arXiv research

Introduces CSST and characterizes its topology.

We show how to associate an R-tree to the set of cut points of a continuum. If X is a continuum without cut points we show how to associate an R-tree to the set of cut pairs of X.

We show that every inner metric space X is the metric quotient of a complete R-tree via a free isometric action, which we call the covering R-tree of X. The quotient mapping is a weak submetry (hence, open) and light. In the case of compact 1-dimensional geodesic space X, the free isometric action is via a subgroup of …

We prove that a continuum $X$ is tree-like (resp. circle-like, chainable) if and only if for each open cover $\U_4=\{U_1,U_2,U_3,U_4\}$ of $X$ there is a $\U_4$-map $f:X\to Y$ onto a tree (resp. onto the circle, onto the interval). A continuum $X$ is an acyclic curve if and only if for each open cover $\U_3=\{U_1,U_2,U…

Derives Black-Scholes model without stochastic calculus or PDEs.

We introduce a concept of tree-graded metric space and we use it to show quasi-isometry invariance of certain classes of relatively hyperbolic groups, to obtain a characterization of relatively hyperbolic groups in terms of their asymptotic cones, to find geometric properties of Cayley graphs of relatively hyperbolic g…

Uniformly branching trees are equivalent to certain metric spaces.

We define and give explicit construction of the universal tree-graded space with a given collection of pieces. We apply that to proving uniqueness of asymptotic cones of relatively hyperbolic groups whose peripheral subgroups have unique asymptotic cones. Modulo the Continuum Hypothesis, we show that if an asymptotic c…

Study shows how discrete graph curvature relates to manifold curvature.

We describe a novel algorithm for noisy global optimisation and continuum-armed bandits, with good convergence properties over any continuous reward function having finitely many polynomial maxima. Over such functions, our algorithm achieves square-root regret in bandits, and inverse-square-root error in optimisation, …

The paper introduces ESG valuation in option pricing using binomial trees.

We analyze convergence of Fermat distances and their application in clustering.

Random trees emerge from geodesics in hyperbolic groups.

Random free group outer automorphisms are geometric and have nongeometric attracting trees.

Riemannian first-passage percolation (FPP) is a continuum model, with a distance function arising from a random Riemannian metric in $\R^d$. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that …

Alpha-trimming prunes trees in random forests to improve predictive performance.

Random trees found in Outer space boundary.

The paper proves Lipschitz regularity of graph Laplacian eigenvectors on random data clouds.

A new randomized tree classifier outperforms traditional CARTs.

Single tree outperforms random forest in testing accuracy.

A single slow-growing tree matches Random Forest's performance.

Gradient boosting with randomized trees reduces discontinuities and complexity.

Study of projective Fraïssé limits of trees with confluent epimorphisms.

A new tree-based model improves uncertainty estimation in sequential optimization.

A new decision tree variant improves linear model performance.

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 methods improve prediction performance and reduce computation time in boosting and random forest models.

A new method for decision tree selection in recommendation systems.

SBT model uses randomized sharding and sub-models to improve Bayesian Additive Regression Trees.

A new random forest algorithm improves tree construction for optimal performance.

Develops RKHS framework for analyzing tree ensembles.

Method uses trinomial trees to price nontraditional options.

RFIT uses interaction trees to estimate individualized treatment effects in randomized trials.

This study argues for pruning trees in random forests to improve performance in low signal-to-noise scenarios.

Detecting correlated trees helps align sparse graphs.

Smooth knots can be embedded into a specific Menger continuum.

Improved Random Forests detect pure interactions better.

Enhances random forest performance with exogenous randomness.

Study a risk model with tree-structured Poisson-Markov random field for rainfall events.

A new Bayesian Decision Tree algorithm for regression and classification.

Paper studies ensemble probabilistic regression trees for smooth approximations.

The paper uses regression trees/random forests to price Bermudan options more efficiently.

Optimizes random forest inference by defining step order to maximize accuracy.

Two algorithms for interpreting and boosting tree-based models using rule covering.

BART's performance improves with more trees, converging to a Gaussian process.

TRUST improves tree models' accuracy while maintaining interpretability.

We prove the following result announced in Todorov and Valov: Any homogeneous, metric $ANR$-continuum is a $V^n_G$-continuum provided $\dim_GX=n\geq 1$ and $\check{H}^n(X;G)\neq 0$, where $G$ is a principal ideal domain. This implies that any homogeneous $n$-dimensional metric $ANR$-continuum with $\check{H}^n(X;G)\neq…

Estimates tree-based density from random vectors.