects with nonlinear relationships.
method Bayesian Additive Regression Trees (BART) for estimating functions and Dirichlet Process mixtures for error terms.
result Dramatic improvements in inference with nonlinear data, no manual tuning required.
Gradient boosting improved with lassoed trees achieves faster convergence.
problem Improving gradient boosting convergence in large nonparametric spaces.
method Lassoed gradient boosted trees with early stopping.
result Achieves faster than n−1/4 L2 convergence rate. NP-HMC extends HMC for nonparametric models in probabilistic programming.
problem Inference for nonparametric models in probabilistic programming.
method Introduces NP-HMC, a generalization of HMC for nonparametric models using tree representable functions.
result Empirically shows significant performance improvements over existing approaches.
Fast nonparametric conditional independence testing via two-stage regression
problem Fast nonparametric conditional independence testing
method BLITZ (Broad-to-Local Independence Testing via residualiZation)
result Better null calibration than fast kernel, random-feature, and regression-based competitors
Convex polytope trees expand decision trees with interpretable boundaries.
problem High accuracy often requires many nodes in decision trees, reducing interpretability.
method CPT uses logical disjunction of weighted linear decision-makers, geometrically a convex polytope.
result CPT achieves high accuracy with fewer nodes compared to existing methods.
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for parameter estimation, inference, and structure learning mainly rely on the Gaussian or…
Tree-based synthesis improves forecast accuracy in GDP and inflation.
problem Improving forecast accuracy in GDP and inflation.
method Developed a nonparametric synthesis function using regression trees.
result Tree-based synthesis leads to improved forecast accuracy.
Statistical machine learning methods, especially nonparametric Bayesian methods, have become increasingly popular to infer clonal population structure of tumors. Here we describe the treeCRP, an extension of the Chinese restaurant process (CRP), a popular construction used in nonparametric mixture models, to infer the …
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.
Given functional data from a survival process with time-dependent covariates, we derive a smooth convex representation for its nonparametric log-likelihood functional and obtain its functional gradient. From this, we devise a generic gradient boosting procedure for estimating the hazard function nonparametrically. An i…
A new predictor learns feature scales to predict discrete labels from continuous features efficiently.
problem Predicting discrete labels from continuous features efficiently and accurately.
method Discretizes feature space with k-d tree and recursively learns feature scales using Bayesian distribution.
result Achieves performance as good as true conditional entropy asymptotically.
ASBART accelerates Soft BART for faster Bayesian regression.
problem Slow computation in Soft BART.
method Proposed ASBART, a variant of Soft BART.
result ASBART is about 10 times faster than Soft BART with similar accuracy.
Adaptive Bayesian model for covariate-dependent power spectra analysis.
problem Estimating complex relationships and interactions between covariates and power spectra.
method Bayesian sum of trees model with local power spectrum estimation and reversible-jump MCMC for tree modifications.
result The method can accurately recover both smooth and abrupt changes in power spectra across multiple covariates.
Bayesian Additive Regression Trees (BART) is a fully Bayesian approach to modeling with ensembles of trees. BART can uncover complex regression functions with high dimensional regressors in a fairly automatic way and provide Bayesian quantification of the uncertainty through the posterior. However, BART assumes IID nor…
We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a finite number of values. Continuous data are different. The Gaussian graphical mode…
In this paper, we propose a compositional nonparametric method in which a model is expressed as a labeled binary tree of 2k+1 nodes, where each node is either a summation, a multiplication, or the application of one of the q basis functions to one of the p covariates. We show that in order to recover a labeled bi…
This study converts BART to Gaussian process regression, revealing its limitations and potential improvements.
problem Understanding the Gaussian process limit of BART and its implications.
method Deriving and computing BART's prior covariance function, implementing the infinite trees limit as GP regression, and tuning hyperparameters.
result The Gaussian process limit of BART is inferior to standard BART but can be made competitive with proper hyperparameter tuning.
Transforms conditional density estimation into a nonparametric regression problem.
problem Conditional density estimation in high dimensions.
method Introduces auxiliary samples to transform into nonparametric regression.
result Estimator converges to true conditional density in data limit.
In our physically inspired in-tree (IT) based clustering algorithm and the series after it, there is only one free parameter involved in computing the potential value of each point. In this work, based on the Delaunay Triangulation or its dual Voronoi tessellation, we propose a nonparametric process to compute potentia…
BoXHED2.0 boosts survival analysis for complex data.
problem Survival analysis with time-dependent covariates.
method Tree-boosted hazard estimator, fully nonparametric, scalable.
result Scalable to parametric boosted survival models in speed.
New model reconstructs cell differentiation paths from single-cell RNA data.
problem Reconstructing dynamic biological phenomena from noisy, heterogeneous, and sparse single-cell RNA-seq data.
method Developed a generative model using Dirichlet diffusion tree and Markov chain Monte Carlo sampler.
result Recovered latent trajectories from simulated single-cell transcriptomes.
Bayesian Additive Distribution Regression (DistBART) predicts distributions from grouped data.
problem Predicting distributions from grouped data with varying characteristics.
method Bayesian nonparametric approach using BART for modeling the regression function.
result Empirical and theoretical evidence supports DistBART's effectiveness in learning from low-dimensional marginals.
The study reveals decision trees' limitations in fitting data from additive models, proving a generalization lower bound.
problem Understanding the generalization performance of decision trees on additive models.
method Analyzing decision tree algorithms with sparse additive models, proving generalization lower bounds.
result Generalization lower bounds for decision trees on sparse additive models are much worse than minimax rates.
New method improves density estimation accuracy and resistance to dimensionality issues.
problem Improving density estimation accuracy and resistance to dimensionality issues.
method Best-scored random forest density estimation method.
result The method achieves better estimation results than other state-of-the-art approaches.
SoftBart improves BART for high-noise modeling in science.
problem High noise in scientific data.
method Soft BART algorithm for Bayesian additive regression trees.
result Improves predictive performance and facilitates larger model integration.
This paper develops a new method to model treatment effects that are heterogeneous across different quantiles.
problem Modeling treatment effects that vary across different quantiles of the outcome distribution.
method The paper combines quantile classification with local polynomial estimation to build a decision tree and forest.
result The proposed QLPRT and QLPRF methods provide a new way to estimate and infer heterogeneous treatment effects.
Unified framework for selecting variables with uncertainty quantification.
problem Uncertainty in nonlinear variable selection for various models.
method Develops a unified framework using integrated partial derivatives for quantifying variable importance and uncertainty.
result The approach provides a principled method for quantifying variable selection uncertainty and is generalizable to non-differentiable models.
Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeab…
Nonparametric Bayesian models are often based on the assumption that the objects being modeled are exchangeable. While appropriate in some applications (e.g., bag-of-words models for documents), exchangeability is sometimes assumed simply for computational reasons; non-exchangeable models might be a better choice for a…
Probit Monotone BART estimates binary outcomes using monotonic functions.
problem Estimating conditional mean functions for binary outcomes with monotonicity constraints.
method Proposes a new BART variant that incorporates monotonicity constraints for binary outcomes.
result Allows for more precise estimation of monotonic functions in binary outcome models.
Bayesian nonparametric method for hierarchical clustering.
problem Hierarchical non-overlapping clustering of a dataset.
method Combining nCRP and HDP for complex latent mixture features.
result Solid empirical results compared to existing algorithms.
Estimates piecewise polynomials and bounded variation functions using optimal decision trees.
problem Estimating piecewise smooth functions in general dimensions.
method Dyadic CART and Optimal Regression Tree (ORT) estimators for piecewise polynomials and bounded variation functions.
result Oracle inequalities and risk bounds for ORT estimators, demonstrating adaptivity and optimality.
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this pap…
Study compares non-parametric models for predicting medical insurance reimbursement delays.
problem Estimating the time-lapse between medical insurance reimbursement.
method Comparative study of four non-parametric regression models (KNNs, SVMs, Decision Trees, Random Forests) using R-squared metric.
result Each model's performance varies with training data size, feature space, and hyperparameters.
GPU-accelerated BART speeds up Bayesian regression.
problem Long running time of BART makes it impractical for large datasets.
method GPU-enabled implementation of BART.
result BART is now 200x faster on GPUs.
While deep reinforcement learning has successfully solved many challenging control tasks, its real-world applicability has been limited by the inability to ensure the safety of learned policies. We propose an approach to verifiable reinforcement learning by training decision tree policies, which can represent complex p…
Develops regression trees for estimating cumulative incidence curves in competing risks.
problem Estimating cumulative incidence functions in competing risks settings.
method Uses augmented estimators of the Brier score risk to build and prune regression trees.
result Demonstrates the utility of the proposed methods through simulation studies and real data.
This work analyzes tree-based methods from a ranking perspective, providing insights and new statistics.
problem Understanding the effectiveness of tree-based methods in finite-sample settings, especially symbolic feature selection.
method Local ranking perspective, finite-sample analysis, oracle bounds, posterior contraction results, concordant divergence statistics.
result New insights and statistics for evaluating symbolic feature mappings.
The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich representational power of neural networks with Bayesian methods. However, most work on VAEs use a rather simple prior over the latent variables such as standard normal distribution, thereby restricting its appli…
Analysis of flow cytometry data is an essential tool for clinical diagnosis of hematological and immunological conditions. Current clinical workflows rely on a manual process called gating to classify cells into their canonical types. This dependence on human annotation limits the rate, reproducibility, and complexity …
Proposes a new model to handle noisy data in scientific research.
problem Measurement error in noisy data settings.
method Measurement error BART (meBART) integrates measurement error in Bayesian additive regression trees.
result meBART provides more accurate parameter estimation, robust uncertainty quantification, and superior predictive performance.