arxiv_ml 80% Match Research Paper Machine learning researchers,Data scientists,Researchers in kernel methods 19 hours ago

A Compositional Kernel Model for Feature Learning

generative-ai › flow-models

📄 Abstract

Abstract: We study a compositional variant of kernel ridge regression in which the predictor is applied to a coordinate-wise reweighting of the inputs. Formulated as a variational problem, this model provides a simple testbed for feature learning in compositional architectures. From the perspective of variable selection, we show how relevant variables are recovered while noise variables are eliminated. We establish guarantees showing that both global minimizers and stationary points discard noise coordinates when the noise variables are Gaussian distributed. A central finding is that $\ell_1$-type kernels, such as the Laplace kernel, succeed in recovering features contributing to nonlinear effects at stationary points, whereas Gaussian kernels recover only linear ones.

Key Contributions

This paper introduces a compositional variant of kernel ridge regression that facilitates feature learning in compositional architectures. It formulates the model as a variational problem and provides theoretical guarantees showing that relevant variables are recovered while noise variables are eliminated, particularly demonstrating that L1-type kernels can recover features contributing to nonlinear effects.

Business Value

Enables the development of more interpretable and robust machine learning models by automatically learning relevant features and discarding noise, improving performance and reducing model complexity in various data-driven applications.

Paper Metadata

Innovation Type

Algorithmic and Theoretical Development

Deployment Feasibility

Theoretical framework, requires implementation and empirical validation.

Limitations Addressed

Challenges in feature learning within compositional models and the effective handling of noisy input variables.

Performance Gains

Theoretical guarantees for variable selection and noise elimination, showing L1 kernels recover nonlinear features.

Technical Tags

kernel ridge regressioncompositional modelsfeature learningvariational problemvariable selectionnoise eliminationl1 kernelsLaplace kernelGaussian kernelnonlinear effects

Research Topics

Machine Learning TheoryKernel MethodsFeature LearningOptimization

Methods & Architectures

Kernel ridge regressionVariational inferenceAnalysis of stationary pointsTheoretical guarantees Compositional Kernel Models

Applications & Tasks

Machine Learning Pattern Recognition Data Analysis Feature learningVariable selectionHandling noisy variablesCompositional modeling Learning features in compositional architecturesRecovering relevant variablesEliminating noise variables

Related Fields

Statistical LearningKernel MethodsMachine Learning Theory

Keywords

kernel ridge regressioncompositional modelsfeature learningvariable selectionnoisel1 kernelLaplace kernelGaussian kernelvariationalnonlinearstationary points

Academic Context

#Machine Learning Theory#Kernel Methods#Feature Learning#Optimization

Commercial Potential

Potential Products

Automated feature engineering toolsRobust regression models

Target Industries

FinanceBiotechnologyAny industry relying on complex data analysis

Use Case Examples

Predictive modeling with high-dimensional, noisy dataDeveloping interpretable models for scientific discoveryBuilding compositional systems for complex tasks

Competitive Edge

Extends kernel methods with compositional structure and provides theoretical guarantees for feature learning and noise handling.

Resource Requirements

Compute Needs

Theoretical analysis; simulations would require standard ML compute resources.

Data Requirements

Requires datasets suitable for compositional modeling and feature learning.

Deployment Constraints

Theoretical results need practical implementation and validation.

Scalability

Scalability depends on the specific kernel and compositional structure used.

Production Readiness

Maturity Level

Theoretical Research

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