Random survival forests (RSF) are a powerful method for risk prediction of right-censored outcomes in biomedical research. RSF use the log-rank split criterion to form an ensemble of survival trees. The most common approach to evaluate the prediction accuracy of a RSF model is Harrell's concordance index for survival d…
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.
168,695 papers · 148 categories
Trend · papers per month
48 results for “splitting criterion”
We define "fat" train tracks and use them to give a combinatorial criterion for the Hempel distance of Heegaard splittings for closed orientable 3-manifolds. We apply this criterion to 3-manifolds obtained from surgery on knots in the three sphere.
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.
We give a parity condition of a Heegaard diagram to show that it is unstabilized. This improves the result of [5]. As an application, we construct unstabilized Heegaard splittings by Dehn twists on any given Heegaard splitting.
We use Heegaard splittings to give a criterion for a tunnel number one knot manifold to be non-fibered and to have large cyclic covers. We also show that such a knot manifold (satisfying the criterion) admits infinitely many virtually Haken Dehn fillings. Using a computer, we apply this criterion to the 2 generator, no…
Improved decision tree learning guarantees for complex functions.
problem Achieving provable guarantees for decision tree induction with complex target functions.
method Introduces a new splitting criterion that considers correlations between target function and subsets of attributes.
result Proves provable guarantees for all target functions with respect to the uniform distribution, circumventing previous impossibility results.
The study shows involutory quandles of certain links are not left-orderable.
problem Determining left-orderability of involutory quandles of links.
method Using a non-left-orderability criterion for involutory quandles of non-split links, the study improved previous results and introduced new families of links.
result The involutory quandles of non-trivial alternating links and certain augmented alternating links are not left-orderable.
Machine learning algorithms aim at minimizing the number of false decisions and increasing the accuracy of predictions. However, the high predictive power of advanced algorithms comes at the costs of transparency. State-of-the-art methods, such as neural networks and ensemble methods, often result in highly complex mod…
We develop a progressive training approach for neural networks which adaptively grows the network structure by splitting existing neurons to multiple off-springs. By leveraging a functional steepest descent idea, we derive a simple criterion for deciding the best subset of neurons to split and a splitting gradient for …
We prove an explicit, quantitative criterion that ensures the Heegaard surfaces in Dehn fillings behave "as expected." Given a cusped hyperbolic manifold X, and a Dehn filling whose meridian and longitude curves are longer than 2pi(2g-1), we show that every genus g Heegaard splitting of the filled manifold is isotopic …
An immersed concordance between two links is a concordance with possible self-intersections. Given an immersed concordance we construct a smooth four-dimensional cobordism between surgeries on links. By applying -invariant inequalities for this cobordism we obtain inequalities between the -functions of links, whi…
Significance-First Splitting: Aligning Treatment Heterogeneity Detection with Honest Estimationstat.ME
A hybrid algorithm fuses significance-based splitting with honest sample-splitting for estimating heterogeneous treatment effects.
problem Estimating heterogeneous treatment effects while maintaining valid inference.
method Significance-first splitting using a squared -statistic for treatment side interaction.
result Achieves approximately 90% CI coverage at the 90% nominal level across various synthetic designs and datasets.
Exact distribution of split conformal prediction coverage found.
problem Determining the reliability of prediction sets in batch mode.
method Analysis of exchangeable data to find universal distribution of empirical coverage.
result Exact distribution of empirical coverage is universal and determined by nominal miscoverage level and calibration sample size.
The splitting number of a link is the minimal number of crossing changes between different components required to convert it into a split link. We obtain a lower bound on the splitting number in terms of the (multivariable) signature and nullity. Although very elementary and easy to compute, this bound turns out to be …
Study rigidity in low-regularity Riemannian and semi-Riemannian metrics.
problem Rigidity problems for low-regularity metrics.
method Proves Cheeger-Gromoll splitting theorem and flatness criterion for semi-Riemannian metrics of regularity.
result Obtains isometry of higher regularity than Lipschitz.
A new method identifies class-specific covariates in multi-class prediction tasks.
problem Identifying covariates specifically associated with one or more outcome classes in multi-class prediction tasks.
method Introducing multi forests (MuFs) with multi-way and binary splits to measure class-associated discriminatory ability.
result The multi-class VIM specifically ranks class-associated covariates highly, unlike conventional VIMs.
We give a simple criterion for a Heegaard splitting to yield a Haken manifold. As a consequence, we construct many Haken manifolds, in particular homology spheres, with prescribed properties, namely Heegaard genus, Heegaard distance and Casson invariant. Along the way we give simpler and shorter proofs of the existence…
In this paper we show that for a given 3-manifold and a given Heegaard splitting there are finitely many preferred decomposing systems of disjoint essential disks. These are characterized by a combinatorial criterion which is a slight strengthening of Casson-Gordon's rectangle condition. This is in contrast to…
We explore the combination theorem for a group G splitting as a graph of relatively hyperbolic groups. Using the fine graph approach to relative hyperbolicity, we find short proofs of the relative hyperbolicity of G under certain conditions. We then provide a criterion for the relative quasiconvexity of a subgroup H de…
It is well known that the out-of-sample performance of Markowitz's mean-variance portfolio criterion can be negatively affected by estimation errors in the mean and covariance. In this paper we address the problem by regularizing the mean-variance objective function with a weighted elastic net penalty. We show that the…
This paper studies a subgroup of the Goeritz group related to Heegaard splittings induced by openbook decompositions.
problem Understanding the subgroup of the Goeritz group associated with Heegaard splittings from openbook decompositions.
method Analyzes the mapping class group of a 3-manifold, focusing on elements that preserve the binding and commute with the monodromy.
result Characterizes the Goeritz group subgroup as a quotient of specific mapping class groups and provides a criterion for certain elements.
Two criteria for a closed connected definite 4-manifold with infinite cyclic fundamental group to be TOP-split are given. One criterion extends a sufficient condition made in a previous paper. The result is equivalent to a purely algebraic result on the question asking when a positive definite Hermitian form over the r…
Study on hyperbolic groups, focusing on separability and splittings.
problem Coarse separability and splittings in hyperbolic groups.
method Quantitative analysis of volume growth and cut-sets, focusing on thickened spheres.
result One-ended hyperbolic groups that are not virtually surface groups are coarsely separable by a subset of subexponential growth if and only if they split over a virtually cyclic subgroup.
The construction of efficient and effective decision trees remains a key topic in machine learning because of their simplicity and flexibility. A lot of heuristic algorithms have been proposed to construct near-optimal decision trees. ID3, C4.5 and CART are classical decision tree algorithms and the split criteria they…
Paper finds a counterexample showing rectangle condition doesn't detect strong irreducibility.
problem Detecting strong irreducibility from the rectangle condition.
method Constructing a double branched cover of a knot in S^3.
result Found a genus 2 Heegaard splitting that is strongly irreducible but fails rectangle condition.
Metric spaces with certain curvature properties are universally infinitesimally Hilbertian.
problem Analyzing the infinitesimal geometry of metric spaces with curvature bounds.
method Proving a metric space with a Gromov-Hausdorff tangent splitting property is universally infinitesimally Hilbertian.
result Metric spaces with curvature bounds are universally infinitesimally Hilbertian.
Covariance-Driven Regression Trees reduce overfitting in CART.
problem Overfitting in CART decision trees, especially with small sample sizes.
method Covariance-driven splitting criterion for regression trees (CovRT).
result CovRT achieves superior prediction accuracy compared to CART in simulations and real-world tasks.
New algorithm reduces discrimination in predictions.
problem Tackles potential discrimination in AI predictions.
method Integrates fairness adjustments into tree-building process.
result Reduces discriminatory predictions without significant loss in accuracy.
The most popular approach for analyzing survival data is the Cox regression model. The Cox model may, however, be misspecified, and its proportionality assumption may not always be fulfilled. An alternative approach for survival prediction is random forests for survival outcomes. The standard split criterion for random…
Given an injective amalgam at the level of fundamental groups and a specific 3-manifold, is there a corresponding geometric-topological decomposition of a given 4-manifold, in a stable sense? We find an algebraic-topological splitting criterion in terms of the orientation classes and universal covers. Also, we equivari…
In hyperbolic space, the angle of intersection and distance classify pairs of totally geodesic hyperplanes. A similar algebraic invariant classifies pairs of hyperplanes in the Einstein universe. In dimension 3, symplectic splittings of a 4-dimensional real symplectic vector space model Einstein hyperplanes and the inv…
Holomorphic Lie algebroid connections on Riemann surfaces are characterized.
problem Characterizing holomorphic Lie algebroid connections on Riemann surfaces.
method Analyzes conditions for holomorphic vector bundles to admit Lie algebroid connections based on Lie algebroid properties.
result Conditions for holomorphic vector bundles to admit holomorphic Lie algebroid connections are determined.
Centroid Decision Foreststat.ML
CDF uses centroids to split features for high-dimensional classification.
problem High-dimensional classification problems with complex class structures.
method CDF introduces a centroid-driven splitting strategy in decision trees.
result CDF outperforms conventional methods in high-dimensional classification.
FedForest adapts RF for federated learning, improving performance and efficiency.
problem Adapting RF for federated learning with heterogeneous data.
method FedForest uses a novel splitting procedure to aggregate client statistics, allowing non-parametric personalization.
result FedForest's federated RF achieves performance close to centralized models while being communication-efficient.
We propose an algorithm named best-scored random forest for binary classification problems. The terminology "best-scored" means to select the one with the best empirical performance out of a certain number of purely random tree candidates as each single tree in the forest. In this way, the resulting forest can be more …
Study equivariant isotopy in higher dimensions, finding exceptions.
problem Under what conditions are equivariant isotopic diffeomorphisms also equivariantly isotopic?
method Construct an invariant valued in the homology of an infinite cover to distinguish isotopic from equivariantly isotopic diffeomorphisms.
result Many equivariant diffeomorphisms are isotopic but not equivariantly isotopic in higher dimensions.
A new method for automatic gradient tree boosting using information theory.
problem Automatic selection of tree complexity and number in gradient boosting.
method Optimism of greedy leaf splitting procedure modeled as a Cox-Ingersoll-Ross process, leading to an information criterion for model selection.
result The method achieves significant speedups (10-1400) compared to xgboost without sacrificing predictive power.
New Random Forest variants estimate heterogeneous treatment effects using Wasserstein distances.
problem Estimating heterogeneous treatment effects in complex situations.
method Proposes natural variants of Random Forests using Wasserstein distances.
result Natural variants of Random Forests are well-suited for estimating conditional distributions.
The paper explores conditions for sections in Lefschetz fibrations and bundles over 2-complexes.
problem Conditions for sections in Lefschetz fibrations and bundles over 2-complexes.
method Algebraic criteria and topological conditions.
result Complete algebraic criterion for sections in Lefschetz fibrations over the disk.
We call a singularity of a presymplectic form removable in its graph if its graph extends to a smooth Dirac structure over the singularity. An example for this is the symplectic form of a magnetic monopole. A criterion for the removability of singularities is given in terms of regularizing functions for pure spinor…
Enhances Random Forest for imbalanced functional data classification.
problem Challenges in classifying imbalanced functional data.
method Functional Random Forest with Adaptive Cost-Sensitive Splitting (FRF-ACS).
result Significantly improves minority class recall and predictive performance.
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.
Paper introduces a novel approach to generalize models without validation data.
problem Achieving generalization in machine learning without validation data.
method Introduces a new risk measure and a novel criterion for training models.
result Demonstrates that the new approach outperforms popular methods in generalization and estimation tasks.
The paper studies weak singular Hermite-Einstein structures on homogeneous vector bundles.
problem Existence of weak singular Hermite-Einstein structures on homogeneous holomorphic vector bundles.
method Using Cartan's highest weight theory, the paper establishes an algebraic criterion for topological splitting and decouples the prescribed mean curvature equation.
result A sufficient algebraic condition for realizing an -function as the mean curvature of a singular Hermitian structure on an irreducible homogeneous bundle.
Proposes a simple solution to Gini importance bias in random forests.
problem Gini importance measure in random forests is biased and unreliable.
method Computes loss reduction on out-of-bag samples instead of in-bag.
result Solves the misleading/untrustworthy Gini importance issue.
Early stopping is a widely used technique to prevent poor generalization performance when training an over-expressive model by means of gradient-based optimization. To find a good point to halt the optimizer, a common practice is to split the dataset into a training and a smaller validation set to obtain an ongoing est…
This paper deals with unsupervised clustering with feature selection. The problem is to estimate both labels and a sparse projection matrix of weights. To address this combinatorial non-convex problem maintaining a strict control on the sparsity of the matrix of weights, we propose an alternating minimization of the Fr…
New statistics improve kernel independence testing efficiency.
problem Improving efficiency in kernel independence testing.
method Adapting martingale MMD construction to joint independence problem.
result Two new statistics achieve finite-sample consistency with linear per-test cost.