Paper analyzes and proves convergence of a new method for solving complex PDEs.
problem Solving high-dimensional nonlinear PDEs and PIDEs with random neural networks.
method Random deep splitting method using random neural networks.
result The method converges to the unique viscosity solution of nonlinear PDEs and PIDEs.
A random Heegaard splitting is a 3-manifold obtained by using a random walk of length n on the mapping class group as the gluing map between two handlebodies. We show that the joint distribution of random walks of length n and their inverses is asymptotically independent, and converges to the product of the harmonic an…
New random forest variants achieve optimal performance in high dimensions.
problem Handling dependencies between features in high-dimensional data.
method Using oblique splits in random forests with general split directions.
result Achieved minimax optimal convergence rates in arbitrary dimension.
The most popular approach for analyzing survival data is the Cox regression model. The Cox model may, however, be misspecified, and its proportionality assumption may not always be fulfilled. An alternative approach for survival prediction is random forests for survival outcomes. The standard split criterion for random…
Uniform models for random 3-manifolds with controlled metrics.
problem Understanding the geometric properties of random 3-manifolds.
method Two constructions of hyperbolic metrics on 3-manifolds with Heegaard splittings.
result The diameter of a random Heegaard splitting grows coarsely linearly in the length of the associated random walk.
New method combines randomization tests and flexible models for valid inference without splitting data.
problem Valid inference in randomized panel experiments with complex effect heterogeneity.
method Model-assisted randomization tests that estimate unsigned CATE from residualized outcomes.
result CATE-assisted tests control Type I error and achieve higher power than alternatives.
We show that, if H is a random subgroup of a finitely generated free group Fk, only inner automorphisms of Fk may leave H invariant. A similar result holds for random subgroups of toral relatively hyperbolic groups, more generally of groups which are hyperbolic relative to slender subgroups. These results fol…
Paper improves anomaly detection by using non-uniform random choices in isolation forests.
problem Detecting clustered diverse outliers more effectively.
method Comparing different split guiding criteria in isolation forests.
result Non-uniform random choices improve outlier discrimination for certain outlier classes.
Improves decision tree performance by correcting split selection errors.
problem Invalid statistical guarantees in split selection for decision trees.
method Introduces anytime-valid inference to provide valid statistical guarantees.
result Provides anytime-valid control of false splits under arbitrary data streams.
DiPriMe forests use private medians to create balanced tree splits for privacy-protected data.
problem Privacy concerns in training random forests due to multiple data queries.
method Proposes DiPriMe forests, which use a private median to generate balanced splits, ensuring differential privacy.
result DiPriMe forests achieve high utility while maintaining differential privacy, as shown both theoretically and empirically.
We propose an algorithm named best-scored random forest for binary classification problems. The terminology "best-scored" means to select the one with the best empirical performance out of a certain number of purely random tree candidates as each single tree in the forest. In this way, the resulting forest can be more …
We show that a random link defined by random bridge splitting is hyperbolic with asymptotic probability 1.
Despite the impressive performance of random forests (RF), its theoretical properties have not been thoroughly understood. In this paper, we propose a novel RF framework, dubbed multinomial random forest (MRF), to analyze the \emph{consistency} and \emph{privacy-preservation}. Instead of deterministic greedy split rule…
A new random forest algorithm improves tree construction for optimal performance.
problem Improving the performance of random forests, especially in complex and smooth scenarios.
method Adaptive split-balancing method using permutation-based splitting criterion.
result Achieves minimax optimality under various Lipschitz and Hölder classes.
A new method for causal inference in high-dimensional data using machine learning.
problem Causal inference in high-dimensional observational data.
method Support Points Sample Splitting (SPSS) for efficient double machine learning (DML) in causal inference.
result Deep learning with SPSS and hybrid methods outperform SVM with SPSS in computational efficiency and estimation quality.
This paper explains CART random forests using stochastic control theory.
problem Understanding the inner workings of CART random forests.
method Developed a stochastic-control perspective on CART random forests, interpreting feature subsampling as a random feasible action set and the split rule as a policy.
result Established that the CART policy is locally stabilizing but globally suboptimal for the forest objective.
SPlit optimizes dataset splitting for better model performance.
problem Improving model performance through optimal dataset splitting.
method Adapting Support Points (SP) algorithm for subsampling and categorical variables in a sequential nearest neighbor approach.
result SPlit significantly improves worst-case testing performance compared to random splitting.
FedForest adapts RF for federated learning, improving performance and efficiency.
problem Adapting RF for federated learning with heterogeneous data.
method FedForest uses a novel splitting procedure to aggregate client statistics, allowing non-parametric personalization.
result FedForest's federated RF achieves performance close to centralized models while being communication-efficient.
This paper optimizes high-dimensional oblique splits for decision trees, enhancing performance and computational efficiency.
problem Enhancing decision tree performance and computational efficiency in high-dimensional data.
method Established Sufficient Impurity Decrease (SID) convergence for s0-sparse oblique splits, proposing progressive trees for iterative refinement. result Demonstrated that SID function class expands with s0-sparsity, enabling capture of complex data-generating processes. Proposes a new cross-validation method to estimate model performance.
problem The standard cross-validation method does not accurately estimate the performance of the recommended model.
method Develops a new random-effects model framework to improve naive cross-validation estimators.
result Proposed estimators outperform conventional and naive methods in estimating model performance.
Enhances Random Forest for imbalanced functional data classification.
problem Challenges in classifying imbalanced functional data.
method Functional Random Forest with Adaptive Cost-Sensitive Splitting (FRF-ACS).
result Significantly improves minority class recall and predictive performance.
Develops a new inference method for split-sample estimators using multiple splits.
problem Statistical dependence and variability in split-sample estimators.
method Averaging across multiple splits, proving a central limit theorem, and developing new inference approaches.
result Valid confidence intervals and improved power in comparing model performance.
Random survival forests (RSF) are a powerful method for risk prediction of right-censored outcomes in biomedical research. RSF use the log-rank split criterion to form an ensemble of survival trees. The most common approach to evaluate the prediction accuracy of a RSF model is Harrell's concordance index for survival d…
We propose a modification that corrects for split-improvement variable importance measures in Random Forests and other tree-based methods. These methods have been shown to be biased towards increasing the importance of features with more potential splits. We show that by appropriately incorporating split-improvement as…
Random forests have become an important tool for improving accuracy in regression and classification problems since their inception by Leo Breiman in 2001. In this paper, we revisit a historically important random forest model originally proposed by Breiman in 2004 and later studied by Gérard Biau in 2012, where a feat…
We prove a law of large numbers for the volumes of families of random hyperbolic mapping tori and Heegaard splittings providing a sharp answer to a conjecture of Dunfield and Thurston.
New inequality for ternary variables improves on existing measures.
problem Analyzing excess losses and weighted majority votes with ternary random variables.
method Developed a split-kl inequality and its PAC-Bayes extension.
result Outperforms existing inequalities in certain regimes.
Assigning significance in high-dimensional regression is challenging. Most computationally efficient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a recent proposal by Wasserman and Roeder (2008) which splits the data into two pa…
This study examines how randomness affects machine learning model performance.
problem The impact of randomness on machine learning model performance.
method Empirical study comparing randomness in model training and dataset partitioning.
result Randomness in model training causes more variation in FFNNs than tree-based methods.
Paper introduces a medoid-based approach for efficient Fréchet regression.
problem Regression in metric spaces with random objects.
method Adapted random forest algorithm with medoid-based splitting rule.
result Asymptotic equivalence and consistency of the regression estimator.
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.
Random Forests (RFs) are strong machine learning tools for classification and regression. However, they remain supervised algorithms, and no extension of RFs to the one-class setting has been proposed, except for techniques based on second-class sampling. This work fills this gap by proposing a natural methodology to e…
Diffusion models' consistency across splits explained by random matrix theory.
problem Consistency of diffusion models trained on non-overlapping subsets.
method Random matrix theory framework to quantify dataset effects on denoiser and sampling map.
result The theory explains and predicts cross-split disagreement in diffusion models.
New algorithms solve nonconvex federated learning problems efficiently.
problem Nonconvex federated composite optimization in federated learning.
method FedDR and asyncFedDR algorithms combining Douglas-Rachford splitting, randomized block-coordinate strategies, and asynchronous implementation.
result Match communication complexity lower bound up to a constant factor.
SBSS uses similarity to split data for better classifier training.
problem Training better classifiers with realistic performance estimation.
method SBSS uses both input and output space information to split data using similarity functions.
result SBSS outperformed ordinary stratified 10-fold cross-validation in 75% of scenarios.
Tests factor models by decomposing market into body and tail legs, revealing inconsistent results.
problem Inconsistency between factor models and market behavior.
method Decomposes market into body and tail legs, testing factor models at daily and monthly frequencies.
result q5 model shows inconsistent results, with negative body and positive tail alphas at all split ratios.
Decision forests, including Random Forests and Gradient Boosting Trees, have recently demonstrated state-of-the-art performance in a variety of machine learning settings. Decision forests are typically ensembles of axis-aligned decision trees; that is, trees that split only along feature dimensions. In contrast, many r…
In a previous paper we introduced a notion of "genericity" for countable sets of curves in the curve complex of a surface S, based on the Lebesgue measure on the space of projective measured laminations in S. With this definition we prove that for each fixed g > 1 the set of irreducible genus g Heegaard splittings of h…
A new method identifies class-specific covariates in multi-class prediction tasks.
problem Identifying covariates specifically associated with one or more outcome classes in multi-class prediction tasks.
method Introducing multi forests (MuFs) with multi-way and binary splits to measure class-associated discriminatory ability.
result The multi-class VIM specifically ranks class-associated covariates highly, unlike conventional VIMs.
DaRE forests enable efficient data deletion from random forests.
problem Efficiently removing data from machine learning models.
method Random Forests with data deletion enabled (DaRE).
result Data deletion from DaRE models is orders of magnitude faster than retraining.
We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on trees. This implies that their Gromov boundaries, defined at density less than 1/2, are Menger curves.
FastForest boosts Random Forest speed by 24%.
problem Efficiency in processing speed for Random Forest.
method Subsample Aggregating, Logarithmic Split-Point Sampling, Dynamic Restricted Subspacing.
result Average 24% increase in processing speed with accuracy maintained.
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.
Split-Merge MCMC (Monte Carlo Markov Chain) is one of the essential and popular variants of MCMC for problems when an MCMC state consists of an unknown number of components. It is well known that state-of-the-art methods for split-merge MCMC do not scale well. Strategies for rapid mixing requires smart and informative …
Optimizes decision-making with uncertain variables using auxiliary observations.
problem Contextual stochastic optimization problems with uncertain variables and rich auxiliary observations.
method Trains forest decision policies by growing trees that optimize downstream decision quality, using optimization perturbation analysis for efficient approximations.
result Proves asymptotic optimality and empirical validation of the method's performance and efficiency.
Proposes autoencoding with random forests using spectral graph theory.
problem Learning low-dimensional embeddings of random forest models.
method Combines nonparametric statistics and spectral graph theory for optimization.
result Establishes a universal consistent decoder for random forest models.
Generalizes data thinning for various distributions.
problem Thinning random variables without losing information.
method Relaxes summation requirement to sufficiency.
result Generalizes thinning to more distributions.
Microbial clades modeling is a challenging problem in biology based on microarray genome sequences, especially in new species gene isolates discovery and category. Marker family genome sequences play important roles in describing specific microbial clades within species, a framework of support vector machine (SVM) base…