Two new Hie-TAN and Hie-TAN-Lite algorithms improve TAN for hierarchical feature spaces.
problem Learning dependencies in hierarchical feature spaces.
method Exploits hierarchical parent-child relationships as constraints to learn a dependency tree.
result Hie-TAN-Lite outperforms Hie-TAN and other methods in predictive accuracy.
SHAP explains boosted trees with additively modeled features.
problem Explaining predictions of boosted trees models with additively modeled features.
method SHAP values for additively modeled features in boosted trees models.
result SHAP dependence plot matches partial dependence plot for additively modeled features.
Study a risk model with tree-structured Poisson-Markov random field for rainfall events.
problem Dependence between rainfall frequencies in insurance portfolios.
method Tree-structured Markov random field with Poisson marginals.
result Asymptotic results for portfolio risk and risk allocation.
A new method, tree-SNE, solves the scale problem in t-SNE.
problem Clustering and visualizing high-dimensional data, especially MNIST digits.
method Revisits t-SNE idea to create a 2+1 dimensional embedding with a scale parameter.
result The optimal embedding depends continuously on the scale parameter for all initial conditions.
The benefits of diversifying risks are difficult to estimate quantitatively because of the uncertainties in the dependence structure between the risks. Also, the modelling of multidimensional dependencies is a non-trivial task. This paper focuses on one such technique for portfolio aggregation, namely the aggregation o…
Mutual info trees show higher risk in Brazilian equity network during transition.
problem Identifying nonlinear dependencies in Brazilian equity network.
method Used mutual information minimum spanning trees to compare with linear correlation.
result Mutual info trees indicate higher risk and power law tail in volatility transmission.
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.
Neural model parses non-projective dependency trees efficiently.
problem Parsing non-projective dependency trees.
method Probabilistic parsing model using neural representations and Kirchhoff's Matrix-Tree Theorem.
result State-of-the-art parsing performance on nine datasets.
Bayesian context trees capture complex dependencies in categorical sequences.
problem Complex, long-range dependencies in categorical sequences are not well captured by simple models.
method Parsimonious Bayesian context trees with model-based agglomerative clustering for efficient inference.
result The proposed framework outperforms existing models on real-world data.
Proposes a new model for flood extent mapping.
problem Noise, obstacles, heterogeneity, and spatial dependency issues in traditional classification methods.
method Geographical hidden Markov tree, incorporating anisotropic spatial dependency.
result Outperforms multiple baselines in flood mapping.
Subagging improves regression tree performance, especially with many splits.
problem Improving regression tree performance with subsample aggregating.
method Formalized bias and variance dependencies, compared subagging to single trees, and analyzed optimal tree sizes.
result Subagging improves tree performance, especially with many splits.
A novel stepwise VI method using vine copulas for complex latent dependence.
problem Modeling complex latent dependence structures in probabilistic models.
method Stepwise estimation of vine copula parameters using Rényi divergence and a stopping criterion.
result Our method outperforms mean-field VI and is more parsimonious in complex applications.
Adaptive Bayesian model for covariate-dependent power spectra analysis.
problem Estimating complex relationships and interactions between covariates and power spectra.
method Bayesian sum of trees model with local power spectrum estimation and reversible-jump MCMC for tree modifications.
result The method can accurately recover both smooth and abrupt changes in power spectra across multiple covariates.
Develops a new multivariate regression model for complex outcomes.
problem Flexible, heterogeneous, and residual-dependent multivariate regression problems.
method MultiVCBART framework with Graphical Horseshoe priors.
result Empirically outperforms existing models on sparse, high-dimensional datasets.
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 present the first tree-based regressor whose convergence rate depends only on the intrinsic dimension of the data, namely its Assouad dimension. The regressor uses the RPtree partitioning procedure, a simple randomized variant of k-d trees.
We study the bilipschitz equivalence type of tree-graded spaces, showing that asymptotic cones of relatively hyperbolic groups (resp. asymptotic cones of groups containing a cut-point) only depend on the bilipschitz equivalence types of the pieces in the standard (resp. minimal) tree-graded structure. In particular, th…
Algorithm removes leaves to find root in uniform trees.
problem Finding the root in large uniform attachment trees.
method Leaf-stripping algorithm recursively removes leaves.
result Set of remaining vertices contains the root with high probability.
New tests for conditional copulas based on decision trees.
problem Testing constancy of conditional dependence structure given conditioning events.
method Data-driven decision trees to maximize differences in conditional Kendall's tau.
result Asymptotic distributions of test statistics under the null hypothesis.
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 …
Locally adaptive clustering for tree delineation.
problem Tree delineation from distance data.
method Locally adaptive hierarchical cluster termination.
result Multi-scale alternative to conventional termination criteria.
We study periodic wind-tree models, billiards in the plane endowed with Z2-periodically located identical connected symmetric right-angled obstacles. We show asymptotic formulas for the number of (isotopy classes of) closed billiard trajectories (up to Z2-translations) on the wind-tree billiard.…
New algorithm efficiently learns sparse staged trees.
problem Scalability issue in existing structural learning algorithms for staged trees.
method Searches over a space of models with limited dependencies.
result First scalable structural learning algorithm for staged trees.
We generate counterfactual explanations for tree-based boosting ensembles.
problem Understanding how tree-based models make predictions.
method Extending a method for random forests to GBDTs, accounting for tree sequential dependency and negative gradients.
result A method to generate counterfactual explanations for GBDTs.
Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that the dynamics of the underlying asset's price forms a binomial tree if a partitio…
In this paper we analyzed dependencies in commodity markets investigating correlations of future contracts for commodities over the period 1998.09.01 - 2007.12.14. We constructed a minimal spanning tree based on the correlation matrix. The tree provides evidence for sector clusterization of investigated contracts. We a…
Dynamic Vine Copulas detect and quantify time-varying higher-order interactions in multivariate systems.
problem Time-varying dependence in multivariate systems, including tail behavior, asymmetry, and conditional structure.
method Dynamic Vine Copulas (DVC) framework for estimating and diagnosing non-Gaussian dependence, using fixed-root-order C-vines and smooth parameter trajectories.
result DVC detects and quantifies time-varying higher-order interactions, distinguishing between pairwise and conditional dependence.
Efficiently models tree-like data with coupled branches using HMMs.
problem Modeling sequential data with coupled branches in biological systems.
method Developed a dynamic programming algorithm for tree-based HMMs with coupled branches.
result Efficiently solves likelihood, decoding, and parameter learning problems for tree-based HMMs with coupled branches.
The ability to adequately model risks is crucial for insurance companies. The method of "Copula-based hierarchical risk aggregation" by Arbenz et al. offers a flexible way in doing so and has attracted much attention recently. We briefly introduce the aggregation tree model as well as the sampling algorithm proposed by…
A new tree-based estimator, FastPD, efficiently estimates PD functions for machine learning models.
problem Efficiently estimating Partial Dependence functions for machine learning models.
method Proposes a new tree-based estimator, FastPD, to estimate PD functions.
result FastPD consistently estimates the desired population quantity and improves complexity from quadratic to linear.
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.
BART's performance improves with more trees, converging to a Gaussian process.
problem Understanding and explaining BART's superior performance in prediction and causal inference.
method Analyzing BART as the number of trees grows towards infinity, showing convergence to a Gaussian process.
result BART converges to a Gaussian process with favorable inferential properties, explaining its excellent performance.
BooST combines boosting and smooth trees for nonlinear regression.
problem Estimating partial effects in nonlinear models.
method Boosting smooth trees for partial effect estimation.
result BooST provides more interpretable partial effects than tree-based models.
New algorithms identify optimal moves in game trees.
problem Identifying the best move in a game tree quickly.
method Best arm identification procedure applied to depth-one summaries.
result New algorithms outperform existing methods.
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.
Let T be a tree with an action of a finitely generated group G. Given a suitable equivalence relation on the set of edge stabilizers of T (such as commensurability, co-elementarity in a relatively hyperbolic group, or commutation in a commutative transitive group), we define a tree of cylinders T_c. This tree only depe…
A simple and computationally efficient scheme for tree-structured vector quantization is presented. Unlike previous methods, its quantization error depends only on the intrinsic dimension of the data distribution, rather than the apparent dimension of the space in which the data happen to lie.
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…
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.
We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a tree-structured graphical model. Treating the problem as a semiparametric statistical prob…
We consider the problem of modeling discrete-valued vector time series data using extensions of Chow-Liu tree models to capture both dependencies across time and dependencies across variables. Conditional Chow-Liu tree models are introduced, as an extension to standard Chow-Liu trees, for modeling conditional rather th…
Infinite BART model selects number of trees and allows different functions for clusters.
problem Regression and classification analysis with automatic tree selection and cluster-specific functions.
method Incorporates an Indian Buffet process prior to select a subset of decision trees for each observation.
result Infinite BART model outperforms classic BART on simulated and real datasets.
A new method explains mixed features for predictive models using conditional inference trees.
problem Explaining complex machine learning models with mixed features.
method Proposes a method to explain mixed features (continuous, discrete, ordinal, categorical) using conditional inference trees.
result Our method often outperforms current industry standards in various simulation studies and real-world financial data.
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.
We present some explicit constructions of universal R-trees with applications to the asymptotic geometry of hyperbolic spaces. In particular, we show that any asymptotic cone of a complete simply connected manifold of negative curvature is a complete homogeneous R-tree with the valency 2ℵ0 at every point. It…
Multi-stage financial decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future returns of the selected assets or asset categories. Various approaches towards an optimal generation of discrete-time, discrete-state approximations…
Proposes a new online learning strategy for multi-target regression in data streams.
problem Challenges in learning from high-throughput data streams, especially in multi-target regression.
method Extends existing online decision tree learning algorithm to consider inter-target dependencies.
result SST-HT presents superior predictive accuracy compared to state-of-the-art algorithms.
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.