GPy/backlog/features/2025-08-15_implement-lfm-kernel-core.md

id	title	status	priority	created	last_updated	owner	github_issue	dependencies	tags
implement-lfm-kernel-core	Implement core LFM kernel functionality	In Progress	High	2025-08-15	2025-08-15	Neil Lawrence		design-modern-lfm-kernel	lfm kernel implementation core

Implement core LFM kernel functionality

Description

Implement the core LFM kernel class with basic functionality including kernel computation, parameter handling, and gradient computation.

Background

• Design phase completed with modern LFM kernel architecture
• Need to implement the core kernel computation methods
• Should follow the mathematical foundations from the papers and MATLAB implementation

Implementation Tasks

• Create test specification for GPy.kern.LFM1 and GPy.kern.LFM2 classes (test-driven design)
• Create GPy.kern.LFM1 class inheriting from appropriate base class
• Create GPy.kern.LFM2 class inheriting from appropriate base class
• Implement parameter handling for mass, damper, spring, sensitivity, delay
• Implement K() method for kernel matrix computation
• Implement Kdiag() method for diagonal computation
• Add parameter constraints and transformations
• Implement basic gradient computation
• Add support for different base kernels for latent functions

Core Methods to Implement

• __init__() - Parameter initialization and validation (LFM1 and LFM2)
• K(X, X2=None) - Kernel matrix computation (LFM1 and LFM2)
• Kdiag(X) - Diagonal computation (LFM1 and LFM2)
• update_gradients_full() - Gradient computation (LFM1 and LFM2)
• update_gradients_diag() - Diagonal gradient computation (LFM1 and LFM2)
• parameters_changed() - Parameter update handling (LFM1 and LFM2)

Acceptance Criteria

• Core LFM kernel class implemented and functional
• Basic kernel computation working correctly
• Parameter handling and constraints implemented
• Gradient computation implemented
• Unit tests passing for core functionality
• Integration with GPy's parameterization system

Implementation Notes

• Follow the mathematical structure from the MATLAB implementation
• Use GPy's parameterization system for constraints
• Implement efficient computation methods
• Ensure proper handling of edge cases and numerical stability
• Add comprehensive docstrings and documentation

Related

• CIP: 0001 (LFM kernel implementation)
• Backlog: design-modern-lfm-kernel
• Papers: Álvarez et al. (2009, 2012)

Progress Updates

2025-08-15

Implementation task started after completion of test-driven design:

• Design phase completed with comprehensive test suite
• Test specification defines expected API and behavior
• Ready to implement LFM1 and LFM2 kernel classes
• Test framework validated and working correctly