Enhances multi-class classification using neural networks and decision trees.
problem Improving multi-class classification accuracy.
method Combines neural networks, decision trees, and random vector functional link networks with oblique decision surfaces.
result Superior performance on multi-class datasets compared to state-of-the-art classifiers.
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.
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.
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. Neural models can realize decision trees with parameter sharing and improved performance.
problem Training and optimizing oblique decision trees.
method Locally constant networks based on ReLU gradients, parameter sharing, and neural tools.
result Locally constant networks can implicitly model oblique decision trees with fewer neurons.
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…
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.
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…
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.
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.
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.
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.
End-to-end learning of deterministic decision trees improves performance.
problem Lack of end-to-end trainable deterministic decision trees.
method Probabilistic decision trees with deterministic annealing, trained using Expectation-Maximization.
result End-to-end trainable deterministic decision trees achieve performance comparable to or better than existing methods.
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.
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 …
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.
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…
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.
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.
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.
GRAF uses global partitioning to improve ensemble classifier performance.
problem Improving ensemble classifier performance.
method GRAF extends oblique decision trees to global partitioning.
result GRAF reduces generalization error and improves performance on benchmark datasets.
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.
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.
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.
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…
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.
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.
MORF improves Forests' performance on manifold data by considering feature indices.
problem Forest methods struggle with structured data like images and text.
method MORF incorporates feature locality by sampling random matrices from manifold-aware distributions.
result MORF outperforms ConvNets and other methods on manifold data.
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.
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%.
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.
New method improves neural network robustness without adversarial training.
problem Adversarial robustness of neural networks under flat loss surface.
method Visualizing decision surfaces in input space to assess robustness.
result Decision surface geometry in input space correlates with adversarial robustness.
Measures neural network decision boundary volume to predict model performance.
problem Understanding the geometry of deep learning models for better performance.
method Local surface volumes to measure decision boundary, applying Weyl's tube formula.
result Smaller surface volume correlates with higher classification accuracy.
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.
Survey on 3-manifold problems and their complexity.
problem Decision problems in 3-manifold theory.
method Tools like normal surfaces, hierarchies, homomorphisms, and hyperbolic structures.
result Discussion of computational complexity of 3-manifold problems.
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…
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.
Decision-alignment evaluates uncertainty quantification for decision-relevant UQ
problem Evaluation of uncertainty quantification metrics
method Introduce decision-alignment
result Proper scoring rules align with decision utility
This review explores causal decision-making to improve decision quality.
problem Effective decision-making requires understanding causal relationships.
method Causal structure learning, causal effect learning, and causal policy learning.
result Challenges in causal decision-making are identified and recent advances are discussed.
Proposes a new BSP-Tree process for flexible space partition modeling.
problem Limited modelling flexibility of axis-aligned partitions in Mondrian process.
method Introduces a self-consistent Binary Space Partitioning (BSP)-Tree process with oblique cuts.
result Clear inferential improvements over standard Mondrian process and related methods.
Researchers compute exact decision boundaries of neural networks.
problem Finding exact decision boundaries of trained neural networks is intractable.
method Developed mathematical tools to investigate decision boundaries of trained deep models.
result Some simplifying assumptions about decision boundaries are unreliable.
Study geodesics on neck-degenerate manifolds, focusing and winding behavior observed.
problem Geodesics behavior on neck-degenerate manifolds with cuspidal singularities.
method Detailed multiscale analysis, blow-up techniques.
result Geodesics exhibit focussing and winding behavior as the neck degenerates.
Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis, such as clustering or classification. Finding reduced-dimension representations tha…
Capacity control, the bias/variance dilemma, and learning unknown functions from data, are all concerned with identifying effective and consistent fits of unknown geometric loci to random data points. A geometric locus is a curve or surface formed by points, all of which possess some uniform property. A geometric locus…