quantrs2_anneal/bayesian_hyperopt/

gaussian_process.rs

//! Gaussian Process Surrogate Models

use super::config::{BayesianOptError, BayesianOptResult};

/// Gaussian process configuration (alias for backward compatibility)
pub type GaussianProcessConfig = GaussianProcessSurrogate;

/// Gaussian process surrogate model
#[derive(Debug, Clone)]
pub struct GaussianProcessSurrogate {
    pub kernel: KernelFunction,
    pub noise_variance: f64,
    pub mean_function: MeanFunction,
}

impl Default for GaussianProcessSurrogate {
    fn default() -> Self {
        Self {
            kernel: KernelFunction::RBF,
            noise_variance: 1e-6,
            mean_function: MeanFunction::Zero,
        }
    }
}

impl GaussianProcessSurrogate {
    /// Simple predict method for compatibility
    pub const fn predict(&self, _x: &[f64]) -> BayesianOptResult<(f64, f64)> {
        // Simplified prediction - in practice would use trained model
        // Returns (mean, variance)
        Ok((0.0, 1.0))
    }
}

/// Kernel functions for Gaussian processes
#[derive(Debug, Clone, PartialEq, Eq)]
pub enum KernelFunction {
    /// Radial Basis Function (RBF) kernel
    RBF,
    /// Matern kernel
    Matern,
    /// Linear kernel
    Linear,
    /// Polynomial kernel
    Polynomial,
    /// Spectral mixture kernel
    SpectralMixture,
}

/// Mean functions for Gaussian processes
#[derive(Debug, Clone, PartialEq)]
pub enum MeanFunction {
    /// Zero mean function
    Zero,
    /// Constant mean function
    Constant(f64),
    /// Linear mean function
    Linear,
    /// Polynomial mean function
    Polynomial { degree: usize },
}

/// Gaussian process hyperparameters
#[derive(Debug, Clone)]
pub struct GPHyperparameters {
    pub length_scales: Vec<f64>,
    pub signal_variance: f64,
    pub noise_variance: f64,
    pub mean_parameters: Vec<f64>,
}

impl Default for GPHyperparameters {
    fn default() -> Self {
        Self {
            length_scales: vec![1.0],
            signal_variance: 1.0,
            noise_variance: 1e-6,
            mean_parameters: vec![0.0],
        }
    }
}

/// Gaussian Process Model implementation
#[derive(Debug, Clone)]
pub struct GaussianProcessModel {
    /// Training input data
    pub x_train: Vec<Vec<f64>>,
    /// Training output data
    pub y_train: Vec<f64>,
    /// GP configuration
    pub config: GaussianProcessConfig,
    /// Learned hyperparameters
    pub hyperparameters: GPHyperparameters,
    /// Precomputed kernel matrix inverse (for efficiency)
    pub k_inv: Option<Vec<Vec<f64>>>,
}

impl GaussianProcessModel {
    /// Create new Gaussian Process model
    pub fn new(
        x_train: Vec<Vec<f64>>,
        y_train: Vec<f64>,
        config: GaussianProcessConfig,
    ) -> BayesianOptResult<Self> {
        if x_train.len() != y_train.len() {
            return Err(BayesianOptError::GaussianProcessError(
                "Training inputs and outputs must have same length".to_string(),
            ));
        }

        if x_train.is_empty() {
            return Err(BayesianOptError::GaussianProcessError(
                "Training data cannot be empty".to_string(),
            ));
        }

        let input_dim = x_train[0].len();
        let hyperparameters = GPHyperparameters {
            length_scales: vec![1.0; input_dim],
            signal_variance: 1.0,
            noise_variance: config.noise_variance,
            mean_parameters: vec![0.0],
        };

        let mut model = Self {
            x_train,
            y_train,
            config,
            hyperparameters,
            k_inv: None,
        };

        // Fit the model (simple implementation)
        model.fit()?;

        Ok(model)
    }

    /// Fit the Gaussian Process model
    pub fn fit(&mut self) -> BayesianOptResult<()> {
        // Simple hyperparameter setting (in practice would optimize via ML-II)
        self.optimize_hyperparameters()?;

        // Precompute kernel matrix inverse for predictions
        self.precompute_kernel_inverse()?;

        Ok(())
    }

    /// Simple hyperparameter optimization (placeholder)
    fn optimize_hyperparameters(&mut self) -> BayesianOptResult<()> {
        let n = self.x_train.len();
        if n == 0 {
            return Ok(());
        }

        // Simple heuristic hyperparameter setting
        let input_dim = self.x_train[0].len();

        // Set length scales based on input ranges
        for dim in 0..input_dim {
            let values: Vec<f64> = self.x_train.iter().map(|x| x[dim]).collect();
            let min_val = values.iter().fold(f64::INFINITY, |a, &b| a.min(b));
            let max_val = values.iter().fold(f64::NEG_INFINITY, |a, &b| a.max(b));
            let range = (max_val - min_val).max(1e-6);

            self.hyperparameters.length_scales[dim] = range / 2.0;
        }

        // Set signal variance based on output variance
        let mean_y = self.y_train.iter().sum::<f64>() / n as f64;
        let var_y = self
            .y_train
            .iter()
            .map(|&y| (y - mean_y).powi(2))
            .sum::<f64>()
            / n as f64;

        self.hyperparameters.signal_variance = var_y.max(1e-6);

        Ok(())
    }

    /// Precompute kernel matrix inverse for efficient predictions
    fn precompute_kernel_inverse(&mut self) -> BayesianOptResult<()> {
        let n = self.x_train.len();

        // Compute kernel matrix
        let mut k_matrix = vec![vec![0.0; n]; n];
        for i in 0..n {
            for j in 0..n {
                k_matrix[i][j] = self.kernel(&self.x_train[i], &self.x_train[j]);
                if i == j {
                    k_matrix[i][j] += self.hyperparameters.noise_variance;
                }
            }
        }

        // Compute matrix inverse (simplified - in practice would use Cholesky decomposition)
        let k_inv = self.matrix_inverse(k_matrix)?;
        self.k_inv = Some(k_inv);

        Ok(())
    }

    /// Simple matrix inverse implementation (for small matrices)
    fn matrix_inverse(&self, mut matrix: Vec<Vec<f64>>) -> BayesianOptResult<Vec<Vec<f64>>> {
        let n = matrix.len();

        // Create augmented matrix [A|I]
        let mut augmented = vec![vec![0.0; 2 * n]; n];
        for i in 0..n {
            for j in 0..n {
                augmented[i][j] = matrix[i][j];
            }
            augmented[i][i + n] = 1.0;
        }

        // Gaussian elimination
        for i in 0..n {
            // Find pivot
            let mut max_row = i;
            for k in (i + 1)..n {
                if augmented[k][i].abs() > augmented[max_row][i].abs() {
                    max_row = k;
                }
            }

            // Swap rows
            if max_row != i {
                augmented.swap(i, max_row);
            }

            // Check for singular matrix
            if augmented[i][i].abs() < 1e-12 {
                return Err(BayesianOptError::GaussianProcessError(
                    "Singular kernel matrix".to_string(),
                ));
            }

            // Scale row
            let pivot = augmented[i][i];
            for j in 0..(2 * n) {
                augmented[i][j] /= pivot;
            }

            // Eliminate column
            for k in 0..n {
                if k != i {
                    let factor = augmented[k][i];
                    for j in 0..(2 * n) {
                        augmented[k][j] -= factor * augmented[i][j];
                    }
                }
            }
        }

        // Extract inverse matrix
        let mut inverse = vec![vec![0.0; n]; n];
        for i in 0..n {
            for j in 0..n {
                inverse[i][j] = augmented[i][j + n];
            }
        }

        Ok(inverse)
    }

    /// Compute kernel function between two points
    fn kernel(&self, x1: &[f64], x2: &[f64]) -> f64 {
        match self.config.kernel {
            KernelFunction::RBF => self.rbf_kernel(x1, x2),
            KernelFunction::Matern => self.matern_kernel(x1, x2),
            KernelFunction::Linear => self.linear_kernel(x1, x2),
            KernelFunction::Polynomial => self.polynomial_kernel(x1, x2),
            KernelFunction::SpectralMixture => self.rbf_kernel(x1, x2), // Fallback to RBF
        }
    }

    /// RBF (Gaussian) kernel
    fn rbf_kernel(&self, x1: &[f64], x2: &[f64]) -> f64 {
        let mut distance_sq = 0.0;
        for (i, (&xi, &xj)) in x1.iter().zip(x2.iter()).enumerate() {
            let length_scale = self.hyperparameters.length_scales.get(i).unwrap_or(&1.0);
            distance_sq += ((xi - xj) / length_scale).powi(2);
        }

        self.hyperparameters.signal_variance * (-0.5 * distance_sq).exp()
    }

    /// Matern kernel (simplified to Matern 3/2)
    fn matern_kernel(&self, x1: &[f64], x2: &[f64]) -> f64 {
        let mut distance = 0.0;
        for (i, (&xi, &xj)) in x1.iter().zip(x2.iter()).enumerate() {
            let length_scale = self.hyperparameters.length_scales.get(i).unwrap_or(&1.0);
            distance += ((xi - xj) / length_scale).powi(2);
        }
        distance = distance.sqrt();

        let sqrt3_r = 3.0_f64.sqrt() * distance;
        self.hyperparameters.signal_variance * (1.0 + sqrt3_r) * (-sqrt3_r).exp()
    }

    /// Linear kernel
    fn linear_kernel(&self, x1: &[f64], x2: &[f64]) -> f64 {
        let dot_product: f64 = x1.iter().zip(x2.iter()).map(|(&xi, &xj)| xi * xj).sum();
        self.hyperparameters.signal_variance * dot_product
    }

    /// Polynomial kernel
    fn polynomial_kernel(&self, x1: &[f64], x2: &[f64]) -> f64 {
        let dot_product: f64 = x1.iter().zip(x2.iter()).map(|(&xi, &xj)| xi * xj).sum();
        self.hyperparameters.signal_variance * (1.0 + dot_product).powi(2)
    }

    /// Make prediction at new point
    pub fn predict(&self, x: &[f64]) -> BayesianOptResult<(f64, f64)> {
        let k_inv = self.k_inv.as_ref().ok_or_else(|| {
            BayesianOptError::GaussianProcessError("Model not fitted".to_string())
        })?;

        // Compute kernel vector between x and training data
        let k_star: Vec<f64> = self
            .x_train
            .iter()
            .map(|x_train| self.kernel(x, x_train))
            .collect();

        // Compute mean prediction
        let mut mean = 0.0;
        for i in 0..self.y_train.len() {
            for j in 0..self.y_train.len() {
                mean += k_star[i] * k_inv[i][j] * self.y_train[j];
            }
        }

        // Add mean function value
        mean += self.mean_function_value(x);

        // Compute variance prediction
        let k_star_star = self.kernel(x, x);
        let mut variance = k_star_star;

        for i in 0..k_star.len() {
            for j in 0..k_star.len() {
                variance -= k_star[i] * k_inv[i][j] * k_star[j];
            }
        }

        // Ensure non-negative variance
        variance = variance.max(1e-12);

        Ok((mean, variance))
    }

    /// Evaluate mean function
    fn mean_function_value(&self, x: &[f64]) -> f64 {
        match self.config.mean_function {
            MeanFunction::Zero => 0.0,
            MeanFunction::Constant(c) => c,
            MeanFunction::Linear => {
                // Simple linear mean: sum of coordinates
                x.iter().sum::<f64>() * self.hyperparameters.mean_parameters.get(0).unwrap_or(&0.0)
            }
            MeanFunction::Polynomial { degree: _ } => {
                // Simplified polynomial mean
                let x_sum = x.iter().sum::<f64>();
                x_sum * self.hyperparameters.mean_parameters.get(0).unwrap_or(&0.0)
            }
        }
    }

    /// Get marginal log-likelihood (for hyperparameter optimization)
    pub fn log_marginal_likelihood(&self) -> BayesianOptResult<f64> {
        let k_inv = self.k_inv.as_ref().ok_or_else(|| {
            BayesianOptError::GaussianProcessError("Model not fitted".to_string())
        })?;

        let n = self.y_train.len();

        // Compute y^T K^(-1) y
        let mut quad_form = 0.0;
        for i in 0..n {
            for j in 0..n {
                quad_form += self.y_train[i] * k_inv[i][j] * self.y_train[j];
            }
        }

        // Compute log determinant (simplified - would use Cholesky in practice)
        let log_det = self.log_determinant()?;

        let log_likelihood = (0.5 * n as f64).mul_add(
            -(2.0 * std::f64::consts::PI).ln(),
            (-0.5f64).mul_add(quad_form, -(0.5 * log_det)),
        );

        Ok(log_likelihood)
    }

    /// Compute log determinant of kernel matrix (simplified)
    fn log_determinant(&self) -> BayesianOptResult<f64> {
        // Simplified computation - in practice would use Cholesky decomposition
        let n = self.x_train.len();

        // Rebuild kernel matrix to compute determinant
        let mut k_matrix = vec![vec![0.0; n]; n];
        for i in 0..n {
            for j in 0..n {
                k_matrix[i][j] = self.kernel(&self.x_train[i], &self.x_train[j]);
                if i == j {
                    k_matrix[i][j] += self.hyperparameters.noise_variance;
                }
            }
        }

        // Compute determinant via LU decomposition (simplified)
        let mut det = 1.0;
        for i in 0..n {
            det *= k_matrix[i][i].max(1e-12);
        }

        Ok(det.ln())
    }
}