A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density estimator. This paper addresses the basic question of quantifying our uncertainty by ass…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,291 papers · 148 categories
Trend · papers per month
48 results for “Order statistic trees”
The paper proposes a method to efficiently predict using labeled binary trees and analyzes the number of samples needed.
problem Efficiently predicting using compositional nonparametric models.
method A compositional nonparametric method expressed as a labeled binary tree, with a greedy algorithm for regression validation.
result The sufficient number of samples is , and the necessary number of samples is .
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models, hidden Markov models, Gaussian mixture models, and Markov evolutionary trees. The …
Finding statistically significant high-order interaction features in predictive modeling is important but challenging task. The difficulty lies in the fact that, for a recent applications with high-dimensional covariates, the number of possible high-order interaction features would be extremely large. Identifying stati…
Integrates differentiable decision trees into neural networks for faster training and inference.
problem Combining differentiability and conditional computation in tree ensembles for neural networks.
method Sparse activation function and specialized forward/backward propagation algorithms for efficient training and inference.
result 10x speed-ups and 20x reduction in parameters compared to existing methods, while maintaining performance.
Mathematical foundation for phylogenetic tree uncertainty quantification.
problem Uncertainty in evolutionary relationships between species.
method Introducing the Wald space as a subset of symmetric positive definite matrices, studying its topology and structure, and proposing a new numerical method for geodesics and curvature.
result Wald space has a topology of disjoint open cubes, is contractible, and is a Whitney stratified space of type (A).
Decision tree learning is a popular approach for classification and regression in machine learning and statistics, and Bayesian formulations---which introduce a prior distribution over decision trees, and formulate learning as posterior inference given data---have been shown to produce competitive performance. Unlike c…
Efficient algorithm for SSVM reduces computation time and scales to large datasets.
problem Efficiently training SSVM for large patient data sets.
method Directly optimizes primal objective function with truncated Newton optimisation and order statistic trees.
result Significantly reduces computational costs and scales to larger datasets.
New algorithm avoids re-planning in tree-search algorithms, reducing suboptimal actions.
problem Avoiding re-planning in tree-search algorithms to reduce suboptimal actions.
method A new algorithm that decides at each step whether to re-plan or use a sub-tree, based on sub-tree statistics.
result The probability of selecting a suboptimal action converges to zero and decays logarithmically.
New method finds significant high-order interactions efficiently.
problem Finding statistically significant high-order interactions in high-dimensional data.
method Extends selective inference to high-order interaction models with pruning strategy.
result Demonstrated efficient and powerful method for high-order interactions.
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.
New method for summarizing ranking distributions using consensus ranking distributions.
problem Summarizing ranking distributions efficiently and accurately.
method Introducing consensus ranking distributions and a top-down tree-structured statistical algorithm.
result Optimal distortion can be expressed as a function of pairwise probabilities, enabling efficient learning methods.
New methods improve tree ensemble models by compressing them while maintaining accuracy.
problem Theoretical understanding and practical compression of tree ensembles like random forests and gradient boosting machines.
method Spectral perspective on tree ensembles, deriving minimax rates and developing compression schemes.
result Leading eigenfunctions/singular vectors capture dominant predictive directions, leading to smaller, competitive models.
New method wraps black-box classifiers to reduce bias.
problem Reduction of bias in black-box predictions.
method Post-processing with α-trees and boosting algorithms.
result Demonstrated effectiveness in reducing bias across multiple fairness metrics.
A new test statistic counts tree co-occurrences to detect edge correlation between networks.
problem Detecting edge correlation between networks using latent vertex correspondence.
method The test statistic is based on counting co-occurrences of signed trees for a family of non-isomorphic trees.
result The test runs in time and succeeds with high probability for large .
The study provides theoretical guarantees for the statistical performance of optimal decision trees.
problem Theoretical limits on the statistical performance of globally optimal decision trees.
method Sharp oracle inequalities and uniform concentration framework based on Rademacher complexity.
result Derivation of minimax optimal rates for piecewise sparse heterogeneous anisotropic Besov space.
Optimizes random forest inference by defining step order to maximize accuracy.
problem Limited inference time in resource-constrained systems.
method Designs anytime random forest algorithm on step granularity, proposing optimal step order.
result Backward Squirrel Order performs nearly as well as the optimal step order.
AutoML uses MCTS to optimize machine learning algorithms and hyperparameters.
problem Optimizing machine learning algorithms and hyperparameters efficiently.
method MCTS-based approach for hybrid optimization of machine learning portfolios.
result Mosaic outperforms Auto-Sklearn on OpenML 100 benchmark and Scikit-learn portfolio.
It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of…
Paper estimates the order of vertices in random recursive trees.
problem Estimating the order of arrival of vertices in random recursive trees.
method Proposes an order estimator based on the Jordan centrality measure and defines risk measures.
result Establishes a nearly optimal estimator for the problem.
Decision trees improve performance in various fields.
problem Improving performance in machine learning and data mining.
method Introduce tree-based models and training techniques.
result Highlight probabilistic characteristics and practical benefits.
TD-GEN generates graphs using tree decomposition, improving efficiency and performance.
problem Efficiently generating graphs with statistical properties.
method Tree decomposition, permutation invariant tree generation, incremental graph generation.
result Improved graph generation efficiency and performance.
Modelling hetegeneous treatment effects by quantitle local polynomial decision tree and forestecon.EM
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.
In this paper, we propose the distributed tree kernels (DTK) as a novel method to reduce time and space complexity of tree kernels. Using a linear complexity algorithm to compute vectors for trees, we embed feature spaces of tree fragments in low-dimensional spaces where the kernel computation is directly done with dot…
The paper proposes a new probability distribution for rooted trees.
problem Overfitting in tree selection for statistical models.
method Bayesian approach with a generalized probability distribution for rooted trees.
result Recursive methods to evaluate the probability distribution without approximations.
Extremely Fast Decision Tree improves accuracy on large datasets.
problem Improving accuracy on large classification datasets.
method Hoeffding Anytime Tree, a modified version of Hoeffding Tree.
result Extremely Fast Decision Tree achieves superior prequential accuracy on most UCI datasets.
Adaptive Bayesian Reticulumstat.ML
Combines neural networks and decision trees for supervised learning.
problem Challenges in optimizing hierarchical parameters and constructing tree structures.
method Probabilistic approach with modified gradient ascent and adaptive tree construction.
result Novel classification and regression technique that combines strengths of neural networks and decision trees.
GAMI-Tree uses model-based trees to fit low-order fANOVA models.
problem Fitting interpretable fANOVA models with low-order interactions.
method GAMI-Tree uses model-based trees and a new interaction filtering method.
result GAMI-Tree outperforms EBM and GAMI-Net in predictive performance and interpretability.
Extreme classification problems are multiclass and multilabel classification problems where the number of outputs is so large that straightforward strategies are neither statistically nor computationally viable. One strategy for dealing with the computational burden is via a tree decomposition of the output space. Whil…
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.
This paper introduces a new method to cluster qualitative attribute data using tree structures.
problem Clustering qualitative attribute data, especially when values are not in Euclidean space.
method Developed a joint learning mechanism to iteratively learn trees representing qualitative values' order relationships.
result The joint learning mechanism successfully clusters qualitative attribute data, yielding accurate results.
ID3 generates near-optimal decision trees for DNFs under product distributions.
problem Understanding the optimality of decision trees generated by ID3.
method Introducing a new metric (MIC) to measure the optimality of ID3-generated trees and comparing it with other algorithms.
result The TopDown variant of ID3 is near-optimal in learning read-once DNFs under product distributions, while another variant is not.
Collaborative Trees model analyzes feature interactions and additive effects.
problem Analyzing complex statistical associations between features and response variables.
method Proposes a novel tree model and its bagging version to decompose mean decrease in impurity and visualize feature contributions.
result Demonstrates the superior capability of the tree model in estimating additive effects and interaction effects.
Flexible tree ensemble learning framework supports arbitrary loss functions and multi-task learning.
problem Limited modeling capabilities of existing tree ensemble learning toolkits.
method Differentiable tree ensembles with tensor-based formulation for efficient training.
result Our framework leads to 100x more compact and 23% more expressive tree ensembles.
Efficient algorithm for matching graphs with community structure.
problem Graph matching between correlated stochastic block models with constant correlation.
method Partition trees rooted from each vertex, comparing edge statistics to different communities.
result First low-order polynomial-time algorithm achieving exact matching with high probability in dense graphs.
Tree-based LSTM improves sequential regression with missing data.
problem Regression for variable-length sequential data with missing samples.
method Tree architecture of LSTM networks, selecting LSTM networks based on presence-pattern of previous inputs.
result Significant performance improvements on financial and real-life datasets.
The paper introduces a method to incorporate feedback into tree-based anomaly detection to reduce false positives.
problem Difficulty in human analysts examining high-ranking anomalies due to false positives.
method Incorporates simple binary feedback into tree-based anomaly detectors, focusing on the Isolation Forest algorithm.
result Significantly improves the performance of the Isolation Forest algorithm by reducing false positives.
This paper solves the open problem of computing Bayes optimal prediction for decision trees using a Markov chain Monte Carlo method.
problem Computing the Bayes optimal prediction for decision trees is infeasible due to an infeasible summation over all division patterns of a feature space.
method Solved the open problem using a Markov chain Monte Carlo method with adaptively tuned step size.
result Computed the Bayes optimal prediction for decision trees using a Markov chain Monte Carlo method.
iRF detects stable high-order interactions in genomics data.
problem Understanding high-order interactions in genomics data.
method Iterative Random Forest algorithm (iRF) for stable high-order interaction detection.
result iRF identifies stable high-order interactions with computational cost similar to Random Forest.
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.
We investigate hierarchical structures of the European countries by using debt as a percentage of Gross Domestic Product (GDP) of the countries as they change over a certain period of time. We obtain the topological properties among the countries based on debt as a percentage of GDP of European countries over the perio…
Energy trees handle complex data structures with multiple variable types.
problem Handling intricate data structures with various types of covariates.
method Energy trees, a regression and classification model, use energy statistics to accommodate structured covariates of different types.
result Energy trees maintain statistical foundations, interpretability, and robustness to overfitting.
Paper proposes a method to estimate confidence bands for survival random forests.
problem No statistically valid and computationally feasible approach for estimating confidence bands for survival random forests.
method Extending recent developments in infinite-order incomplete U-statistics, the paper proposes an unbiased confidence band estimation.
result The proposed method accurately estimates the confidence band and achieves desired coverage rate.
BART and MOTR-BART improve tree-based predictions with local linear models.
problem Non-linearity and high-order interactions in data.
method Bayesian Additive Regression Trees (BART) and Model Trees BART (MOTR-BART) using piecewise linear functions.
result MOTR-BART achieves equal or better performance with fewer trees than BART.
Proposes a new method for subgroup analysis using optimal trees with parameter fusion.
problem Challenges of greedy heuristics and overfitting in tree-based recursive partitioning methods.
method Fused optimal causal tree method leveraging mixed integer optimization (MIO) for globally optimal partitions and parameter fusion.
result Substantial improvement in subgroup discovery accuracy and statistical efficiency.
This paper uses ML and EVT to analyze tree ring data, improving accuracy of predictions.
problem Analyzing tree ring data for climate modeling and historical studies.
method Combines machine learning algorithms with extreme value theory for data analysis.
result Random Forest method yields the most accurate results for tree ring data analysis.
Ensembles of randomized decision trees, usually referred to as random forests, are widely used for classification and regression tasks in machine learning and statistics. Random forests achieve competitive predictive performance and are computationally efficient to train and test, making them excellent candidates for r…
The paper stabilizes tree-based explanations for machine learning models.
problem Stability of tree-based explanations in machine learning models.
method Develops tests and stopping rules to ensure stability of decision tree explanations.
result Ensures that tree-based explanations are robust to small changes in training data.