We propose a tree regularization framework, which enables many tree models to perform feature selection efficiently. The key idea of the regularization framework is to penalize selecting a new feature for splitting when its gain (e.g. information gain) is similar to the features used in previous splits. The regularizat…
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48 results for “regular trees”
Proposes regional tree regularization for interpretable deep models.
problem Lack of interpretability in deep neural networks.
method Encourages deep models to be well-approximated by separate decision trees for predefined regions of the input space.
result Regional tree regularization delivers more accurate predictions than training separate decision trees for each region, while producing simpler explanations.
Study shows critical exponents for tree-acting groups.
problem Understanding critical exponents of discrete groups on trees.
method Explicit construction of edge-indexed graphs.
result Proven existence of groups with specific critical exponents.
Tree regularization makes deep models interpretable by approximating them with simple decision trees.
problem Lack of interpretability in deep neural networks.
method Tree regularization to train deep models to resemble compact, axis-aligned decision trees.
result Tree regularized models are easier for humans to interpret without sacrificing accuracy.
L1-orthogonal regularization improves decision tree explainability of deep neural networks.
problem Lack of explainability in deep neural networks.
method L1-orthogonal regularization during training of decision trees.
result Decision trees closely approximate trained deep neural networks with improved accuracy and fidelity.
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 regularization, variable selection procedure.
result New high-probability generalization error bounds for piecewise-linear regression trees.
The paper studies quasi-Sturmian colorings on regular trees, distinguishing bounded and unbounded types.
problem Coloring regular trees with quasi-Sturmian properties.
method Developed an induction algorithm similar to Sturmian colorings, distinguishing types by recurrence function.
result Obtained an induction algorithm for quasi-Sturmian colorings on regular trees.
A new algorithm, Regular Tree Search, tackles non-convex simulation optimization problems.
problem Non-convex objective functions in simulation optimization.
method Integrates adaptive sampling with recursive partitioning of the search space.
result Proves global convergence and reliably identifies the global optimum.
New method for comparing different mass measures on tree structures using entropy partial transport.
problem Comparing nonnegative measures with different masses on tree structures.
method Entropy Partial Transport (EPT) on extended trees, regularized for fast computation and negative definiteness.
result First closed-form solution for unbalanced OT on tree structures.
Proposes new attribution methods for trees with regularization.
problem Feature attribution for trees trained with regularization.
method Prediction Decomposition Attribution (PreDecomp) and TreeInner.
result TreeInner shows state-of-the-art feature selection performance.
HS improves tree-based models' accuracy and interpretability without changing their structure.
problem Overfitting in tree-based models.
method Hierarchical Shrinkage (HS) post-hoc algorithm that shrinks tree predictions towards ancestor means.
result HS significantly improves predictive performance and interpretability of decision trees and RFs.
Boulevard boosts trees with regularization, converging to a normal distribution.
problem Improving regression model accuracy and uncertainty quantification.
method Regularized stochastic gradient boosting trees with subsampling and shrinkage.
result The algorithm converges to a normal distribution, enabling uncertainty characterization.
Enhancing Robustness of Gradient-Boosted Decision Trees through One-Hot Encoding and Regularizationstat.ML
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, or regularization.
result Regularization enhances GBDT robustness.
This study argues for pruning trees in random forests to improve performance in low signal-to-noise scenarios.
problem Improving random forest performance in scenarios with low signal-to-noise ratio.
method Using regularization theory, the study re-examines the depth of trees in random forests and provides evidence that shallow trees are advantageous.
result Random forests with shallow trees are advantageous when the signal-to-noise ratio is low.
Dynamic CBDT improves treatment effect estimation in clinical data.
problem Estimating heterogeneous treatment effects in observational data with high accuracy and interpretability.
method Dynamic Regularized Causal Boosted Decision Trees (CBDT) integrating variance regularization and calibration.
result Significantly improved estimation accuracy and reliable coverage of true treatment effects.
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.
New framework optimizes classification trees with logistic loss and regularization.
problem Improving interpretability and generalization of classification trees.
method Developed a generalized framework for CTs, incorporating logistic loss and regularization.
result Optimal Logistic Tree model outperforms state-of-the-art MIP-based approaches in terms of interpretability and generalization.
Regularizes decision trees to reduce inference time by up to 4x with minimal accuracy loss.
problem Optimizing decision tree execution time on resource-constrained devices.
method Regularizes impurity computation during CART algorithm training to favor highly asymmetric distributions.
result Reduces inference time by up to 4x with minimal accuracy loss.
New method improves feature selection in tree-based models.
problem Previous feature selection methods in tree-based models lack sufficient regularization and sub-optimal performance.
method Developed a new gain penalization approach for tree-based models that allows for flexible feature-specific importance weights.
result The new method improves out-of-sample performance, especially with correlated features.
The lack of interpretability remains a key barrier to the adoption of deep models in many applications. In this work, we explicitly regularize deep models so human users might step through the process behind their predictions in little time. Specifically, we train deep time-series models so their class-probability pred…
We consider certain groups of tree automorphisms as so-called diffeological groups. The notion of diffeology, due to Souriau, allows to endow non-manifold topological spaces, such as regular trees that we look at, with a kind of a differentiable structure that in many ways is close to that of a smooth manifold; a suita…
Symmetric TSP is structurally equivalent to a constrained Group Steiner Tree Problem.
problem Finding the shortest tour in a symmetric TSP.
method Structural equivalence between symmetric TSP and constrained Group Steiner Tree Problem.
result Maximizing net weight in the cGSTP is equivalent to minimizing the TSP tour length.
Why do Random Forests Work? Understanding Tree Ensembles as Self-Regularizing Adaptive Smoothersstat.ML
Paper explains how tree ensembles improve predictions by smoothing and regulating smoothness.
problem Understanding why tree ensembles perform well despite their complexity.
method Interpreting tree ensembles as adaptive and self-regularizing smoothers.
result Ensemble trees make more smooth predictions than individual trees and adjust smoothness based on input dissimilarity.
Let G be a finitely presented group. Scott and Swarup have constructed a canonical splitting of G which encloses all almost invariant sets over virtually polycyclic subgroups of a given length. We give an alternative construction of this regular neighbourhood, by showing that it is the tree of cylinders of a JSJ splitt…
Phylogenetic tree inference using deep DNA sequencing is reshaping our understanding of rapidly evolving systems, such as the within-host battle between viruses and the immune system. Densely sampled phylogenetic trees can contain special features, including "sampled ancestors" in which we sequence a genotype along wit…
Tree ensembles such as random forests and boosted trees are accurate but difficult to understand, debug and deploy. In this work, we provide the inTrees (interpretable trees) framework that extracts, measures, prunes and selects rules from a tree ensemble, and calculates frequent variable interactions. An rule-based le…
New method aggregates nodes in sparse graphical models.
problem Estimating edge-sparse graphical models.
method Tree-aggregated graphical lasso (tag-lasso) method.
result Aggregates nodes in a data-driven fashion using a tree.
Paper shows MCTS approximates policy optimization, proposing an improved variant.
problem Improving AI performance through better MCTS algorithms.
method Shows MCTS approximates policy optimization problem, proposes a new algorithm.
result Proposed algorithm reliably outperforms original AlphaZero in multiple domains.
We study the problem of identifying the source of a diffusion spreading over a regular tree. When the degree of each node is at least three, we show that it is possible to construct confidence sets for the diffusion source with size independent of the number of infected nodes. Our estimators are motivated by analogous …
Paper introduces XBART for nonlinear regression, outperforming XGBoost.
problem Nonlinear regression problems, especially in speed and accuracy.
method Combines Bayesian modeling and recursive partitioning for efficient, accurate predictions.
result XBART provides faster and more accurate predictions than XGBoost.
Sharp bounds for spanning tree entropy in planar lattices.
problem Estimating spanning tree entropy in planar lattice graphs.
method Using hyperbolic geometry and polyhedra volumes.
result Proved bounds are easy to compute and provide excellent estimates.
Forest Garrotestat.ML
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…
A Novel Hyperparameter-free Approach to Decision Tree Construction that Avoids Overfitting by Designcs.LG
A new decision tree method avoids overfitting without hyperparameters.
problem Overfitting in decision trees.
method Hyperparameter-free approach that constructs smaller, shallower trees.
result Avoids overfitting without compromising accuracy or training time.
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.
New algorithm improves convergence of gradient boosting trees.
problem Global convergence of Newton boosting in tabular machine learning.
method Introduces Gradient Regularized Newton Descent for GBDTs, proving linear convergence for smooth, strongly convex losses and rate for general convex losses.
result Achieves globally convergent second-order GBDT algorithm with rate matching first-order boosting.
Groups acting on product trees are boundary rigid.
problem Understanding boundary rigidity of groups acting on product trees.
method Analyzing geometric actions and visual boundaries of groups.
result Visual boundaries of CAT(0) spaces are homeomorphic to a join of two Cantor sets.
A new gradient tree boosting framework reduces variance and accelerates performance.
problem High variance in stochastic gradient boosting.
method Combining gradient tree boosting with importance sampling and a regularizer.
result Achieves a linear convergence rate on logistic loss and 2.5x--18x acceleration on LogitBoost and LambdaMART.
TF Boosted Trees (TFBT) is a new open-sourced frame-work for the distributed training of gradient boosted trees. It is based on TensorFlow, and its distinguishing features include a novel architecture, automatic loss differentiation, layer-by-layer boosting that results in smaller ensembles and faster prediction, princ…
KTBoost combines tree and kernel boosting for better function learning.
problem Learning functions with varying degrees of regularity.
method Combines regression trees and RKHS regression in each boosting iteration.
result KTBoost significantly outperforms tree and kernel boosting in predictive accuracy.
SVR-Tree improves classification trees for imbalanced and sparse data.
problem Classification difficulties in imbalanced and sparse data.
method Proposes SVR-Tree, penalizing the Surface-to-Volume Ratio of decision sets.
result SVR-Tree improves generalization error compared to other imbalance algorithms.
Invariant detects triple points in sphere immersions.
problem Detecting regular homotopy classes of triple-point-free sphere immersions.
method Defining an invariant using a directed tree and integer-valued function.
result Space of triple-point-free spheres has infinitely many regular homotopy classes.
We consider the problem of learning a forest of nonlinear decision rules with general loss functions. The standard methods employ boosted decision trees such as Adaboost for exponential loss and Friedman's gradient boosting for general loss. In contrast to these traditional boosting algorithms that treat a tree learner…
ControlBurn selects few features from tree ensembles for better model interpretability.
problem Improving model interpretability in machine learning models.
method Sparse tree ensembles with lasso optimization.
result ControlBurn selects feature-sparse subsets for better model interpretability.
Tree density estimationmath.ST
Estimates tree-based density from random vectors.
problem Estimating the density of a random vector in high dimensions.
method Optimal spanning tree minimizes Kullback-Leibler divergence; tree density estimate constructed from i.i.d. data.
result Tree density estimate converges to true density as sample size increases.
Universal inequalities for Laplacian eigenvalues on discrete groups.
problem Proving inequalities for Laplacian eigenvalues on discrete groups.
method Analyzing Laplacian eigenvalues with Dirichlet boundary conditions on subsets of discrete groups.
result Yang-type universal inequalities for Cayley graphs of amenable groups and the d-regular tree.
We present a construction, called the limit of a tree system of spaces (or, less formally, a tree of spaces). The construction is designed to produce compact metric spaces that resemble fractals, out of more regular spaces, such as closed manifolds, compact polyhedra, compact Menger manifolds, etc. Such spaces are pote…
Multivariate boosted trees improve forecasting and control by capturing correlated predictions.
problem Capturing multivariate target cross-correlations and applying structured penalties to predictions.
method A computationally efficient algorithm for fitting multivariate boosted trees.
result Multivariate trees outperform univariate counterparts in correlated prediction scenarios.
This study investigates self-supervised learning with Wasserstein distance on tree structures.
problem Improving self-supervised learning methods using Wasserstein distance.
method Utilized Tree-Wasserstein distance (TWD) and Jeffrey divergence regularization for training.
result A simple combination of softmax function and Tree-Wasserstein distance outperforms cosine similarity-based methods.