There has been significant recent work on the theory and application of randomized coordinate descent algorithms, beginning with the work of Nesterov [SIAM J. Optim., 22(2), 2012], who showed that a random-coordinate selection rule achieves the same convergence rate as the Gauss-Southwell selection rule. This result su…
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48 results for “Gauss-Southwell rule”
New solver speeds up Lasso-type problems by using screening rules and working sets.
problem Efficiently solving large-scale Lasso-type problems.
method Combining Gauss-Southwell rule with aggressive Gap Safe screening rules and working set strategy.
result Achieves state-of-the-art performance on sparse learning problems.
New derivation shows how a three-factor learning rule is derived from Oja's rule.
problem Deriving a three-factor learning rule from Oja's rule.
method Using frame theory to systematically derive EGHR-PCA from Oja's rule.
result A principled derivation of a biologically plausible learning rule.
DeepCTRL integrates rules into deep learning models, allowing flexible control at inference.
problem Lack of flexibility in incorporating rules into deep learning models.
method Integrates rule representations into deep neural networks, enabling flexible control at inference.
result Improves rule verification ratio and accuracy gains at downstream tasks.
New methods prune unpromising rules from KGs, improving scalability and runtime.
problem Scalability issues in walk-based rule learning from KGs.
method Rule Hierarchy Framework (RHF) and Hierarchical Pruning (HPMs).
result Significant reductions in runtime and number of learned rules without compromising predictive performance.
Study defines new slant ruled surfaces in Minkowski 3-space.
problem Characterizing non-null ruled surfaces in Minkowski 3-space.
method Introduced new types of non-null ruled surfaces and their characterizations.
result Established relationships between non-null slant ruled surfaces and their striction lines.
Subcartesian spaces follow Leibniz' rule, simplifying differential calculus.
problem Simplifying differential calculus in subcartesian spaces.
method Showed derivations satisfy the chain rule and have maximal integral curves.
result Subcartesian spaces follow Leibniz' rule, simplifying differential calculus.
In this study, we give the relationships between the conical curvatures of ruled surfaces drawn by the unit vectors of the ruling, central normal and central tangent of a regular ruled surface in the Euclidean -space. We obtain the differential equations characterizing slant ruled surfaces and if the reference ruled su…
New framework learns interpretable rule ensembles without sacrificing accuracy.
problem Trade-off between accuracy and interpretability in rule ensembles.
method Introduces local interpretability and a regularizer to promote it, using coordinate descent with local search.
result Learns rule ensembles with fewer rules to explain individual predictions, maintaining comparable accuracy.
R2N learns interpretable rules and literals from numerical features.
problem Lack of expressive vocabulary in rule-based decision models.
method Relational Rule Network (R2N) learns literals and rules end-to-end.
result Learned literals improve prediction accuracy and rule conciseness.
Study ruled surfaces with finite multiplicity, focusing on their curves and singularities.
problem Understanding ruled surfaces with finite multiplicity.
method Analyzing striction curves and singularities of ruled surfaces.
result Geometric meanings of invariants related to ruled surfaces.
All finite subdivision rules are combinatorially equivalent to three-dimensional subdivision rulesmath.GT
Finite subdivision rules in high dimensions are shown to be equivalent to 3D rules.
problem Visualization and construction of high-dimensional subdivision rules.
method Characterized history graphs and defined combinatorial subdivision rules.
result Finite subdivision rules in arbitrary dimensions are combinatorially equivalent to 3D rules.
Paper classifies ruled surfaces in Lorentz-Minkowski space for a specific flow.
problem Classifying ruled surfaces in Lorentz-Minkowski space.
method Examining homothetic self-similar solutions of the inverse mean curvature flow.
result Existence of two classes of non-cylindrical homothetic solitons.
Slant Ruled Surfacesmath.DG
In this study, we define some new types of ruled surfaces called slant ruled surfaces. We give some characterizations for a regular ruled surface to be a slant ruled surface in Euclidean 3- space. We show that if the slant ruled surface is developable then the striction curve is a general helix or a slant helix accordi…
In this paper we use fuzzy systems theory to convert the technical trading rules commonly used by stock practitioners into excess demand functions which are then used to drive the price dynamics. The technical trading rules are recorded in natural languages where fuzzy words and vague expressions abound. In Part I of t…
Subdivision rules create sequences of nested cell structures on CW-complexes, and they frequently arise from groups. In this paper, we develop several tools for classifying subdivision rules. We give a criterion for a subdivision rule to represent a Gromov hyperbolic space, and show that a subdivision rule for a hyperb…
In this article supervised learning problems are solved using soft rule ensembles. We first review the importance sampling learning ensembles (ISLE) approach that is useful for generating hard rules. The soft rules are then obtained with logistic regression from the corresponding hard rules. In order to deal with the p…
Advances rule-based multi-label classification using conformal prediction.
problem Improving accuracy and decision making in multi-label classification.
method Combines conformal prediction with rule-based learning to provide natural conformity scores and calibrate rule assessments.
result Calibrated conformity scores enhance prediction accuracy and decision making.
The Lamarle Formula, given by Kruppa in \cite{Kr}, is known as a relationship between the Gaussian curvature and the distribution parameter of a ruled surface in the surface theory. The ruled surfaces were investigated in 3 different classes with respect to the character of base curves and rulings, \cite{Tu1},\cite{Tu2…
In this paper, we consider non developable ruled surface with spacelike ruling, timelike ruling, respectively. We give the relations between the structure functions with the curvature and torsion of the striction line of the timelike and spacelike non developable ruled surfaces. Also, we have calculated the gaussian an…
The paper proposes a method to optimize rule-based models for better accuracy and interpretability.
problem Developing rule-based models for regression and classification with better accuracy and interpretability.
method Column generation to optimize over an exponentially large space of rules, using integer programming or a heuristic.
result The proposed methods achieve better accuracy-complexity trade-offs than existing rule ensemble algorithms.
Generative models learn rules at different timescales, revealing a 'innovation window'.
problem Generative models' convergence to empirical training distribution rather than population distribution.
method Rule-valid synthetic tasks, analyzing and across training timescales.
result The 'innovation window' widens with increasing dataset size and narrows with rule complexity.
Darboux Slant Ruled Surfacesmath.DG
In this study, we introduce Darboux slant ruled surfaces in the Euclidean 3-space which is defined by the property that the Darboux vector of orthonormel frame of ruled surface makes a constant angle with a fixed, non-zero direction. We obtain the characterizations of Darboux slant ruled surfaces regarding the conical …
FedRule uses graph neural networks to recommend rules for smart homes without centralizing data.
problem Manual rule setup for smart devices is inefficient and privacy-compromising.
method FedRule constructs user-specific graphs for rule recommendation, using federated learning to protect privacy.
result FedRule achieves comparable performance to centralized methods and outperforms others.
Paper explores folding patterns of curved creases preserving their geometric properties.
problem Investigating rigid-ruling folding motions of curved crease-rule patterns.
method Deriving conditions for rigid-ruling foldability and analyzing combinations of creases.
result Constant fold-angle creases are only compatible with other constant fold-angle creases.
Study on hypersurfaces with minimized distance between rulings.
problem Characterizing singularities and properties of two-ruled hypersurfaces.
method Characterization through striction curves and examination of pseudo-non-degenerate properties.
result Two-ruled hypersurfaces constructed from specific curves are pseudo-non-degenerate.
NeuRules learns interpretable rule lists from data without pre-discretization.
problem Interpretable rule lists for high-stakes decisions in machine learning.
method Neuro-symbolic continuous optimization with temperature annealing.
result NeuRules outperforms existing methods in learning interpretable rule lists.
Model selects and generates music rules for realization and understanding.
problem Selecting and generating music rules that follow given constraints.
method Formulated as a bi-convex problem, derived efficient algorithm.
result Demonstrated model's effectiveness in music composition and analysis.
Paper extends transfer learning for decision rules, improving treatment rule estimation.
problem Estimating optimal individualized treatment rules under changing conditions.
method Bayes decision rules and low-dimensional empirical risk minimization.
result Consistent estimators and risk bounds established under mild conditions.
Study embeds ruled surfaces into symplectic manifolds, finds Stein fillability results.
problem Embedding rational ruled surfaces into symplectic manifolds.
method Analyzes symplectic hyperplane sections of rational ruled surfaces.
result Obtains Stein fillability results for rational ruled surfaces.
FIRE extracts interpretable rules from tree ensembles.
problem Building sparse and interpretable rule sets from tree ensembles.
method Optimization-based framework with fusion regularization and sparsity-inducing penalties.
result FIRE outperforms state-of-the-art rule ensemble algorithms.
Optimal classification rules control error rates in multiclass mixture models.
problem Classifying observations in multiclass mixture models while controlling error rates.
method Finding optimal classification rules by searching an optimal region in the observation space, using Maximum A Posteriori (MAP) rule and heuristic computation.
result The FDR-like optimal rule can be significantly less conservative than thresholded MAP rules.
Mannheim Offsets of the Timelike Ruled Surfaces with Spacelike Rulings in Dual Lorentzian Spacemath.DG
In this paper, we obtain the characterizations of Mannheim offsets of the timelike ruled surface with spacelike rulings in dual Lorentzian space. We give the relations between terms of their integral invariants and also we give the new characterization of the Mannheim offsets of developable timelike ruled surface. More…
The paper explores new rules for analyzing label rankings and pairwise preferences.
problem Mining patterns in multi-target relations for label ranking.
method Developed two types of association rules: Label Ranking Association Rules (LRAR) and Pairwise Association Rules (PAR). Conducted sensitivity analysis on similarity measures.
result Both LRAR and PAR show potential in analyzing multi-target relations.
Cannon and Swenson have shown that each hyperbolic 3-manifold group has a natural subdivision rule on the space at infinity, and that this subdivision rule captures the action of the group on the sphere. Explicit subdivision rules have also been found for some closed and finite-volume hyperbolic manifolds, as well as a…
A new screening rule improves SLOPE efficiency for high-dimensional data.
problem Efficiently selecting relevant predictors in high-dimensional data.
method Developed a screening rule for SLOPE based on its subdifferential.
result The screening rule improves SLOPE's performance significantly in high-dimensional settings.
We classify ruled minimal surfaces in with density It is showed that there is no noncylindrical ruled minimal surface and there is a family of cylindrical ruled minimal surfaces in with density It is also proved that all translation minimal surfaces are ruled.
A New Causal Rule Learning Approach to Interpretable Estimation of Heterogeneous Treatment Effectcs.LG
CRL approach improves understanding of heterogeneous treatment effects in complex diseases.
problem Estimating heterogeneous treatment effects in complex diseases.
method Causal rule learning (CRL) workflow consisting of rule discovery, selection, and analysis.
result CRL outperforms other methods in providing interpretable estimates of HTE.
Study ruled minimal surfaces in solvable Lie groups, classifying and constructing examples.
problem Classifying and constructing ruled minimal surfaces in solvable Lie groups.
method Classification and construction of ruled surfaces, parametrization for specific cases.
result Classification and construction of ruled minimal surfaces in solvable Lie groups.
LoRMIkA finds k-optimal association rules for local model interpretability.
problem Ensuring trust in machine learning predictions.
method Model-agnostic approach using k-optimal association rules from a neighbourhood.
result Achieves competitive results in local accuracy and interpretability.
Study shows LLMs can extrapolate rules from out-of-distribution prompts.
problem Understanding LLMs' ability to generalize from unexpected inputs.
method Formal languages and rule-based scenarios to evaluate LLMs' OOD behavior.
result LLMs can extrapolate rules from out-of-distribution prompts, even in complex scenarios.
A method for collecting human supervision that combines rules and instance labels.
problem Lack of labeled data and inefficient human supervision.
method Rule-exemplar method with training algorithm for joint denoising and model training.
result Our algorithm is more accurate than existing methods and effectively denoises rules.
Pareto's 80/20 rule follows a Gaussian distribution with twice the mean standard deviation.
problem Understanding variations in the 80/20 rule across different contexts.
method Identifying the statistical distribution of the 80/20 rule and its variations.
result The 80/20 rule follows a Gaussian distribution with a standard deviation twice the mean.
The study examines singularities of ruled surfaces using RM vectors.
problem Analyzing singularities of ruled surfaces.
method Using Legendre curves and rotation minimizing frames.
result Classification of singularities of ruled surfaces.
The Hessian Screening Rulestat.ML
A new screening rule improves lasso solving speed.
problem Efficiently solving lasso problems with high correlation.
method Uses second-order information from the Hessian to screen predictors.
result Outperforms alternatives on simulated and real data.
SRF learns sparse rule models by screening out features efficiently.
problem Learning optimal sparse rule models is computationally intractable due to the large number of possible rules.
method SRF uses meta safe screening (mSS) to efficiently screen out multiple features, improving the learning of sparse rule models.
result SRF provides a general framework for fitting sparse rule models and can handle group regularization.
Paper develops rules for autonomous driving using semantic memory.
problem Creating rules for autonomous driving systems.
method Uses real driving data and semantic memory for rule learning.
result Automatic rule learning for autonomous driving.
Study on ruled surfaces over elliptic curves, focusing on Poisson deformations.
problem Obstructedness or unobstructedness of Poisson deformations of ruled surfaces.
method Analysis of ruled surfaces over elliptic curves, focusing on Poisson deformations.
result Determination of obstructedness or unobstructedness of Poisson deformations.