Kernel clustering methods have biases due to density, which can be corrected.
problem Density biases in kernel clustering methods.
method Theoretical analysis and proposed solutions to density biases.
result Density biases can be corrected by density equalization using locally adaptive weights or kernels.
Leo Breiman's Rashomon Effect and Occam Dilemma are re-evaluated in the context of modern machine learning.
problem The tradeoff between model complexity and accuracy in machine learning.
method Modern perspective on Breiman's arguments using current computational capabilities.
result Algorithmic models can be accurate without being complex, nullifying the Occam Dilemma.
Breiman's two cultures reconciled through blending statistical thinking.
problem Tension between parametric statistical and machine learning approaches.
method Establishing a link between parametric statistical and machine learning frameworks.
result Integrated statistical thinking can bridge the gap between two cultures.
Breiman's data analysis dichotomy is outdated, offering a third approach: mechanistic models.
problem Data analysis dichotomy between data modelers and algorithmic modelers.
method Interpolating between simple interpretable models and flexible function approximations using mechanistic models.
result Flexible, interpretable, and scientifically-informed hybrids can provide accurate and robust predictions.
Breiman's paper sparked debate on the future of statistics and machine learning.
problem The tension between traditional statistical modeling and model-free machine learning approaches.
method Discussion of the implications of machine learning's success and the need for new inferential approaches.
result The importance of understanding 'why' and 'if' questions in machine learning is now recognized.
RFX-Fuse combines Breiman and Cutler's Random Forest with modern ML capabilities.
problem Lack of a unified ML engine with diverse capabilities.
method Unified ML engine with native GPU/CPU support, delivering 5+ functionalities in one model.
result Native explainable similarity and imputation validation.
This paper resolves Breiman's dilemma in neural networks by analyzing phase transitions of margin dynamics.
problem Breiman's dilemma in neural networks: uniform margin improvement does not guarantee reduced generalization errors.
method Revisiting Breiman's dilemma in deep neural networks with spectrally normalized margins, analyzing phase transitions of normalized margin distributions.
result Margin-based generalization bounds can predict test error trends during training phase transitions.
Breiman discusses two statistical cultures, advocating for more research on 'before' and 'after' the black box.
problem Statistical modeling lacks exploration of processes before and after the 'black box'.
method Analyzes Breiman's visual metaphor of two statistical cultures.
result Promotes the importance of studying the 'before' and 'after' of data transformations.
New method debiases feature importance in Random Forests.
problem MDI feature importance measure incorrectly assigns high importance to noisy features.
method Derive a new analytical expression for MDI and propose MDI-oob debiased feature importance measure.
result MDI-oob achieves state-of-the-art performance in feature selection from Random Forests.
The paper studies bias and adaptivity of CART regression trees.
problem Bias and adaptivity of CART regression trees.
method Derives an interesting connection between bias and MDI measure of variable importance.
result Decision trees with CART have small bias and are adaptive to signal strength and direction.
Random forests handle categorical predictors natively but overlook 'absent levels' can bias models.
problem Bias in decision tree models due to 'absent levels' problem.
method Examined with Leo Breiman and Adele Cutler's random forests FORTRAN code and the randomForest R package.
result Simple heuristics can help mitigate the effects of the absent levels problem.
The Shannon theorem is extended to locally compact groups.
problem Identifying the Poisson boundary of locally compact groups.
method Random walks and Shannon-McMillan-Breiman theorem.
result Generalized criteria for identifying Poisson boundaries.
Random forests are a scheme proposed by Leo Breiman in the 2000's for building a predictor ensemble with a set of decision trees that grow in randomly selected subspaces of data. Despite growing interest and practical use, there has been little exploration of the statistical properties of random forests, and little is …
Commentary on Rashomon Effect complicating model selection.
problem Many models equally predict data; hard to draw conclusions.
method Connections to recent ML literature exploring implications.
result Grasping Rashomon Effect can foster collaboration.
Breiman (2001) proposed to statisticians awareness of two cultures: 1. Parametric modeling culture, pioneered by R.A.Fisher and Jerzy Neyman; 2. Algorithmic predictive culture, pioneered by machine learning research. Parzen (2001), as a part of discussing Breiman (2001), proposed that researchers be aware of many cultu…
New Random Forest variants estimate heterogeneous treatment effects using Wasserstein distances.
problem Estimating heterogeneous treatment effects in complex situations.
method Proposes natural variants of Random Forests using Wasserstein distances.
result Natural variants of Random Forests are well-suited for estimating conditional distributions.
ggRandomForests package visualizes random forest models for survival data.
problem Analyzing time to event data using random forest methods.
method Unified random forest package for survival analysis with visualizations.
result Demonstrates the strength of random forest methods for prediction and information retrieval in time to event data.
NN-Stacking improves predictive power of regression models by adjusting stacking coefficients with features.
problem Low predictive power of linear stacking methods.
method NN-Stacking uses neural networks to estimate adaptive stacking coefficients.
result NN-Stacking leads to better predictive power, especially in large datasets.
Examines algorithmic modeling across three cultures.
problem Tackles algorithmic modeling in different cultural contexts.
method Uses parametric regressions, interpretable algorithms, and complex algorithms.
result Extension of Leo Breiman's thesis to include cultural differences.
Random forests are a learning algorithm proposed by Breiman [Mach. Learn. 45 (2001) 5--32] that combines several randomized decision trees and aggregates their predictions by averaging. Despite its wide usage and outstanding practical performance, little is known about the mathematical properties of the procedure. This…
The paper studies a rebalanced dataset for imbalanced classification using Centered Random Forests.
problem Imbalanced classification where one class is underrepresented.
method Theoretical analysis of Centered Random Forests (CRF) with rebalanced datasets and debiasing techniques.
result Theoretical Central Limit Theorem (CLT) for the infinite CRF and debiased estimator IS-ICRF.
Improved analysis of a random forest model reduces prediction error.
problem Improving prediction accuracy in random forest models.
method Revisited a historical random forest model, analyzing feature selection and splits.
result Mean-squared prediction error rate is improved to O((n(\log n)^{(S-1)/2})^{-\frac{1}{S\log2+1}}).
Two new methods reduce random forest latency and improve accuracy.
problem High latency and memory demands in deep random forest models.
method DiNo and RanBu convert shallow random forests into efficient predictors.
result RanBu matches or exceeds full-depth random forest accuracy with up to 95% reduction in time.
This paper is a comment on the survey paper by Biau and Scornet (2016) about random forests. We focus on the problem of quantifying the impact of each ingredient of random forests on their performance. We show that such a quantification is possible for a simple pure forest , leading to conclusions that could apply more…
Random Forests [Breiman:2001] (RF) are a fully non-parametric statistical method requiring no distributional assumptions on covariate relation to the response. RF are a robust, nonlinear technique that optimizes predictive accuracy by fitting an ensemble of trees to stabilize model estimates. The randomForestSRC packag…
The aim of this work is to extend the capital growth theory developed by Kelly, Breiman, Cover and others to asset market models with transaction costs. We define a natural generalization of the notion of a numeraire portfolio proposed by Long and show how such portfolios can be used for constructing growth-optimal inv…
New NMF method recovers archetypes without separability condition.
problem Non-negative matrix factorization (NMF) for non-separable data.
method Optimizes convex envelope of archetypes and data points, with regularization.
result Estimator is robust and finds good solutions for real and synthetic data.
Improved bounds for neural network approximations of functions.
problem Bounding the width of neural networks for function approximation.
method Extending Radon-based norms to bounded open sets and deriving new approximation bounds.
result Improved sparse approximation bounds for neural networks.
RFX accelerates and compresses Random Forests for large datasets.
problem Memory bottleneck in proximity matrices limits Random Forest analysis.
method QLORA compression, CPU TriBlock storage, GPU batch sizing, 3D MDS visualization.
result Proximity-based Random Forest analysis on larger datasets is feasible.
New method calculates tail probabilities of random vectors under linear transformations.
problem Computing tail probabilities of random vectors under linear transformations.
method Characterization of regular variation on cones in [0,∞)d under random linear transformations. result Allows computation of probabilities of tail events that were previously negligible.
Given an ensemble of randomized regression trees, it is possible to restructure them as a collection of multilayered neural networks with particular connection weights. Following this principle, we reformulate the random forest method of Breiman (2001) into a neural network setting, and in turn propose two new hybrid p…
Risk bounds for Classification and Regression Trees (CART, Breiman et. al. 1984) classifiers are obtained under a margin condition in the binary supervised classification framework. These risk bounds are obtained conditionally on the construction of the maximal deep binary tree and permit to prove that the linear penal…
The random forest algorithm, proposed by L. Breiman in 2001, has been extremely successful as a general-purpose classification and regression method. The approach, which combines several randomized decision trees and aggregates their predictions by averaging, has shown excellent performance in settings where the number…
Weak supervision challenges black-box models, suggesting fusion of modeling cultures.
problem Challenges of strong supervision in achieving accurate predictions.
method Integrating data modeling into algorithmic modeling for weak supervision.
result Integration of data modeling culture improves model stability and accuracy.
Random forests can be slow or inconsistent in certain models.
problem Performance issues of random forests in specific data-generating models.
method Intuitive arguments and numerical experiments, combined with variable use and importance statistics.
result Simple methods can create a better predictor using a forced random forest.
We introduce a useful tool for analyzing boosting algorithms called the ``smooth margin function,'' a differentiable approximation of the usual margin for boosting algorithms. We present two boosting algorithms based on this smooth margin, ``coordinate ascent boosting'' and ``approximate coordinate ascent boosting,'' w…
Survival trees exhibit end-cut preference, leading to biased splits.
problem End-cut preference in survival trees causes biased splits and poor interpretability.
method Proposed a smooth sigmoid surrogate (SSS) approach to replace hard-threshold indicator function.
result Smooth sigmoid surrogate (SSS) effectively mitigates end-cut preference in survival trees.
This paper examines from an experimental perspective random forests, the increasingly used statistical method for classification and regression problems introduced by Leo Breiman in 2001. It first aims at confirming, known but sparse, advice for using random forests and at proposing some complementary remarks for both …
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.
We improve random forest consistency and performance with DMRF, a new variant.
problem Improving the consistency and performance of random forest models.
method Developed DMRF, a data-driven multinomial random forest, by modifying proof methods and improving data utilization.
result DMRF achieves strong consistency with probability 1, surpassing previous models in classification tasks.
We introduce a dynamical system which we call the AdaBoost flow. The flow is defined by a system of ODEs with control. We show that three algorithms of the AdaBoost family (i) the AdaBoost algorithm of Schapire and Freund (ii) the arc-gv algorithm of Breiman (iii) the confidence rated prediction of Schapire and Singer …
A greedy active learning algorithm for logistic regression reduces model size and training size.
problem Binary classification with reduced model size and training size.
method Modified batch subject selection strategy with greedy variable selection.
result Competitive performance with smaller training size and model size.
Baccalaureate institutions seek to integrate statistics into data science.
problem Graduate statisticians losing ground in data science.
method Reviewing historical contributions of statisticians and calling for integration.
result Baccalaureate institutions need to integrate statistics into data science education.
AA extracts archetypes from data for clear feature extraction.
problem Non-convex optimization problem in AA.
method Computational procedure extracting archetypes as convex combinations of data.
result AA offers interpretable representations for high-dimensional data.
Decision trees are consistent for regression and classification tasks even with many predictors.
problem Consistency of decision trees with many predictors.
method CART and C4.5 methodology, oracle inequality, sparsity constraints.
result Decision trees and random forests are consistent for various types of data.
A new random forest method for multivariate distributions.
problem Estimating complex multivariate distributions with heterogeneity.
method A novel splitting criterion based on MMD for multivariate responses.
result Estimates full conditional distribution for arbitrary targets.
Proposes GBBHE for efficient large-scale regression.
problem Large-scale regression problems.
method Gradient Boosting with binary histogram partition and ensemble learning.
result Improves computational efficiency and performance on large datasets.
Many scientific and engineering challenges -- ranging from personalized medicine to customized marketing recommendations -- require an understanding of treatment effect heterogeneity. In this paper, we develop a non-parametric causal forest for estimating heterogeneous treatment effects that extends Breiman's widely us…