This paper optimizes high-dimensional oblique splits for decision trees, enhancing performance and computational efficiency.
problem Enhancing decision tree performance and computational efficiency in high-dimensional data.
method Established Sufficient Impurity Decrease (SID) convergence for s0-sparse oblique splits, proposing progressive trees for iterative refinement. result Demonstrated that SID function class expands with s0-sparsity, enabling capture of complex data-generating processes. FoLDTree improves oblique decision trees with ULDA, enhancing accuracy and feature selection.
problem Axis-orthogonal splits limit traditional decision trees' performance on oblique decision boundaries.
method Integrates ULDA into decision tree structure for efficient oblique splits, feature selection, and handling missing values.
result FoLDTree outperforms other methods in accuracy and feature selection, comparable to random forest.
Decision trees are a popular technique in statistical data classification. They recursively partition the feature space into disjoint sub-regions until each sub-region becomes homogeneous with respect to a particular class. The basic Classification and Regression Tree (CART) algorithm partitions the feature space using…
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 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.
Decision forests, including Random Forests and Gradient Boosting Trees, have recently demonstrated state-of-the-art performance in a variety of machine learning settings. Decision forests are typically ensembles of axis-aligned decision trees; that is, trees that split only along feature dimensions. In contrast, many r…
Proposes oblique predictive clustering trees for faster, more efficient learning.
problem Learning time scales poorly with output space dimensionality and cannot exploit data sparsity.
method Design and implement oblique splits using linear combinations of features.
result Achieves performance on-par with state-of-the-art methods and is orders of magnitude faster.
New random forest variants achieve optimal performance in high dimensions.
problem Handling dependencies between features in high-dimensional data.
method Using oblique splits in random forests with general split directions.
result Achieved minimax optimal convergence rates in arbitrary dimension.
Machine learning identifies chimera states in complex dynamical systems.
problem Chimera states are hard to identify due to their varied appearance and peculiar nature.
method Machine learning techniques, specifically random forest and oblique random forest with null space regularization.
result High accuracy in identifying chimera states across different dynamical models.
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.
Conventional decision trees have a number of favorable properties, including interpretability, a small computational footprint and the ability to learn from little training data. However, they lack a key quality that has helped fuel the deep learning revolution: that of being end-to-end trainable, and to learn from scr…
Efficient oblique RSF method improves prediction and interpretability.
problem Limited computational efficiency and difficulty in interpreting oblique RSF ensembles.
method Newton-Raphson scoring for computational efficiency and negation importance for variable importance estimation.
result The method reduces computational overhead by 450 times and improves prediction accuracy.
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.
Proposes PredVAR model for reduced-dimensional dynamics from noisy data.
problem Extracting low-dimensional dynamics from high-dimensional noisy data.
method Probabilistic reduced-dimensional vector autoregressive model with oblique projection.
result Iterative algorithm yields dynamic latent variables with rank-ordered predictability.
Unified theory and debiasing framework for random oblique projections in high dimensions.
problem Systematic statistical bias in random oblique projections induced by sampling.
method Unified non-asymptotic theory and debiasing framework.
result Sharp bias--variance characterizations and improved approximation accuracy.
Sparse oblique decision tree improves security rules for renewable power systems.
problem Identifying secure operating conditions in power systems with high renewable energy.
method Sparse weighted oblique decision tree to learn and embed linear security rules.
result The method significantly increases secure states and reduces solution time.
Develops an oblique projection technique to approximate a foliation for non-normal dynamics.
problem Modeling dynamics far from a primary Spectral Submanifold (SSM) in non-normal systems.
method Oblique projection technique based on experimental data.
result Approximates a stable invariant foliation for non-normal dynamics efficiently.
Both neural networks and decision trees are popular machine learning methods and are widely used to solve problems from diverse domains. These two classifiers are commonly used base classifiers in an ensemble framework. In this paper, we first present a new variant of oblique decision tree based on a linear classifier,…
Resource-efficient oblique trees reduce neural signal classification costs.
problem Implementing efficient neural signal classifiers on resource-constrained devices.
method Integrating model compression, probabilistic routing, and cost-aware learning.
result Significant reduction in model size and feature extraction cost compared to state-of-the-art models.
We show how neural models can be used to realize piece-wise constant functions such as decision trees. The proposed architecture, which we call locally constant networks, builds on ReLU networks that are piece-wise linear and hence their associated gradients with respect to the inputs are locally constant. We formally …
We introduce canonical correlation forests (CCFs), a new decision tree ensemble method for classification and regression. Individual canonical correlation trees are binary decision trees with hyperplane splits based on local canonical correlation coefficients calculated during training. Unlike axis-aligned alternatives…
Surface area and mean width of a cylinder (the convex hull of two parallel disks) in R^3 are computed. It is more difficult to obtain analogous results for a cone (the convex hull of a disk D and a point p). Oblique formulas for mean width, as well as those for mean curvature, are new. Let L denote the unique diameter …
New algorithms improve policy evaluation in reinforcement learning.
problem Off-policy stability and on-policy efficiency issues in policy evaluation.
method Introduced novel algorithms using oblique projection method.
result Demonstrated both off-policy stability and on-policy efficiency.
The paper simplifies hedging and portfolio allocation in markets without a risk-free asset.
problem Optimal hedging and portfolio allocation in markets without a risk-free asset.
method Establishes equivalence between hedging with and without numeraire change, uses oblique projections.
result Explicit expressions for optimal strategies and efficient frontier computation.
Study integrates reliability constraints into generation planning models.
problem Challenges in integrating reliability constraints with generation planning models.
method Leverages a weighted oblique decision tree (WODT) technique to embed reliability verification constraints.
result Demonstrates effectiveness in achieving reliable and optimal planning solutions.
The study calculates the average genus of 2-bridge knots based on their crossing numbers.
problem Determining the average genus of 2-bridge knots with a given crossing number.
method Analytical approach focusing on the properties of 2-bridge knots.
result Obtained the oblique asymptote of the average genus as crossing numbers increase.
A new topology design improves zero-shot classification performance in contrastive learning.
problem Improving zero-shot classification performance in contrastive visual-textual alignment.
method Proposed an alternative topology design using multiple class tokens and an oblique manifold with negative inner product.
result Improves zero-shot classification performance by an average of 6.1%.
In this paper we propose a synergistic melting of neural networks and decision trees (DT) we call neural decision trees (NDT). NDT is an architecture a la decision tree where each splitting node is an independent multilayer perceptron allowing oblique decision functions or arbritrary nonlinear decision function if more…
NSOTree combines neural networks and trees for better survival analysis interpretability.
problem Survival analysis event prediction with interpretability.
method Proposes NSOTree integrating neural networks and trees for better interpretability.
result NSOTree improves both performance and interpretability in survival analysis.
We present a new way of constructing an ensemble classifier, named the Guided Random Forest (GRAF) in the sequel. GRAF extends the idea of building oblique decision trees with localized partitioning to obtain a global partitioning. We show that global partitioning bridges the gap between decision trees and boosting alg…
Decision forests (Forests), in particular random forests and gradient boosting trees, have demonstrated state-of-the-art accuracy compared to other methods in many supervised learning scenarios. In particular, Forests dominate other methods in tabular data, that is, when the feature space is unstructured, so that the s…
NR retraction approximates geodesics on submanifolds efficiently.
problem Efficiently approximating geodesics on submanifolds for practical algorithms.
method Introducing Newton retraction (NR) as a class of retractions on submanifolds induced by a foliation of the ambient manifold.
result NR is more stable and computationally cheaper than oblique projection, with superlinear convergence regions.
This paper presents four different ways of looking at the well-known Least Squares Temporal Differences (LSTD) algorithm for computing the value function of a Markov Reward Process, each of them leading to different insights: the operator-theory approach via the Galerkin method, the statistical approach via instrumenta…
Adapts Stein's method for geometric inequalities, addressing boundary terms.
problem Geometric inequalities and their stability under constraints.
method Uses elliptic PDE with oblique boundary condition to handle boundary terms.
result Stability results for various geometric inequalities with respect to a new distance.
We study an agent-based stock market model with heterogeneous agents and friction. Our model is based on that of Foellmer-Schweizer(1993): The process of a stock price in a discrete-time framework is determined by temporary equilibria via agents' excess demand functions, and the diffusion approximation approach is appl…
The Mondrian process represents an elegant and powerful approach for space partition modelling. However, as it restricts the partitions to be axis-aligned, its modelling flexibility is limited. In this work, we propose a self-consistent Binary Space Partitioning (BSP)-Tree process to generalize the Mondrian process. Th…
Single tree outperforms random forest in testing accuracy.
problem The challenge of improving single decision tree performance.
method Gradient-based entire tree optimization framework, scaled sigmoid approximation, numerical stability algorithm, subtree polish strategy.
result Optimized single tree outperforms classic random forest by 2.03% on average.
New spectral estimates for minimal surfaces with boundary conditions.
problem Quantifying the Morse index of free boundary minimal surfaces.
method Adapted Montiel-Ros partitioning methods to compact manifolds with boundary, accounting for mixed and group actions.
result Explicit two-sided linear bounds on the Morse index for minimal surfaces.
SPlit optimizes dataset splitting for better model performance.
problem Improving model performance through optimal dataset splitting.
method Adapting Support Points (SP) algorithm for subsampling and categorical variables in a sequential nearest neighbor approach.
result SPlit significantly improves worst-case testing performance compared to random splitting.
The paper extends keenness concept to bridge splittings and finds conditions for existence.
problem Extending keenness concept to bridge splittings and finding conditions for existence.
method Extending the concept of keenness to bridge splittings and proving existence conditions.
result Existence of strongly keen (g,b)-splitting of a link with distance n for certain integers g, b, and n. Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split structures appear in the first case as deformations of a split reduction and in the …
Study flippable Heegaard splittings in Seifert fibered spaces.
problem Identifying flippable Heegaard splittings in Seifert fibered spaces.
method Examining isotopies that interchange Heegaard splitting sides in Seifert fibered spaces.
result Characterized which Heegaard splittings are flippable in Seifert fibered spaces.
We study the self-dual Yang-Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described.
New methods improve prediction regions for high-dimensional data.
problem Creating effective prediction regions for high-dimensional data.
method CD-split and HPD-split methods that combine split method and data-driven partition.
result CD-split and HPD-split converge to oracle highest predictive density set and satisfy local and asymptotic conditional validity.
New spheres can split a 4D link in ways not possible in 3D.
problem Exploring how splitting spheres behave in 4D space.
method Constructing specific 2-component surface-links in S4. result Found non-isotopic splitting spheres in S4∖Lm,n. This paper studies properties of weak reducing pairs in critical Heegaard splittings.
problem Characterize weak reducing pairs in critical Heegaard splittings.
method Analyze the properties of weak reducing pairs in critical Heegaard splittings.
result Provide a necessary condition for a Heegaard surface to be critical.
We show that if a split link is obtained from a split link L in S3 by 1/n-Dehn surgery along a trivial knot C, then the link L∪C is splittable. That is to say, it is impossible to obtain a split link from a split link via a non-trivial twisting. As its corollary, we completely determine when a trivial li…
Study evaluates when splitting classifiers can improve performance despite disparate treatment.
problem Impact of disparate treatment in classification models.
method Comparison of split classifiers and group-blind classifiers, quantifying performance improvement.
result Proves an equivalent expression for the benefit-of-splitting which can be efficiently computed.