A new decision tree variant improves linear model performance.
problem Improving decision tree performance on non-linear data.
method Extremely random tree with non-linear data transformation and linear observer.
result Outperforms linear models on benchmark dataset.
PILOT is a fast algorithm for linear model trees that outperforms existing methods.
problem Fitting linear model trees to large datasets efficiently and accurately.
method Greedy training with L2 boosting and model selection rule. result PILOT outperforms standard decision trees and other linear model trees on various datasets.
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.
Piecewise-linear regression trees improve tree-based regression with theoretical and practical benefits.
problem Improving tree-based regression models with theoretical guarantees and practical tractability.
method Regularized piecewise-linear node-splitting criterion, LASSO-type and ℓ2 regularization, variable selection procedure. result New high-probability generalization error bounds for piecewise-linear regression trees.
A new tree-based model for multivariate responses interprets piecewise linear regimes.
problem Recovering piecewise multivariate linear regimes in complex data.
method Twoblock clustering trees with coskewness-based dimension reduction.
result Recovery of piecewise linear regimes in data.
Optimal diagram found for complete graphs with linear trees.
problem Finding optimal diagrams for complete graphs.
method Using a linear tree structure to minimize crossing numbers.
result Optimal diagrams without free hamiltonian cycles for odd n≥7. Paper proposes a novel SVM method for creating survival trees.
problem Creating non-linear survival trees for right-censored data.
method L2-regularized dipole splitting criteria with kernel methods.
result Non-linear splits using polynomial and Gaussian kernels show similar predictive power but often smaller tree sizes.
GLMM trees identify subgroups with different growth patterns in longitudinal data.
problem Identifying subgroups with distinct growth trajectories in longitudinal studies.
method Extended GLMM trees for longitudinal data.
result Extended GLMM trees outperform other methods in accuracy and speed.
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.
Enhanced ODT with Feature Concatenation boosts learning efficiency.
problem Insufficient learning efficiency of ODT due to linear projections not being transmitted to child nodes.
method Feature Concatenation ( exttt{FC-ODT}) to transmit linear projections along decision paths.
result Experiments show exttt{FC-ODT} outperforms state-of-the-art decision trees with a limited tree depth.
New method estimates root-directed tree from extreme data.
problem Discovering causality in river networks from extreme flow data.
method Qualitative max-linear Bayesian network approach to estimate bivariate scores and root-directed spanning tree.
result The new estimator is consistent under max-linear Bayesian network model with noise.
LGB+ improves macroeconomic forecasting by combining linear and tree models.
problem Efficiency in small samples for forecasting with mixed linear and nonlinear dynamics.
method LGB+ is a boosting procedure that evaluates both tree and linear candidates at each step, advancing only the winner. It decomposes forecasts into linear and nonlinear contributions.
result LGB+ delivers strong gains for targets with pronounced autoregressive dynamics or mixed signals.
dtControl uses decision trees to represent controllers efficiently and explainably.
problem Representing controllers concisely and explainably.
method dtControl uses decision tree learning algorithms to represent controllers. Novel techniques for determinizing controllers are introduced.
result Novel techniques for determinizing controllers during decision tree construction are extremely efficient, yielding small decision trees.
Proposes a sparse linear classifier for classification with pairwise dependencies.
problem Classification accuracy is limited by tree-structured graphical models.
method Semi-parametric approach using sparse linear combination of univariate and bivariate log-transformed densities.
result SLB classifier is competitive with popular methods.
The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered trees on the basis of their subpaths, which are vertical substructures of trees resp…
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…
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
problem Efficiently solving unbalanced optimal transport problems on trees.
method Proposed an algorithm that solves a more general unbalanced optimal transport problem exactly in quasi-linear time on a tree metric.
result Solves unbalanced optimal transport on trees in quasi-linear time (less than one second for a tree with one million nodes).
New method identifies causal parameters in tree-shaped linear models using cycles.
problem Identifying causal parameters from correlations in tree-shaped linear models.
method Investigates tree-shaped linear models, uses missing cycles to identify causal parameters, solves quadratic equations.
result Shows how missing cycles can be combined to obtain a unique solution for causal parameters.
Regression Trees analyze stock returns, revealing market excess return as the most informative factor.
problem Understanding informational content of three factors in stock returns.
method Joint regression tree analysis of daily stock return data for 5 major US corporations.
result The market excess return factor is always the most informative in all cases (solo and joint).
The paper uses Column Generation for faster construction of binary decision trees.
problem Constructing efficient univariate binary decision trees for classification tasks.
method Proposes an Integer Linear Programming (ILP) formulation and solves it via Column Generation based heuristic.
result The approach is competitive with state-of-the-art ILP-based algorithms and can handle large datasets.
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…
The paper tackles the computational complexity of PLT algorithms, providing tractable solutions.
problem Finding a tree structure that results in a PLT with low computational costs and low statistical error.
method The paper shows that finding an optimal tree structure is NP-complete. It provides linear time solutions for specific cases and an O(logm) approximation for the general case. result The paper provides tractable solutions for finding a tree structure with low computational costs and low statistical error.
The paper proposes a tree model for interval-valued regression.
problem Learning a real-valued function from interval-valued data.
method Minimizing a margin-based discriminative objective function using a tree structure and dynamic programming.
result The proposed algorithm achieves state-of-the-art speed and accuracy.
We learn sensor trees from training data to minimize sensor acquisition costs during test time. Our system adaptively selects sensors at each stage if necessary to make a confident classification. We pose the problem as empirical risk minimization over the choice of trees and node decision rules. We decompose the probl…
Novel algorithm optimizes decision trees for nonlinear metrics.
problem Optimizing decision trees for nonlinear metrics like F1-score.
method Bi-objective optimisation approach to find optimal trees on Pareto frontier.
result The optimal tree for nonlinear metrics lies on the Pareto frontier.
New algorithm speeds up robustness verification for tree-based models.
problem Formal robustness verification of tree-based models, especially ensembles.
method Reformulated as max-clique problem on a multi-partite graph with bounded boxicity; developed efficient multi-level verification algorithm.
result Tight lower bounds on robustness of decision tree ensembles, hundreds of times faster than previous approach.
Improves tree-based models' interpretability for medical applications.
problem Lack of explainability in tree-based models.
method Developed new algorithms and tools for local and global model understanding.
result Combining local explanations reveals global model structure and identifies non-linear interactions.
This paper uses supervised learning to predict optimal chunk-size for parallel linear algebra operations.
problem Finding the optimal chunk-size for parallel linear algebra operations.
method The paper uses supervised learning models (logistic regression, neural networks, decision trees) to predict the optimal chunk-size for multiple linear algebra operations.
result The custom decision tree model outperforms classical decision trees and other models in predicting optimal chunk-size for linear algebra operations.
Researchers improve tree model recovery from noisy data.
problem Learning tree structured models from corrupted data.
method Linear latent tree models and continuous corruption model.
result Chow-Liu algorithm consistently learns tree from noisy data.
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 …
Enhances GBDT robustness with one-hot encoding and regularization.
problem Low robustness of GBDT models against covariate perturbation.
method One-hot encoding to linear framework, risk decomposition, L1 or L2 regularization. result Regularization enhances GBDT robustness.
A novel tree algorithm improves time series forecasting accuracy.
problem Improving accuracy in non-linear time series forecasting.
method Developed a hierarchical TAR model as a regression tree that trains globally across series, introducing a forecasting-specific tree algorithm with cross-series learning.
result Significantly higher accuracy than state-of-the-art tree-based algorithms and benchmarks across four metrics.
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.
Develops a new method for decision trees using categorical variable structure.
problem Lack of structure in treating categorical variables as predictors.
method Introduces a mathematical framework to represent categorical structure and generalizes decision trees to utilize this structure.
result Improves prediction accuracy on weather data using the new method.
The theme in this paper is the recombining binomial tree to price American put option when the underlying stock follows constant elasticity of variance(CEV) process. Recombining nodes of binomial tree are decided from finite difference scheme to emulate CEV process and the tree has a linear complexity. Also it is deriv…
This paper approximates 1-Wasserstein distance using tree-based embedding.
problem Computational inefficiency of estimating 1-Wasserstein distance.
method L1-regularized approach to learn tree weights, using shortest path distance as a linear model.
result Tree-Wasserstein distance (TWD) approximates 1-Wasserstein distance efficiently.
Variable selection for high-dimensional linear models has received a lot of attention lately, mostly in the context of l1-regularization. Part of the attraction is the variable selection effect: parsimonious models are obtained, which are very suitable for interpretation. In terms of predictive power, however, these re…
Ensemble of regression trees have become popular statistical tools for the estimation of conditional mean given a set of predictors. However, quantile regression trees and their ensembles have not yet garnered much attention despite the increasing popularity of the linear quantile regression model. This work proposes a…
Tree-LIME explains deep learning models using decision trees.
problem Deep learning models are black boxes, making them hard to explain and prone to biases.
method Developed a Tree-LIME approach using decision trees to explain predictions of deep learning models.
result Tree-LIME can capture nonlinear interactions and creates more reliable explanations.
Proposes extensions to semi-parametric models using BART for shared covariates.
problem Avoiding poor coverage properties and reducing bias in linear predictor estimates.
method Modifies tree-generation moves in BART to handle shared covariates between linear and non-parametric components.
result Competitive performance in modelling complex interactions and predicting student achievements.
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.
Two algorithms for interpreting and boosting tree-based models using rule covering.
problem Interpreting and boosting tree-based ensemble methods.
method Mathematical programming models constructed from decision tree rules.
result Selects a few rules that closely match the accuracy of the model.
Kauri is a novel unsupervised binary tree for clustering that outperforms existing methods.
problem Learning a tree end-to-end for clustering without labels is an open challenge.
method Greedy maximization of the kernel KMeans objective without centroids.
result Kauri often outperforms existing unsupervised clustering methods, especially with non-linear kernels.
Linear-time algorithm for optimal assignment in graph matching.
problem Finding optimal assignments between graph vertices efficiently.
method Developed an algorithm for linear-time optimal assignment using tree distances.
result Approximated edit distance between graphs in linear time.
Study finds a linear lower bound on conformal dimension for random hyperbolic groups.
problem Understanding conformal dimension in random hyperbolic groups.
method Building undistorted round trees from lower density groups.
result Achieves a linear lower bound in l at all densities 0<d<1/2. AGBoost uses attention weights to improve GBM for regression problems.
problem Improving gradient boosting machine for regression tasks.
method Attention-based modification of GBM with trainable attention weights.
result AGBoost achieves better performance on regression datasets.
Paper proposes a new method for density estimation using tree tensor-network states.
problem Density estimation for complex graphical models with loops.
method Determines tree topology with Chow-Liu algorithm and uses sketching techniques to define tensor-network components.
result Sample complexity guarantees and empirical validation provided.
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are disjoint. This differs from junction-trees, where two clusters connected by an edge al…