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- Link implementation plan steps to specific backlog items - Add related backlog items section - Update implementation status with backlog references - Create clear traceability between CIP and detailed tasks
137 lines
6.1 KiB
Markdown
137 lines
6.1 KiB
Markdown
---
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author: "Neil Lawrence"
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created: "2025-08-15"
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id: "0001"
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last_updated: "2025-08-15"
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status: proposed
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tags:
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- cip
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- kernel
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- lfm
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- implementation
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title: "Implement Linear Filter Model (LFM) Kernel"
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---
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# CIP-0001: Implement Linear Filter Model (LFM) Kernel
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## Summary
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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.
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## Motivation
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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:
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- **Systems biology**: Modeling gene expression across multiple time points
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- **Signal processing**: Multi-channel signal analysis
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- **Environmental modeling**: Multiple sensor readings from the same system
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- **Neuroscience**: Multi-electrode recordings
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While GPy has existing ODE-based kernels (`EQ_ODE1`, `EQ_ODE2`) and an IBP LFM model, these implementations have limitations:
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- They don't use GPy's modern multioutput kernel approach
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- Limited integration with the current multioutput framework
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- Inconsistent API design compared to other GPy kernels
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- Missing comprehensive documentation and tests
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## Detailed Description
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The LFM kernel models the relationship between inputs and multiple outputs through:
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1. **Latent Functions**: A set of Q shared latent functions f_q(x)
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2. **Mixing Matrix**: A matrix S that maps latent functions to outputs
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3. **Noise Model**: Independent noise for each output
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The kernel function for outputs i and j is:
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K_ij(x,x') = Σ_q S_iq S_jq k_q(x,x') + δ_ij σ²_i
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Where:
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- S_iq is the mixing coefficient for output i and latent function q
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- k_q(x,x') is the kernel for latent function q
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- σ²_i is the noise variance for output i
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## Implementation Plan
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1. **Code Review and Documentation** (Backlog: `lfm-kernel-code-review`):
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- Review existing `EQ_ODE1`, `EQ_ODE2`, and IBP LFM implementations
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- Document current limitations and inconsistencies
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- Identify what can be reused and what needs modernization
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- Analyze MATLAB LFM implementation structure and patterns
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2. **Design Modern LFM Kernel** (Backlog: `design-modern-lfm-kernel`):
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- Create `GPy.kern.LFM` class following GPy's current patterns
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- Use GPy's multioutput kernel approach with output index as input
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- Design consistent API with other GPy kernels
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- Implement proper parameter handling and constraints
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3. **Core Implementation** (Backlog: `implement-lfm-kernel-core`):
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- Implement K() and Kdiag() methods
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- Add support for different base kernels for each latent function
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- Implement efficient gradient computation
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- Ensure compatibility with existing GP models
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4. **Testing and Validation**:
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- Create comprehensive unit tests
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- Reproduce results from published LFM papers
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- Compare with existing implementations
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- Validate on real multi-output datasets
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5. **Documentation and Examples**:
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- Write comprehensive docstrings
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- Create example notebooks
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- Update API documentation
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- Provide migration guide from old implementations
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## Backward Compatibility
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This implementation will maintain backward compatibility:
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- New LFM kernel class will not affect existing code
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- Existing `EQ_ODE1`, `EQ_ODE2`, and IBP LFM implementations will remain functional
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- Users can gradually migrate to the new implementation
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- Provide migration guide and compatibility layer if needed
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## Testing Strategy
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1. **Unit Tests**:
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- Test kernel computation for various input sizes
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- Verify gradient computation accuracy
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- Test parameter constraints and transformations
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2. **Integration Tests**:
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- Test with GPRegression models
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- Verify multi-output prediction capabilities
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- Test with different base kernels
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3. **Example Validation**:
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- Reproduce results from published LFM papers
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- Test on real multi-output datasets
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- Compare with existing implementations
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## Related Requirements
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This CIP addresses the following requirements:
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- **Multi-output modeling capability**: Enables principled modeling of related outputs
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- **Flexible kernel composition**: Allows different base kernels for different latent functions
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- **Scalable implementation**: Efficient computation for large datasets
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Specifically, it implements solutions for:
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- Multi-output Gaussian process regression
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- Latent function modeling
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- Flexible kernel parameterization
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- Efficient gradient computation
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## Related Backlog Items
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- **lfm-kernel-code-review**: Review existing LFM implementations
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- **design-modern-lfm-kernel**: Design modern LFM kernel architecture
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- **implement-lfm-kernel-core**: Implement core LFM kernel functionality
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## Implementation Status
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- [ ] Review existing LFM implementations (Backlog: `lfm-kernel-code-review`)
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- [ ] Document current limitations and design decisions (Backlog: `lfm-kernel-code-review`)
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- [ ] Design modern LFM kernel architecture (Backlog: `design-modern-lfm-kernel`)
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- [ ] Implement core LFM kernel computation (Backlog: `implement-lfm-kernel-core`)
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- [ ] Add parameter handling and constraints (Backlog: `implement-lfm-kernel-core`)
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- [ ] Implement gradient computation (Backlog: `implement-lfm-kernel-core`)
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- [ ] Create comprehensive unit tests
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- [ ] Write documentation and examples
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- [ ] Integration testing with existing GPy infrastructure
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- [ ] Performance optimization and validation
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## References
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- Álvarez, M. A., & Lawrence, N. D. (2011). Computationally efficient convolved multiple output Gaussian processes. Journal of Machine Learning Research, 12, 1459-1500.
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- 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.
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- Existing GPy kernel implementations for reference patterns
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