From 90805ba02689775034963bb2de6ce98174658295 Mon Sep 17 00:00:00 2001 From: Neil Lawrence Date: Fri, 15 Aug 2025 08:22:38 +0200 Subject: [PATCH] Update CIP-0001: Modernize LFM kernel implementation - Acknowledge existing ODE-based LFM implementations (EQ_ODE1, EQ_ODE2) - Identify limitations of current implementations - Propose modernization using GPy's multioutput kernel approach - Update implementation plan to include code review and documentation - Emphasize backward compatibility and gradual migration --- cip/cip0001.md | 131 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 131 insertions(+) create mode 100644 cip/cip0001.md diff --git a/cip/cip0001.md b/cip/cip0001.md new file mode 100644 index 00000000..b2443e54 --- /dev/null +++ b/cip/cip0001.md @@ -0,0 +1,131 @@ +--- +author: "Neil Lawrence" +created: "2025-08-15" +id: "0001" +last_updated: "2025-08-15" +status: proposed +tags: +- cip +- kernel +- lfm +- implementation +title: "Implement Linear Filter Model (LFM) Kernel" +--- + +# CIP-0001: Implement Linear Filter Model (LFM) Kernel + +## Summary +Modernize and complete the Latent Force Model (LFM) kernel implementation in GPy. While there are existing ODE-based kernels (`EQ_ODE1`, `EQ_ODE2`) and an IBP LFM model, these implementations don't use GPy's modern multioutput kernel approach that uses output index as input. This CIP proposes creating a unified LFM kernel that follows GPy's current architectural patterns and provides better integration with the multioutput framework. + +## Motivation +Many real-world applications involve multiple outputs that are related through underlying physical or biological processes. The LFM kernel provides a principled way to model these relationships by introducing latent functions that are shared across outputs. This is particularly useful in: + +- **Systems biology**: Modeling gene expression across multiple time points +- **Signal processing**: Multi-channel signal analysis +- **Environmental modeling**: Multiple sensor readings from the same system +- **Neuroscience**: Multi-electrode recordings + +While GPy has existing ODE-based kernels (`EQ_ODE1`, `EQ_ODE2`) and an IBP LFM model, these implementations have limitations: +- They don't use GPy's modern multioutput kernel approach +- Limited integration with the current multioutput framework +- Inconsistent API design compared to other GPy kernels +- Missing comprehensive documentation and tests + +## Detailed Description +The LFM kernel models the relationship between inputs and multiple outputs through: + +1. **Latent Functions**: A set of Q shared latent functions f_q(x) +2. **Mixing Matrix**: A matrix S that maps latent functions to outputs +3. **Noise Model**: Independent noise for each output + +The kernel function for outputs i and j is: +K_ij(x,x') = Σ_q S_iq S_jq k_q(x,x') + δ_ij σ²_i + +Where: +- S_iq is the mixing coefficient for output i and latent function q +- k_q(x,x') is the kernel for latent function q +- σ²_i is the noise variance for output i + +## Implementation Plan + +1. **Code Review and Documentation**: + - Review existing `EQ_ODE1`, `EQ_ODE2`, and IBP LFM implementations + - Document current limitations and inconsistencies + - Identify what can be reused and what needs modernization + +2. **Design Modern LFM Kernel**: + - Create `GPy.kern.LFM` class following GPy's current patterns + - Use GPy's multioutput kernel approach with output index as input + - Design consistent API with other GPy kernels + - Implement proper parameter handling and constraints + +3. **Core Implementation**: + - Implement K() and Kdiag() methods + - Add support for different base kernels for each latent function + - Implement efficient gradient computation + - Ensure compatibility with existing GP models + +4. **Testing and Validation**: + - Create comprehensive unit tests + - Reproduce results from published LFM papers + - Compare with existing implementations + - Validate on real multi-output datasets + +5. **Documentation and Examples**: + - Write comprehensive docstrings + - Create example notebooks + - Update API documentation + - Provide migration guide from old implementations + +## Backward Compatibility +This implementation will maintain backward compatibility: +- New LFM kernel class will not affect existing code +- Existing `EQ_ODE1`, `EQ_ODE2`, and IBP LFM implementations will remain functional +- Users can gradually migrate to the new implementation +- Provide migration guide and compatibility layer if needed + +## Testing Strategy +1. **Unit Tests**: + - Test kernel computation for various input sizes + - Verify gradient computation accuracy + - Test parameter constraints and transformations + +2. **Integration Tests**: + - Test with GPRegression models + - Verify multi-output prediction capabilities + - Test with different base kernels + +3. **Example Validation**: + - Reproduce results from published LFM papers + - Test on real multi-output datasets + - Compare with existing implementations + +## Related Requirements +This CIP addresses the following requirements: + +- **Multi-output modeling capability**: Enables principled modeling of related outputs +- **Flexible kernel composition**: Allows different base kernels for different latent functions +- **Scalable implementation**: Efficient computation for large datasets + +Specifically, it implements solutions for: +- Multi-output Gaussian process regression +- Latent function modeling +- Flexible kernel parameterization +- Efficient gradient computation + +## Implementation Status +- [ ] Review existing LFM implementations +- [ ] Document current limitations and design decisions +- [ ] Design modern LFM kernel architecture +- [ ] Implement core LFM kernel computation +- [ ] Add parameter handling and constraints +- [ ] Implement gradient computation +- [ ] Create comprehensive unit tests +- [ ] Write documentation and examples +- [ ] Integration testing with existing GPy infrastructure +- [ ] Performance optimization and validation + +## References +- Álvarez, M. A., & Lawrence, N. D. (2011). Computationally efficient convolved multiple output Gaussian processes. Journal of Machine Learning Research, 12, 1459-1500. +- Álvarez, M. A., Luengo, D., & Lawrence, N. D. (2012). Linear latent force models using Gaussian processes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(11), 2693-2705. +- Existing GPy kernel implementations for reference patterns