Ridge Regression

crates/RustQuant_ml/src/lib.rs

@@ -33,3 +33,8 @@ pub use linear_regression::*;
 /// Logistic regression.
 pub mod logistic_regression;
 pub use logistic_regression::*;
+
+/// Ridge regression.
+pub mod ridge_regression;
+pub use ridge_regression::*;
+

crates/RustQuant_ml/src/ridge_regression.rs

@@ -0,0 +1,256 @@
+// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+// RustQuant: A Rust library for quantitative finance tools.
+// Copyright (C) 2023 https://github.com/avhz
+// Dual licensed under Apache 2.0 and MIT.
+// See:
+//      - LICENSE-APACHE.md
+//      - LICENSE-MIT.md
+// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+//! Module for ridge regression algorithms.
+
+// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+// IMPORTS
+// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+use nalgebra::{DMatrix, DVector};
+
+use RustQuant_error::RustQuantError;
+
+// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+// STRUCTS, ENUMS, AND TRAITS
+// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+/// Struct to hold the input data for a ridge regression.
+#[allow(clippy::module_name_repetitions)]
+#[derive(Clone, Debug)]
+pub struct RidgeRegressionInput<T> {
+    /// The features matrix.
+    pub x: DMatrix<T>,
+    /// The output data vector, also known as the response vector.
+    pub y: DVector<T>,
+    /// The regularization parameter.
+    pub lambda: T,
+    /// Include the intercept.
+    pub fit_intercept: bool,
+    /// The maximum number of iterations for training.
+    pub max_iter: usize,
+    /// The tolerance for the convergence.
+    pub tolerance: T,
+}
+
+/// Struct to hold the output data for a ridge regression.
+#[allow(clippy::module_name_repetitions)]
+#[derive(Clone, Debug)]
+pub struct RidgeRegressionOutput<T> {
+    /// The intercept of the ridge regression,
+    pub intercept: T,
+    /// The coefficients of the ridge regression,
+    pub coefficients: DVector<T>,
+}
+
+// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+// IMPLEMENTATIONS
+// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+impl RidgeRegressionInput<f64> {
+    /// Create a new `RidgeRegressionInput` struct.
+    #[must_use]
+    pub fn new(
+        x: DMatrix<f64>,
+        y: DVector<f64>,
+        lambda: f64,
+        fit_intercept: bool,
+        max_iter: usize,
+        tolerance: f64,
+    ) -> Self {
+        Self { x, y, lambda, fit_intercept, max_iter, tolerance }
+    }
+
+    /// Fits a ridge regression to the input data.
+    /// Returns the intercept and coefficients.
+    /// The intercept is the first value of the coefficients.
+    pub fn fit(&self) -> Result<RidgeRegressionOutput<f64>, RustQuantError> {
+
+        let features_matrix = if self.fit_intercept {
+            self.x.clone().insert_column(0, 1.)
+        } else {
+            self.x.clone()
+        };
+
+        let n_col: usize = features_matrix.ncols();
+        let features_matrix_transpose = features_matrix.transpose();
+        let mut regularisation_matrix = DMatrix::<f64>::identity(n_col, n_col);
+
+        if self.fit_intercept { regularisation_matrix[(0,0)] = 0.0; }
+
+        let ridge_matrix = (&features_matrix_transpose * features_matrix) + self.lambda * regularisation_matrix;
+
+        let ridge_matrix_inv = ridge_matrix
+            .try_inverse()
+            .ok_or(RustQuantError::MatrixInversionFailed)?;
+
+        let mut coefficients = ridge_matrix_inv * &features_matrix_transpose * &self.y;
+        let intercept: f64 =  if self.fit_intercept {
+            coefficients[0]
+        } else {
+            coefficients = coefficients.insert_row(0, 0.0); 
+            0.0
+        };
+
+        Ok(RidgeRegressionOutput {
+            intercept,
+            coefficients,
+        })
+    }
+}
+
+impl RidgeRegressionOutput<f64> {
+    /// Predicts the output for the given input data.
+    pub fn predict(&self, input: DMatrix<f64>) -> Result<DVector<f64>, RustQuantError> {
+        let intercept = DVector::from_element(input.nrows(), self.intercept);
+        let coefficients = self.coefficients.clone().remove_row(0);
+        let predictions = input * coefficients + intercept;
+        Ok(predictions)
+    }
+}
+
+// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+// UNIT TESTS
+// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+#[cfg(test)]
+mod tests_ridge_regression {
+    use super::*;
+    use RustQuant_utils::assert_approx_equal;
+
+    struct DataForTests {
+        training_set: DMatrix<f64>,
+        testing_set: DMatrix<f64>,
+        response: DVector<f64>,
+    }
+
+    fn setup_test() -> DataForTests {
+        DataForTests {
+            training_set: DMatrix::from_row_slice(
+            4,
+            3,
+        &[
+                -0.083_784_355, -0.633_485_70, -0.399_266_60,
+                -0.982_943_745,  1.090_797_46, -0.468_123_05,
+                -1.875_067_321, -0.913_727_27,  0.326_962_08,
+                -0.186_144_661,  1.001_639_71, -0.412_746_90],
+            ),
+
+            testing_set: DMatrix::from_row_slice(
+            4,
+            3,
+            &[
+                0.562_036_47, 0.595_846_45, -0.411_653_01,
+                0.663_358_26, 0.452_091_83, -0.294_327_15,
+                -0.602_897_28, 0.896_743_96, 1.218_573_96,
+                0.698_377_69, 0.572_216_51, 0.244_111_43],
+            ),
+
+            response: DVector::from_row_slice(
+                &[
+                    -0.445_151_96,
+                    -1.847_803_64,
+                    -0.628_825_31,
+                    -0.861_080_69
+                ]
+            ),
+        }
+    }
+
+    #[test]
+    fn test_ridge_regression_without_intercept() -> Result<(), RustQuantError> {
+
+        let data: DataForTests = setup_test();
+
+        let input: RidgeRegressionInput<f64> = RidgeRegressionInput {
+            x: data.training_set,
+            y: data.response,
+            lambda: 1.0,
+            fit_intercept: false,
+            max_iter: 1000,
+            tolerance: 1e-4,
+        };
+
+        let output = input.fit()?;
+
+        for (i, coefficient) in output.coefficients.iter().enumerate() {
+            assert_approx_equal!(
+                coefficient,
+                &[
+                    0.0,
+                    0.620_453_495_948_496_1,
+                    -0.420_204_780_485_896_43,
+                    0.490_065_457_911_238_96
+                ][i],
+                f64::EPSILON
+            );
+        }
+
+        let predictions = output.predict(data.testing_set)?;
+        for (i, pred) in predictions.iter().enumerate() {
+            assert_approx_equal!(
+                pred,
+                &[
+                    -0.103_396_954_909_688_48,
+                    0.077_372_233_758_234_32,
+                    -0.153_704_818_231_581,
+                    0.312_493_346_002_296_7
+                ][i],
+                f64::EPSILON
+            );
+        }
+        Ok(())
+    }
+
+    #[test]
+    fn test_ridge_regression_with_intercept() -> Result<(), RustQuantError> {
+
+        let data: DataForTests = setup_test();
+
+        let input: RidgeRegressionInput<f64> = RidgeRegressionInput {
+            x: data.training_set,
+            y: data.response,
+            lambda: 1.0,
+            fit_intercept: true,
+            max_iter: 1000,
+            tolerance: 1e-4,
+        };
+
+        let output = input.fit()?;
+
+        for (i, coefficient) in output.coefficients.iter().enumerate() {
+            assert_approx_equal!(
+                coefficient,
+                &[
+                    -0.701_404_539_262_792_8,
+                    0.215_855_099_335_031_66,
+                    -0.371_997_155_606_467_07,
+                    0.104_115_015_026_450_71,
+                ][i],
+                f64::EPSILON
+            );
+        }
+
+        let predictions = output.predict(data.testing_set)?;
+
+        for (i, pred) in predictions.iter().enumerate() {
+            assert_approx_equal!(
+                pred,
+                &[
+                    -0.844_598_545_101_076_9,
+                    -0.757_036_026_633_643_9,
+                    -1.038_257_347_797_051_1,
+                    -0.738_103_402_522_953_9,
+                ][i],
+                f64::EPSILON
+            );
+        }
+        Ok(())
+    }
+}