use std::fmt::Debug;
use serde::{Deserialize, Serialize};
use crate::api::{Predictor, SupervisedEstimator};
use crate::error::Failed;
use crate::linalg::BaseVector;
use crate::linalg::Matrix;
use crate::math::num::RealNumber;
#[derive(Serialize, Deserialize, Debug, Clone)]
pub enum RidgeRegressionSolverName {
Cholesky,
SVD,
}
#[derive(Serialize, Deserialize, Debug, Clone)]
pub struct RidgeRegressionParameters<T: RealNumber> {
pub solver: RidgeRegressionSolverName,
pub alpha: T,
pub normalize: bool,
}
#[derive(Serialize, Deserialize, Debug)]
pub struct RidgeRegression<T: RealNumber, M: Matrix<T>> {
coefficients: M,
intercept: T,
solver: RidgeRegressionSolverName,
}
impl<T: RealNumber> RidgeRegressionParameters<T> {
pub fn with_alpha(mut self, alpha: T) -> Self {
self.alpha = alpha;
self
}
pub fn with_solver(mut self, solver: RidgeRegressionSolverName) -> Self {
self.solver = solver;
self
}
pub fn with_normalize(mut self, normalize: bool) -> Self {
self.normalize = normalize;
self
}
}
impl<T: RealNumber> Default for RidgeRegressionParameters<T> {
fn default() -> Self {
RidgeRegressionParameters {
solver: RidgeRegressionSolverName::Cholesky,
alpha: T::one(),
normalize: true,
}
}
}
impl<T: RealNumber, M: Matrix<T>> PartialEq for RidgeRegression<T, M> {
fn eq(&self, other: &Self) -> bool {
self.coefficients == other.coefficients
&& (self.intercept - other.intercept).abs() <= T::epsilon()
}
}
impl<T: RealNumber, M: Matrix<T>> SupervisedEstimator<M, M::RowVector, RidgeRegressionParameters<T>>
for RidgeRegression<T, M>
{
fn fit(
x: &M,
y: &M::RowVector,
parameters: RidgeRegressionParameters<T>,
) -> Result<Self, Failed> {
RidgeRegression::fit(x, y, parameters)
}
}
impl<T: RealNumber, M: Matrix<T>> Predictor<M, M::RowVector> for RidgeRegression<T, M> {
fn predict(&self, x: &M) -> Result<M::RowVector, Failed> {
self.predict(x)
}
}
impl<T: RealNumber, M: Matrix<T>> RidgeRegression<T, M> {
pub fn fit(
x: &M,
y: &M::RowVector,
parameters: RidgeRegressionParameters<T>,
) -> Result<RidgeRegression<T, M>, Failed> {
let (n, p) = x.shape();
if n <= p {
return Err(Failed::fit(
"Number of rows in X should be >= number of columns in X",
));
}
if y.len() != n {
return Err(Failed::fit("Number of rows in X should = len(y)"));
}
let y_column = M::from_row_vector(y.clone()).transpose();
let (w, b) = if parameters.normalize {
let (scaled_x, col_mean, col_std) = Self::rescale_x(x)?;
let x_t = scaled_x.transpose();
let x_t_y = x_t.matmul(&y_column);
let mut x_t_x = x_t.matmul(&scaled_x);
for i in 0..p {
x_t_x.add_element_mut(i, i, parameters.alpha);
}
let mut w = match parameters.solver {
RidgeRegressionSolverName::Cholesky => x_t_x.cholesky_solve_mut(x_t_y)?,
RidgeRegressionSolverName::SVD => x_t_x.svd_solve_mut(x_t_y)?,
};
for (i, col_std_i) in col_std.iter().enumerate().take(p) {
w.set(i, 0, w.get(i, 0) / *col_std_i);
}
let mut b = T::zero();
for (i, col_mean_i) in col_mean.iter().enumerate().take(p) {
b += w.get(i, 0) * *col_mean_i;
}
let b = y.mean() - b;
(w, b)
} else {
let x_t = x.transpose();
let x_t_y = x_t.matmul(&y_column);
let mut x_t_x = x_t.matmul(x);
for i in 0..p {
x_t_x.add_element_mut(i, i, parameters.alpha);
}
let w = match parameters.solver {
RidgeRegressionSolverName::Cholesky => x_t_x.cholesky_solve_mut(x_t_y)?,
RidgeRegressionSolverName::SVD => x_t_x.svd_solve_mut(x_t_y)?,
};
(w, T::zero())
};
Ok(RidgeRegression {
intercept: b,
coefficients: w,
solver: parameters.solver,
})
}
fn rescale_x(x: &M) -> Result<(M, Vec<T>, Vec<T>), Failed> {
let col_mean = x.mean(0);
let col_std = x.std(0);
for (i, col_std_i) in col_std.iter().enumerate() {
if (*col_std_i - T::zero()).abs() < T::epsilon() {
return Err(Failed::fit(&format!(
"Cannot rescale constant column {}",
i
)));
}
}
let mut scaled_x = x.clone();
scaled_x.scale_mut(&col_mean, &col_std, 0);
Ok((scaled_x, col_mean, col_std))
}
pub fn predict(&self, x: &M) -> Result<M::RowVector, Failed> {
let (nrows, _) = x.shape();
let mut y_hat = x.matmul(&self.coefficients);
y_hat.add_mut(&M::fill(nrows, 1, self.intercept));
Ok(y_hat.transpose().to_row_vector())
}
pub fn coefficients(&self) -> &M {
&self.coefficients
}
pub fn intercept(&self) -> T {
self.intercept
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::linalg::naive::dense_matrix::*;
use crate::metrics::mean_absolute_error;
#[test]
fn ridge_fit_predict() {
let x = DenseMatrix::from_2d_array(&[
&[234.289, 235.6, 159.0, 107.608, 1947., 60.323],
&[259.426, 232.5, 145.6, 108.632, 1948., 61.122],
&[258.054, 368.2, 161.6, 109.773, 1949., 60.171],
&[284.599, 335.1, 165.0, 110.929, 1950., 61.187],
&[328.975, 209.9, 309.9, 112.075, 1951., 63.221],
&[346.999, 193.2, 359.4, 113.270, 1952., 63.639],
&[365.385, 187.0, 354.7, 115.094, 1953., 64.989],
&[363.112, 357.8, 335.0, 116.219, 1954., 63.761],
&[397.469, 290.4, 304.8, 117.388, 1955., 66.019],
&[419.180, 282.2, 285.7, 118.734, 1956., 67.857],
&[442.769, 293.6, 279.8, 120.445, 1957., 68.169],
&[444.546, 468.1, 263.7, 121.950, 1958., 66.513],
&[482.704, 381.3, 255.2, 123.366, 1959., 68.655],
&[502.601, 393.1, 251.4, 125.368, 1960., 69.564],
&[518.173, 480.6, 257.2, 127.852, 1961., 69.331],
&[554.894, 400.7, 282.7, 130.081, 1962., 70.551],
]);
let y: Vec<f64> = vec![
83.0, 88.5, 88.2, 89.5, 96.2, 98.1, 99.0, 100.0, 101.2, 104.6, 108.4, 110.8, 112.6,
114.2, 115.7, 116.9,
];
let y_hat_cholesky = RidgeRegression::fit(
&x,
&y,
RidgeRegressionParameters {
solver: RidgeRegressionSolverName::Cholesky,
alpha: 0.1,
normalize: true,
},
)
.and_then(|lr| lr.predict(&x))
.unwrap();
assert!(mean_absolute_error(&y_hat_cholesky, &y) < 2.0);
let y_hat_svd = RidgeRegression::fit(
&x,
&y,
RidgeRegressionParameters {
solver: RidgeRegressionSolverName::SVD,
alpha: 0.1,
normalize: false,
},
)
.and_then(|lr| lr.predict(&x))
.unwrap();
assert!(mean_absolute_error(&y_hat_svd, &y) < 2.0);
}
#[test]
fn serde() {
let x = DenseMatrix::from_2d_array(&[
&[234.289, 235.6, 159.0, 107.608, 1947., 60.323],
&[259.426, 232.5, 145.6, 108.632, 1948., 61.122],
&[258.054, 368.2, 161.6, 109.773, 1949., 60.171],
&[284.599, 335.1, 165.0, 110.929, 1950., 61.187],
&[328.975, 209.9, 309.9, 112.075, 1951., 63.221],
&[346.999, 193.2, 359.4, 113.270, 1952., 63.639],
&[365.385, 187.0, 354.7, 115.094, 1953., 64.989],
&[363.112, 357.8, 335.0, 116.219, 1954., 63.761],
&[397.469, 290.4, 304.8, 117.388, 1955., 66.019],
&[419.180, 282.2, 285.7, 118.734, 1956., 67.857],
&[442.769, 293.6, 279.8, 120.445, 1957., 68.169],
&[444.546, 468.1, 263.7, 121.950, 1958., 66.513],
&[482.704, 381.3, 255.2, 123.366, 1959., 68.655],
&[502.601, 393.1, 251.4, 125.368, 1960., 69.564],
&[518.173, 480.6, 257.2, 127.852, 1961., 69.331],
&[554.894, 400.7, 282.7, 130.081, 1962., 70.551],
]);
let y = vec![
83.0, 88.5, 88.2, 89.5, 96.2, 98.1, 99.0, 100.0, 101.2, 104.6, 108.4, 110.8, 112.6,
114.2, 115.7, 116.9,
];
let lr = RidgeRegression::fit(&x, &y, Default::default()).unwrap();
let deserialized_lr: RidgeRegression<f64, DenseMatrix<f64>> =
serde_json::from_str(&serde_json::to_string(&lr).unwrap()).unwrap();
assert_eq!(lr, deserialized_lr);
}
}