tensorlogic-sklears-kernels 0.1.0-beta.1

Logic-derived similarity kernels for SkleaRS integration
Documentation
# Beta.1 Release Status ✅

**Version**: 0.1.0-beta.1
**Status**: Production Ready (Further Enhanced)

This crate is part of the TensorLogic v0.1.0-beta.1 release with:
- Zero compiler warnings
- 100% test pass rate (391 tests)
- Complete documentation
- Production-ready quality
- **New: Advanced GP kernels, kernel selection, Random Fourier Features, and KPCA utilities**

See main [TODO.md](../../TODO.md) for overall project status.

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# tensorlogic-sklears-kernels TODO

## Completed ✓

- [x] Basic crate structure
- [x] **Logic-derived similarity kernels**
  - [x] Rule-based similarity (RuleSimilarityKernel)
  - [x] Predicate overlap kernel (PredicateOverlapKernel)
- [x] **Tensor-based kernels**
  - [x] Linear kernel
  - [x] RBF (Gaussian) kernel
  - [x] Polynomial kernel
  - [x] Cosine similarity kernel
  - [x] Laplacian kernel
  - [x] Sigmoid (Tanh) kernel
  - [x] Chi-squared kernel
  - [x] Histogram Intersection kernel
  - [x] Matérn kernel (nu=0.5, 1.5, 2.5)
  - [x] Rational Quadratic kernel
  - [x] Periodic kernel
- [x] **Kernel transformation utilities**
  - [x] Kernel matrix normalization
  - [x] Kernel matrix centering (for kernel PCA)
  - [x] Kernel matrix standardization
  - [x] NormalizedKernel wrapper
- [x] **Kernel utilities for ML workflows**
  - [x] Kernel-target alignment (KTA) for kernel selection
  - [x] Median heuristic bandwidth selection
  - [x] Kernel matrix validation
  - [x] Gram matrix computation utilities
  - [x] Row normalization
- [x] Implement SkleaRS-compatible kernel trait
- [x] Efficient kernel matrix computation
- [x] Comprehensive test suite (334 tests) **UPDATED**
- [x] Extensive documentation and examples
- [x] Zero warnings (clippy clean)

## High Priority 🔴 ✅ COMPLETED

### Advanced Kernel Types ✅ COMPLETE
- [x] **Graph kernels from TLExpr**
  - [x] Subgraph matching kernel
  - [x] Walk-based kernels (Random walk)
  - [x] Weisfeiler-Lehman kernel
- [x] **Tree kernels for structured data**  - [x] Subtree kernel
  - [x] Subset tree kernel
  - [x] Partial tree kernel
- [x] **Composite kernels**
  - [x] Weighted sum of kernels
  - [x] Product kernels
  - [x] Kernel alignment

### Performance Optimizations ✅ COMPLETE
- [x] Sparse kernel matrix support (CSR format, builder pattern)
- [x] Kernel caching (CachedKernel, KernelMatrixCache)
- [x] **Low-rank approximations (Nyström method)**  - [x] Three sampling methods (Uniform, First, K-means++)
  - [x] Configurable regularization
  - [x] Compression ratio tracking
- [x] **Performance benchmarks**  - [x] Kernel computation benchmarks (10 groups)
  - [x] Matrix operations benchmarks (10 groups)
  - [x] Caching performance benchmarks (8 groups)
  - [x] Composite kernels benchmarks (10 groups)
  - [x] Graph kernels benchmarks (9 groups)
- [x] **Online kernel updates**  - [x] OnlineKernelMatrix - Incremental O(n) updates
  - [x] WindowedKernelMatrix - Sliding window for time series
  - [x] ForgetfulKernelMatrix - Exponential decay for concept drift
  - [x] AdaptiveKernelMatrix - Automatic bandwidth adjustment
  - [x] Comprehensive tests (25 tests)
  - [x] Example: online_kernel_updates.rs
- [ ] GPU acceleration (FUTURE)

## Medium Priority 🟡 ✅ COMPLETE

### Advanced Kernel Methods
- [x] **String kernels for text data** (NGram, Subsequence, EditDistance) ✅
- [x] **Tree kernels for structured data** (Subtree, Subset, Partial) ✅
- [x] **Multi-task kernel learning**  - [x] IndexKernel - Task-based similarity
  - [x] ICMKernel - Intrinsic Coregionalization Model (B ⊗ K)
  - [x] LMCKernel - Linear Model of Coregionalization (Σ B_q ⊗ K_q)
  - [x] HadamardTaskKernel - Element-wise product
  - [x] MultiTaskKernelBuilder - Builder pattern
  - [x] Comprehensive tests (30 tests)
  - [x] Example: multitask_learning.rs
- [ ] Deep kernel learning (FUTURE)

### Integration Enhancements
- [x] **Automatic feature extraction** from TLExpr (FeatureExtractor) ✅
- [x] **Provenance tracking for kernel computations**  - [x] ProvenanceRecord with rich metadata
  - [x] ProvenanceTracker with query interface
  - [x] ProvenanceKernel wrapper
  - [x] JSON export/import
  - [x] Performance statistics
  - [x] Tagged experiments
  - [x] Comprehensive tests (15 tests)
  - [x] Example: provenance_tracking.rs
- [x] **Symbolic kernel composition**  - [x] KernelExpr with algebraic operations (scale, add, multiply, power)
  - [x] SymbolicKernel for expression evaluation
  - [x] KernelBuilder for declarative construction
  - [x] Expression simplification
  - [x] PSD property checking
  - [x] Comprehensive tests (14 tests)
  - [x] Example: symbolic_kernels.rs

## Beta.1 Enhancements 🆕 ✅ NEW

### ARD (Automatic Relevance Determination) Kernels ✅ NEW
Per-dimension length scales for automatic feature relevance learning:
- [x] **ArdRbfKernel** - ARD version of RBF/Gaussian kernel
  - [x] Per-dimension length scales
  - [x] Signal variance parameter
  - [x] Gradient computation for hyperparameter optimization
- [x] **ArdMaternKernel** - ARD Matérn kernel (nu=0.5, 1.5, 2.5)
  - [x] Exponential, nu_3_2, nu_5_2 convenience constructors
- [x] **ArdRationalQuadraticKernel** - ARD Rational Quadratic
- [x] Comprehensive tests (35+ tests)

### GP Utility Kernels ✅ NEW
Essential kernels for Gaussian Process modeling:
- [x] **WhiteNoiseKernel** - i.i.d. observation noise (K(x,y) = σ² if x==y, else 0)
- [x] **ConstantKernel** - Constant covariance (K(x,y) = σ²)
- [x] **DotProductKernel** - Linear kernel with variance and bias
- [x] **ScaledKernel<K>** - Generic wrapper to scale any kernel

### Spectral Kernels ✅ NEW
Kernels for discovering periodic patterns:
- [x] **SpectralMixtureKernel** - Mixture of spectral components
  - [x] SpectralComponent with weight, mean frequency, variance
  - [x] Multi-dimensional support
  - [x] Multiple component composition
- [x] **ExpSineSquaredKernel** - Periodic kernel (scikit-learn compatible)
- [x] **LocallyPeriodicKernel** - RBF × Periodic for decaying periodicity
- [x] **RbfLinearKernel** - RBF × Linear product kernel
- [x] Comprehensive tests (25+ tests)

### Kernel Selection & Cross-Validation ✅ NEW
Tools for hyperparameter tuning and model selection:
- [x] **KernelSelector** - Comprehensive kernel selection utilities
  - [x] kernel_target_alignment() - KTA metric
  - [x] centered_kernel_target_alignment() - Centered KTA
  - [x] compare_kernels_kta() - Compare multiple kernels
  - [x] loo_error_estimate() - Leave-one-out error
  - [x] k_fold_cv() - K-fold cross-validation
  - [x] grid_search_rbf_gamma() - RBF gamma optimization
- [x] **KFoldConfig** - K-fold CV configuration with shuffle
- [x] **CrossValidationResult** - Fold scores with statistics
- [x] **KernelComparison** - Multi-kernel comparison results
- [x] **GammaSearchResult** - Grid search results
- [x] Comprehensive tests (20+ tests)

### Random Fourier Features (RFF) ✅ NEW
Scalable kernel approximation for large datasets:
- [x] **RandomFourierFeatures** - O(nd) approximate kernel computation
  - [x] Support for RBF, Laplacian, Matérn kernels
  - [x] Configurable number of components
  - [x] Transform and approximate_kernel methods
- [x] **OrthogonalRandomFeatures** - Improved variance via orthogonal projection
- [x] **NystroemFeatures** - Nyström-based feature approximation
- [x] **RffConfig** - Configuration with seed support
- [x] **KernelType** - Enum for supported kernel types
- [x] Comprehensive tests (10+ tests)

### Kernel Gradient Computation ✅ NEW
Gradients for hyperparameter optimization:
- [x] **Element-wise gradients** for standard kernels
  - [x] RbfKernel: compute_with_gradient(), compute_with_length_scale_gradient()
  - [x] PolynomialKernel: compute_with_constant_gradient(), compute_with_all_gradients()
  - [x] MaternKernel: compute_with_length_scale_gradient() (nu=0.5, 1.5, 2.5)
  - [x] LaplacianKernel: compute_with_gradient(), compute_with_sigma_gradient()
  - [x] RationalQuadraticKernel: compute_with_length_scale_gradient(), compute_with_alpha_gradient()
- [x] **Matrix-level gradient computation** (gradient module)
  - [x] compute_rbf_gradient_matrix() - Full N×N gradient matrices
  - [x] compute_polynomial_gradient_matrix()
  - [x] compute_matern_gradient_matrix()
  - [x] compute_laplacian_gradient_matrix()
  - [x] compute_rational_quadratic_gradient_matrix()
  - [x] KernelGradientMatrix, GradientComponent structs
  - [x] trace_product(), frobenius_norm() utilities
- [x] Comprehensive tests (30+ tests)

### Kernel PCA (KPCA) ✅ NEW
Nonlinear dimensionality reduction:
- [x] **KernelPCA** - Full KPCA implementation
  - [x] fit() - Fit model to training data
  - [x] transform() - Project new data
  - [x] transform_training() - Project training data
  - [x] eigenvalues() - Access eigenvalues
  - [x] explained_variance_ratio() - Variance explained per component
  - [x] cumulative_variance_explained() - Cumulative variance
- [x] **KernelPCAConfig** - Configuration with centering option
- [x] **center_kernel_matrix()** - Utility function
- [x] **select_n_components()** - Automatic component selection
- [x] **reconstruction_error()** - Error analysis
- [x] Comprehensive tests (11 tests)

## Low Priority 🟢 ✅ COMPLETE

### Documentation
- [x] Add README.md with architecture overview ✅
- [x] Kernel design guide ✅
- [x] **Performance benchmarks** (5 benchmark suites, 47 groups) ✅
- [ ] Case studies (SVM, GP, etc.) (FUTURE)

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**Total Items:** 52 tasks (38 original + 14 new)
**Completion:** 🎉 **100% (52/52)** 🎉 **ALL TASKS COMPLETE!**

**Beta.1 New Features Summary:**
- **ARD Kernels** (3 kernels + gradient support, 35+ tests)
  - ArdRbfKernel with per-dimension length scales
  - ArdMaternKernel with ARD support
  - ArdRationalQuadraticKernel
  - KernelGradient for hyperparameter optimization

- **GP Utility Kernels** (4 kernels, 10+ tests)
  - WhiteNoiseKernel for observation noise
  - ConstantKernel for constant covariance
  - DotProductKernel for linear models
  - ScaledKernel<K> for variance scaling

- **Spectral Kernels** (4 kernels, 25+ tests)
  - SpectralMixtureKernel for pattern discovery
  - ExpSineSquaredKernel (periodic)
  - LocallyPeriodicKernel (decaying periodicity)
  - RbfLinearKernel (product kernel)

- **Kernel Selection** (comprehensive module, 20+ tests)
  - KernelSelector with KTA, LOO, K-fold CV
  - Grid search for RBF gamma
  - Kernel comparison utilities

- **Random Fourier Features** (3 classes, 10+ tests) **NEW**
  - RandomFourierFeatures for O(nd) kernel approximation
  - OrthogonalRandomFeatures for improved variance
  - NystroemFeatures for landmark-based approximation
  - Support for RBF, Laplacian, Matérn kernels

- **Kernel Gradient Computation** (comprehensive, 30+ tests) **NEW**
  - Element-wise gradients for RBF, Polynomial, Matérn, Laplacian, RationalQuadratic
  - Matrix-level gradient computation (dK/dθ)
  - Utilities for GP hyperparameter optimization

- **Kernel PCA (KPCA)** (full implementation, 11 tests) **NEW**
  - KernelPCA with fit/transform interface
  - Eigenvalue-based variance analysis
  - Automatic component selection

**Test Count: 391 tests (100% passing, zero warnings)**

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**Previous Features:**
- ✅ Multi-task Kernel Learning (30 tests)
- ✅ Online Kernel Updates (25 tests)
- ✅ Symbolic Kernel Composition (14 tests)
- ✅ Provenance Tracking System (15 tests)
- ✅ Performance benchmarks (5 benchmark suites)
- ✅ Tree kernels (16 tests)
- ✅ Low-rank approximations (10 tests)
- ✅ String kernels
- ✅ Graph kernels
- ✅ Kernel caching
- ✅ Sparse kernel matrices