sklears_kernel_approximation/sparse_gp/

mod.rs

//! Sparse Gaussian Process implementations with comprehensive approximation methods
//!
//! This module provides a complete sparse GP framework with multiple approximation methods,
//! SIMD acceleration, scalable inference, and structured kernel interpolation.

pub mod approximations;
pub mod core;
pub mod inference;
pub mod kernels;
pub mod simd_operations;
pub mod ski;
pub mod variational;

// Re-export main types and traits
pub use approximations::{InducingPointSelector, SparseApproximationMethods};
pub use core::*;
pub use inference::{LanczosMethod, PreconditionedCG, ScalableInference};
pub use kernels::{KernelOps, MaternKernel, RBFKernel, SparseKernel};
pub use simd_operations::simd_sparse_gp;
pub use ski::{FittedTensorSKI, TensorSKI};
pub use variational::{StochasticVariationalInference, VariationalFreeEnergy};

use scirs2_core::ndarray::{Array1, Array2};
use scirs2_core::random::essentials::Normal as RandNormal;
use scirs2_core::random::Distribution;
use scirs2_core::random::{thread_rng, Rng};
use sklears_core::error::{Result, SklearsError};
use sklears_core::traits::{Fit, Predict};

/// Main sparse Gaussian Process implementation
impl<K: SparseKernel> SparseGaussianProcess<K> {
    /// Create new sparse Gaussian Process with specified inducing points and kernel
    pub fn new(num_inducing: usize, kernel: K) -> Self {
        Self {
            num_inducing,
            kernel,
            approximation: SparseApproximation::FullyIndependentConditional,
            inducing_strategy: InducingPointStrategy::KMeans,
            noise_variance: 1e-6,
            max_iter: 100,
            tol: 1e-6,
        }
    }

    /// Select inducing points based on the configured strategy
    pub fn select_inducing_points(&self, x: &Array2<f64>) -> Result<Array2<f64>> {
        InducingPointSelector::select_points(
            &self.inducing_strategy,
            x,
            self.num_inducing,
            &self.kernel,
        )
    }

    /// Fit the sparse GP model using the configured approximation method
    fn fit_approximation(
        &self,
        x: &Array2<f64>,
        y: &Array1<f64>,
        inducing_points: &Array2<f64>,
    ) -> Result<(Array1<f64>, Array2<f64>, Option<VariationalParams>)> {
        match &self.approximation {
            SparseApproximation::SubsetOfRegressors => {
                let (alpha, k_mm_inv) = SparseApproximationMethods::fit_sor(
                    x,
                    y,
                    inducing_points,
                    &self.kernel,
                    self.noise_variance,
                )?;
                Ok((alpha, k_mm_inv, None))
            }

            SparseApproximation::FullyIndependentConditional => {
                let (alpha, k_mm_inv) = SparseApproximationMethods::fit_fic(
                    x,
                    y,
                    inducing_points,
                    &self.kernel,
                    self.noise_variance,
                )?;
                Ok((alpha, k_mm_inv, None))
            }

            SparseApproximation::PartiallyIndependentConditional { block_size } => {
                let (alpha, k_mm_inv) = SparseApproximationMethods::fit_pic(
                    x,
                    y,
                    inducing_points,
                    &self.kernel,
                    self.noise_variance,
                    *block_size,
                )?;
                Ok((alpha, k_mm_inv, None))
            }

            SparseApproximation::VariationalFreeEnergy {
                whitened,
                natural_gradients,
            } => {
                let (alpha, k_mm_inv, vfe_params) = VariationalFreeEnergy::fit(
                    x,
                    y,
                    inducing_points,
                    &self.kernel,
                    self.noise_variance,
                    *whitened,
                    *natural_gradients,
                    self.max_iter,
                    self.tol,
                )?;
                Ok((alpha, k_mm_inv, Some(vfe_params)))
            }
        }
    }
}

/// Fit implementation for sparse GP
impl<K: SparseKernel> Fit<Array2<f64>, Array1<f64>> for SparseGaussianProcess<K> {
    type Fitted = FittedSparseGP<K>;

    fn fit(self, x: &Array2<f64>, y: &Array1<f64>) -> Result<Self::Fitted> {
        // Validate input dimensions
        if x.nrows() != y.len() {
            return Err(SklearsError::InvalidInput(
                "Number of samples must match between X and y".to_string(),
            ));
        }

        if self.num_inducing > x.nrows() {
            return Err(SklearsError::InvalidInput(
                "Number of inducing points cannot exceed number of data points".to_string(),
            ));
        }

        // Select inducing points
        let inducing_points = self.select_inducing_points(x)?;

        // Validate inducing points configuration
        utils::validate_inducing_points(self.num_inducing, x.ncols(), &self.inducing_strategy)?;

        // Fit using the specified approximation method
        let (alpha, k_mm_inv, variational_params) =
            self.fit_approximation(x, y, &inducing_points)?;

        Ok(FittedSparseGP {
            inducing_points,
            kernel: self.kernel,
            approximation: self.approximation,
            alpha,
            k_mm_inv,
            noise_variance: self.noise_variance,
            variational_params,
        })
    }
}

/// Prediction implementation for fitted sparse GP
impl<K: SparseKernel> Predict<Array2<f64>, Array1<f64>> for FittedSparseGP<K> {
    fn predict(&self, x: &Array2<f64>) -> Result<Array1<f64>> {
        let k_star_m = self.kernel.kernel_matrix(x, &self.inducing_points);

        // Use SIMD-accelerated prediction when available
        let predictions = simd_sparse_gp::simd_posterior_mean(&k_star_m, &self.alpha);

        Ok(predictions)
    }
}

impl<K: SparseKernel> FittedSparseGP<K> {
    /// Predict with uncertainty quantification
    pub fn predict_with_variance(&self, x: &Array2<f64>) -> Result<(Array1<f64>, Array1<f64>)> {
        let k_star_m = self.kernel.kernel_matrix(x, &self.inducing_points);

        // Use SIMD-accelerated posterior mean computation
        let mean = simd_sparse_gp::simd_posterior_mean(&k_star_m, &self.alpha);

        // SIMD-accelerated predictive variance computation
        let v = self.k_mm_inv.dot(&k_star_m.t());
        let k_star_star = self.kernel.kernel_diagonal(x);
        let variance = simd_sparse_gp::simd_posterior_variance(&k_star_star, &v);

        Ok((mean, variance))
    }

    /// Scalable prediction using different inference methods
    pub fn predict_scalable(
        &self,
        x: &Array2<f64>,
        method: ScalableInferenceMethod,
    ) -> Result<Array1<f64>> {
        let k_star_m = self.kernel.kernel_matrix(x, &self.inducing_points);

        ScalableInference::predict(
            &method,
            &k_star_m,
            &self.inducing_points,
            &self.alpha,
            &self.kernel,
            self.noise_variance,
        )
    }

    /// Compute log marginal likelihood for model selection
    pub fn log_marginal_likelihood(&self) -> Result<f64> {
        if let Some(vfe_params) = &self.variational_params {
            // Use ELBO as approximation to log marginal likelihood
            Ok(vfe_params.elbo)
        } else {
            // Compute approximate log marginal likelihood for other methods
            let m = self.inducing_points.nrows();

            // Log determinant from inverse (simplified)
            let log_det = self
                .k_mm_inv
                .diag()
                .mapv(|x| if x > 1e-10 { -x.ln() } else { 23.0 })
                .sum();

            // Data fit term
            let data_fit = self.alpha.dot(&self.alpha);

            // Marginal likelihood approximation
            let log_ml = -0.5 * (data_fit + log_det + m as f64 * (2.0 * std::f64::consts::PI).ln());

            Ok(log_ml)
        }
    }

    /// Sample from the posterior predictive distribution
    pub fn sample_posterior(&self, x: &Array2<f64>, num_samples: usize) -> Result<Array2<f64>> {
        let (mean, var) = self.predict_with_variance(x)?;
        let n_test = x.nrows();

        let mut samples = Array2::zeros((num_samples, n_test));
        let mut rng = thread_rng();

        for i in 0..num_samples {
            for j in 0..n_test {
                let std_dev = var[j].sqrt();
                let normal = RandNormal::new(mean[j], std_dev).unwrap();
                samples[(i, j)] = rng.sample(normal);
            }
        }

        Ok(samples)
    }

    /// Compute acquisition function for active learning
    pub fn acquisition_function(
        &self,
        x: &Array2<f64>,
        acquisition_type: &str,
    ) -> Result<Array1<f64>> {
        let (mean, var) = self.predict_with_variance(x)?;

        match acquisition_type {
            "variance" => Ok(var),
            "entropy" => {
                // Predictive entropy: 0.5 * log(2πe * σ²)
                let entropy =
                    var.mapv(|v| 0.5 * (2.0 * std::f64::consts::PI * std::f64::consts::E * v).ln());
                Ok(entropy)
            }
            "upper_confidence_bound" => {
                // Upper confidence bound with β = 2
                let ucb = &mean + 2.0 * &var.mapv(|v| v.sqrt());
                Ok(ucb)
            }
            _ => Err(SklearsError::InvalidInput(format!(
                "Unknown acquisition function: {}",
                acquisition_type
            ))),
        }
    }
}

/// Utility functions and helpers
pub mod utils {
    pub use super::core::utils::*;
    use super::*;

    /// Compute effective degrees of freedom for sparse GP
    pub fn effective_degrees_of_freedom<K: SparseKernel>(
        fitted_gp: &FittedSparseGP<K>,
        x: &Array2<f64>,
    ) -> Result<f64> {
        let k_nm = fitted_gp
            .kernel
            .kernel_matrix(x, &fitted_gp.inducing_points);
        let k_mm_inv_k_mn = fitted_gp.k_mm_inv.dot(&k_nm.t());

        // Trace of the hat matrix approximation
        let mut trace = 0.0;
        for i in 0..k_nm.nrows() {
            trace += k_nm.row(i).dot(&k_mm_inv_k_mn.column(i));
        }

        Ok(trace)
    }

    /// Compute model complexity penalty
    pub fn model_complexity_penalty<K: SparseKernel>(fitted_gp: &FittedSparseGP<K>) -> f64 {
        // Simplified complexity penalty based on number of inducing points
        fitted_gp.inducing_points.nrows() as f64 * (fitted_gp.inducing_points.nrows() as f64).ln()
    }

    /// Optimize hyperparameters using gradient-based methods
    pub fn optimize_hyperparameters<K: SparseKernel>(
        sparse_gp: &mut SparseGaussianProcess<K>,
        x: &Array2<f64>,
        y: &Array1<f64>,
        max_iter: usize,
        learning_rate: f64,
    ) -> Result<f64> {
        let mut best_likelihood = f64::NEG_INFINITY;

        for _iter in 0..max_iter {
            // Fit current model
            let fitted = sparse_gp.clone().fit(x, y)?;

            // Compute log marginal likelihood
            let log_ml = fitted.log_marginal_likelihood()?;

            if log_ml > best_likelihood {
                best_likelihood = log_ml;
            }

            // Compute gradients (simplified - would use automatic differentiation)
            let gradients = sparse_gp
                .kernel
                .parameter_gradients(&fitted.inducing_points, &fitted.inducing_points);

            // Update kernel parameters (simplified gradient step)
            let mut params = sparse_gp.kernel.parameters();
            for (i, grad_matrix) in gradients.iter().enumerate() {
                let grad_scalar =
                    grad_matrix.sum() / (grad_matrix.nrows() * grad_matrix.ncols()) as f64;
                params[i] += learning_rate * grad_scalar;
                params[i] = params[i].max(1e-6); // Ensure positivity
            }
            sparse_gp.kernel.set_parameters(&params);
        }

        Ok(best_likelihood)
    }
}