605 lines
21 KiB
Rust
605 lines
21 KiB
Rust
//! # Epsilon-Support Vector Regression.
|
|
//!
|
|
//! Support Vector Regression (SVR) is a popular algorithm used for regression that uses the same principle as SVM.
|
|
//!
|
|
//! Just like [SVC](../svc/index.html) SVR finds optimal decision boundary, \\(f(x)\\) that separates all training instances with the largest margin.
|
|
//! Unlike SVC, in \\(\epsilon\\)-SVR regression the goal is to find a function \\(f(x)\\) that has at most \\(\epsilon\\) deviation from the
|
|
//! known targets \\(y_i\\) for all the training data. To find this function, we need to find solution to this optimization problem:
|
|
//!
|
|
//! \\[\underset{w, \zeta}{minimize} \space \space \frac{1}{2} \lVert \vec{w} \rVert^2 + C\sum_{i=1}^m \zeta_i \\]
|
|
//!
|
|
//! subject to:
|
|
//!
|
|
//! \\[\lvert y_i - \langle\vec{w}, \vec{x}_i \rangle - b \rvert \leq \epsilon + \zeta_i \\]
|
|
//! \\[\lvert \langle\vec{w}, \vec{x}_i \rangle + b - y_i \rvert \leq \epsilon + \zeta_i \\]
|
|
//! \\[\zeta_i \geq 0 for \space any \space i = 1, ... , m\\]
|
|
//!
|
|
//! Where \\( m \\) is a number of training samples, \\( y_i \\) is a target value and \\(\langle\vec{w}, \vec{x}_i \rangle + b\\) is a decision boundary.
|
|
//!
|
|
//! The parameter `C` > 0 determines the trade-off between the flatness of \\(f(x)\\) and the amount up to which deviations larger than \\(\epsilon\\) are tolerated
|
|
//!
|
|
//! Example:
|
|
//!
|
|
//! ```
|
|
//! use smartcore::linalg::naive::dense_matrix::*;
|
|
//! use smartcore::linear::linear_regression::*;
|
|
//! use smartcore::svm::*;
|
|
//! use smartcore::svm::svr::{SVR, SVRParameters};
|
|
//!
|
|
//! // Longley dataset (https://www.statsmodels.org/stable/datasets/generated/longley.html)
|
|
//! 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 svr = SVR::fit(&x, &y, SVRParameters::default().with_eps(2.0).with_c(10.0)).unwrap();
|
|
//!
|
|
//! let y_hat = svr.predict(&x).unwrap();
|
|
//! ```
|
|
//!
|
|
//! ## References:
|
|
//!
|
|
//! * ["Support Vector Machines", Kowalczyk A., 2017](https://www.svm-tutorial.com/2017/10/support-vector-machines-succinctly-released/)
|
|
//! * ["A Fast Algorithm for Training Support Vector Machines", Platt J.C., 1998](https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/tr-98-14.pdf)
|
|
//! * ["Working Set Selection Using Second Order Information for Training Support Vector Machines", Rong-En Fan et al., 2005](https://www.jmlr.org/papers/volume6/fan05a/fan05a.pdf)
|
|
//! * ["A tutorial on support vector regression", Smola A.J., Scholkopf B., 2003](https://alex.smola.org/papers/2004/SmoSch04.pdf)
|
|
//!
|
|
//! <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
|
|
//! <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
|
|
|
|
use std::cell::{Ref, RefCell};
|
|
use std::fmt::Debug;
|
|
use std::marker::PhantomData;
|
|
|
|
#[cfg(feature = "serde")]
|
|
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;
|
|
use crate::svm::{Kernel, Kernels, LinearKernel};
|
|
|
|
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
|
|
#[derive(Debug, Clone)]
|
|
/// SVR Parameters
|
|
pub struct SVRParameters<T: RealNumber, M: Matrix<T>, K: Kernel<T, M::RowVector>> {
|
|
/// Epsilon in the epsilon-SVR model.
|
|
pub eps: T,
|
|
/// Regularization parameter.
|
|
pub c: T,
|
|
/// Tolerance for stopping criterion.
|
|
pub tol: T,
|
|
/// The kernel function.
|
|
pub kernel: K,
|
|
/// Unused parameter.
|
|
m: PhantomData<M>,
|
|
}
|
|
|
|
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
|
|
#[derive(Debug)]
|
|
#[cfg_attr(
|
|
feature = "serde",
|
|
serde(bound(
|
|
serialize = "M::RowVector: Serialize, K: Serialize, T: Serialize",
|
|
deserialize = "M::RowVector: Deserialize<'de>, K: Deserialize<'de>, T: Deserialize<'de>",
|
|
))
|
|
)]
|
|
|
|
/// Epsilon-Support Vector Regression
|
|
pub struct SVR<T: RealNumber, M: Matrix<T>, K: Kernel<T, M::RowVector>> {
|
|
kernel: K,
|
|
instances: Vec<M::RowVector>,
|
|
w: Vec<T>,
|
|
b: T,
|
|
}
|
|
|
|
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
|
|
#[derive(Debug)]
|
|
struct SupportVector<T: RealNumber, V: BaseVector<T>> {
|
|
index: usize,
|
|
x: V,
|
|
alpha: [T; 2],
|
|
grad: [T; 2],
|
|
k: T,
|
|
}
|
|
|
|
/// Sequential Minimal Optimization algorithm
|
|
struct Optimizer<'a, T: RealNumber, M: Matrix<T>, K: Kernel<T, M::RowVector>> {
|
|
tol: T,
|
|
c: T,
|
|
svmin: usize,
|
|
svmax: usize,
|
|
gmin: T,
|
|
gmax: T,
|
|
gminindex: usize,
|
|
gmaxindex: usize,
|
|
tau: T,
|
|
sv: Vec<SupportVector<T, M::RowVector>>,
|
|
kernel: &'a K,
|
|
}
|
|
|
|
struct Cache<T: Clone> {
|
|
data: Vec<RefCell<Option<Vec<T>>>>,
|
|
}
|
|
|
|
impl<T: RealNumber, M: Matrix<T>, K: Kernel<T, M::RowVector>> SVRParameters<T, M, K> {
|
|
/// Epsilon in the epsilon-SVR model.
|
|
pub fn with_eps(mut self, eps: T) -> Self {
|
|
self.eps = eps;
|
|
self
|
|
}
|
|
/// Regularization parameter.
|
|
pub fn with_c(mut self, c: T) -> Self {
|
|
self.c = c;
|
|
self
|
|
}
|
|
/// Tolerance for stopping criterion.
|
|
pub fn with_tol(mut self, tol: T) -> Self {
|
|
self.tol = tol;
|
|
self
|
|
}
|
|
/// The kernel function.
|
|
pub fn with_kernel<KK: Kernel<T, M::RowVector>>(&self, kernel: KK) -> SVRParameters<T, M, KK> {
|
|
SVRParameters {
|
|
eps: self.eps,
|
|
c: self.c,
|
|
tol: self.tol,
|
|
kernel,
|
|
m: PhantomData,
|
|
}
|
|
}
|
|
}
|
|
|
|
impl<T: RealNumber, M: Matrix<T>> Default for SVRParameters<T, M, LinearKernel> {
|
|
fn default() -> Self {
|
|
SVRParameters {
|
|
eps: T::from_f64(0.1).unwrap(),
|
|
c: T::one(),
|
|
tol: T::from_f64(1e-3).unwrap(),
|
|
kernel: Kernels::linear(),
|
|
m: PhantomData,
|
|
}
|
|
}
|
|
}
|
|
|
|
impl<T: RealNumber, M: Matrix<T>, K: Kernel<T, M::RowVector>>
|
|
SupervisedEstimator<M, M::RowVector, SVRParameters<T, M, K>> for SVR<T, M, K>
|
|
{
|
|
fn fit(x: &M, y: &M::RowVector, parameters: SVRParameters<T, M, K>) -> Result<Self, Failed> {
|
|
SVR::fit(x, y, parameters)
|
|
}
|
|
}
|
|
|
|
impl<T: RealNumber, M: Matrix<T>, K: Kernel<T, M::RowVector>> Predictor<M, M::RowVector>
|
|
for SVR<T, M, K>
|
|
{
|
|
fn predict(&self, x: &M) -> Result<M::RowVector, Failed> {
|
|
self.predict(x)
|
|
}
|
|
}
|
|
|
|
impl<T: RealNumber, M: Matrix<T>, K: Kernel<T, M::RowVector>> SVR<T, M, K> {
|
|
/// Fits SVR to your data.
|
|
/// * `x` - _NxM_ matrix with _N_ observations and _M_ features in each observation.
|
|
/// * `y` - target values
|
|
/// * `kernel` - the kernel function
|
|
/// * `parameters` - optional parameters, use `Default::default()` to set parameters to default values.
|
|
pub fn fit(
|
|
x: &M,
|
|
y: &M::RowVector,
|
|
parameters: SVRParameters<T, M, K>,
|
|
) -> Result<SVR<T, M, K>, Failed> {
|
|
let (n, _) = x.shape();
|
|
|
|
if n != y.len() {
|
|
return Err(Failed::fit(
|
|
&"Number of rows of X doesn\'t match number of rows of Y".to_string(),
|
|
));
|
|
}
|
|
|
|
let optimizer = Optimizer::new(x, y, ¶meters.kernel, ¶meters);
|
|
|
|
let (support_vectors, weight, b) = optimizer.smo();
|
|
|
|
Ok(SVR {
|
|
kernel: parameters.kernel,
|
|
instances: support_vectors,
|
|
w: weight,
|
|
b,
|
|
})
|
|
}
|
|
|
|
/// Predict target values from `x`
|
|
/// * `x` - _KxM_ data where _K_ is number of observations and _M_ is number of features.
|
|
pub fn predict(&self, x: &M) -> Result<M::RowVector, Failed> {
|
|
let (n, _) = x.shape();
|
|
|
|
let mut y_hat = M::RowVector::zeros(n);
|
|
|
|
for i in 0..n {
|
|
y_hat.set(i, self.predict_for_row(x.get_row(i)));
|
|
}
|
|
|
|
Ok(y_hat)
|
|
}
|
|
|
|
pub(in crate) fn predict_for_row(&self, x: M::RowVector) -> T {
|
|
let mut f = self.b;
|
|
|
|
for i in 0..self.instances.len() {
|
|
f += self.w[i] * self.kernel.apply(&x, &self.instances[i]);
|
|
}
|
|
|
|
f
|
|
}
|
|
}
|
|
|
|
impl<T: RealNumber, M: Matrix<T>, K: Kernel<T, M::RowVector>> PartialEq for SVR<T, M, K> {
|
|
fn eq(&self, other: &Self) -> bool {
|
|
if (self.b - other.b).abs() > T::epsilon() * T::two()
|
|
|| self.w.len() != other.w.len()
|
|
|| self.instances.len() != other.instances.len()
|
|
{
|
|
false
|
|
} else {
|
|
for i in 0..self.w.len() {
|
|
if (self.w[i] - other.w[i]).abs() > T::epsilon() {
|
|
return false;
|
|
}
|
|
}
|
|
for i in 0..self.instances.len() {
|
|
if !self.instances[i].approximate_eq(&other.instances[i], T::epsilon()) {
|
|
return false;
|
|
}
|
|
}
|
|
true
|
|
}
|
|
}
|
|
}
|
|
|
|
impl<T: RealNumber, V: BaseVector<T>> SupportVector<T, V> {
|
|
fn new<K: Kernel<T, V>>(i: usize, x: V, y: T, eps: T, k: &K) -> SupportVector<T, V> {
|
|
let k_v = k.apply(&x, &x);
|
|
SupportVector {
|
|
index: i,
|
|
x,
|
|
grad: [eps + y, eps - y],
|
|
k: k_v,
|
|
alpha: [T::zero(), T::zero()],
|
|
}
|
|
}
|
|
}
|
|
|
|
impl<'a, T: RealNumber, M: Matrix<T>, K: Kernel<T, M::RowVector>> Optimizer<'a, T, M, K> {
|
|
fn new(
|
|
x: &M,
|
|
y: &M::RowVector,
|
|
kernel: &'a K,
|
|
parameters: &SVRParameters<T, M, K>,
|
|
) -> Optimizer<'a, T, M, K> {
|
|
let (n, _) = x.shape();
|
|
|
|
let mut support_vectors: Vec<SupportVector<T, M::RowVector>> = Vec::with_capacity(n);
|
|
|
|
for i in 0..n {
|
|
support_vectors.push(SupportVector::new(
|
|
i,
|
|
x.get_row(i),
|
|
y.get(i),
|
|
parameters.eps,
|
|
kernel,
|
|
));
|
|
}
|
|
|
|
Optimizer {
|
|
tol: parameters.tol,
|
|
c: parameters.c,
|
|
svmin: 0,
|
|
svmax: 0,
|
|
gmin: T::max_value(),
|
|
gmax: T::min_value(),
|
|
gminindex: 0,
|
|
gmaxindex: 0,
|
|
tau: T::from_f64(1e-12).unwrap(),
|
|
sv: support_vectors,
|
|
kernel,
|
|
}
|
|
}
|
|
|
|
fn find_min_max_gradient(&mut self) {
|
|
self.gmin = T::max_value();
|
|
self.gmax = T::min_value();
|
|
|
|
for i in 0..self.sv.len() {
|
|
let v = &self.sv[i];
|
|
let g = -v.grad[0];
|
|
let a = v.alpha[0];
|
|
if g < self.gmin && a > T::zero() {
|
|
self.gmin = g;
|
|
self.gminindex = 0;
|
|
self.svmin = i;
|
|
}
|
|
if g > self.gmax && a < self.c {
|
|
self.gmax = g;
|
|
self.gmaxindex = 0;
|
|
self.svmax = i;
|
|
}
|
|
|
|
let g = v.grad[1];
|
|
let a = v.alpha[1];
|
|
if g < self.gmin && a < self.c {
|
|
self.gmin = g;
|
|
self.gminindex = 1;
|
|
self.svmin = i;
|
|
}
|
|
if g > self.gmax && a > T::zero() {
|
|
self.gmax = g;
|
|
self.gmaxindex = 1;
|
|
self.svmax = i;
|
|
}
|
|
}
|
|
}
|
|
|
|
/// Solvs the quadratic programming (QP) problem that arises during the training of support-vector machines (SVM) algorithm.
|
|
/// Returns:
|
|
/// * support vectors
|
|
/// * hyperplane parameters: w and b
|
|
fn smo(mut self) -> (Vec<M::RowVector>, Vec<T>, T) {
|
|
let cache: Cache<T> = Cache::new(self.sv.len());
|
|
|
|
self.find_min_max_gradient();
|
|
|
|
while self.gmax - self.gmin > self.tol {
|
|
let v1 = self.svmax;
|
|
let i = self.gmaxindex;
|
|
let old_alpha_i = self.sv[v1].alpha[i];
|
|
|
|
let k1 = cache.get(self.sv[v1].index, || {
|
|
self.sv
|
|
.iter()
|
|
.map(|vi| self.kernel.apply(&self.sv[v1].x, &vi.x))
|
|
.collect()
|
|
});
|
|
|
|
let mut v2 = self.svmin;
|
|
let mut j = self.gminindex;
|
|
let mut old_alpha_j = self.sv[v2].alpha[j];
|
|
|
|
let mut best = T::zero();
|
|
let gi = if i == 0 {
|
|
-self.sv[v1].grad[0]
|
|
} else {
|
|
self.sv[v1].grad[1]
|
|
};
|
|
for jj in 0..self.sv.len() {
|
|
let v = &self.sv[jj];
|
|
let mut curv = self.sv[v1].k + v.k - T::two() * k1[v.index];
|
|
if curv <= T::zero() {
|
|
curv = self.tau;
|
|
}
|
|
|
|
let mut gj = -v.grad[0];
|
|
if v.alpha[0] > T::zero() && gj < gi {
|
|
let gain = -((gi - gj) * (gi - gj)) / curv;
|
|
if gain < best {
|
|
best = gain;
|
|
v2 = jj;
|
|
j = 0;
|
|
old_alpha_j = self.sv[v2].alpha[0];
|
|
}
|
|
}
|
|
|
|
gj = v.grad[1];
|
|
if v.alpha[1] < self.c && gj < gi {
|
|
let gain = -((gi - gj) * (gi - gj)) / curv;
|
|
if gain < best {
|
|
best = gain;
|
|
v2 = jj;
|
|
j = 1;
|
|
old_alpha_j = self.sv[v2].alpha[1];
|
|
}
|
|
}
|
|
}
|
|
|
|
let k2 = cache.get(self.sv[v2].index, || {
|
|
self.sv
|
|
.iter()
|
|
.map(|vi| self.kernel.apply(&self.sv[v2].x, &vi.x))
|
|
.collect()
|
|
});
|
|
|
|
let mut curv = self.sv[v1].k + self.sv[v2].k - T::two() * k1[self.sv[v2].index];
|
|
if curv <= T::zero() {
|
|
curv = self.tau;
|
|
}
|
|
|
|
if i != j {
|
|
let delta = (-self.sv[v1].grad[i] - self.sv[v2].grad[j]) / curv;
|
|
let diff = self.sv[v1].alpha[i] - self.sv[v2].alpha[j];
|
|
self.sv[v1].alpha[i] += delta;
|
|
self.sv[v2].alpha[j] += delta;
|
|
|
|
if diff > T::zero() {
|
|
if self.sv[v2].alpha[j] < T::zero() {
|
|
self.sv[v2].alpha[j] = T::zero();
|
|
self.sv[v1].alpha[i] = diff;
|
|
}
|
|
} else if self.sv[v1].alpha[i] < T::zero() {
|
|
self.sv[v1].alpha[i] = T::zero();
|
|
self.sv[v2].alpha[j] = -diff;
|
|
}
|
|
|
|
if diff > T::zero() {
|
|
if self.sv[v1].alpha[i] > self.c {
|
|
self.sv[v1].alpha[i] = self.c;
|
|
self.sv[v2].alpha[j] = self.c - diff;
|
|
}
|
|
} else if self.sv[v2].alpha[j] > self.c {
|
|
self.sv[v2].alpha[j] = self.c;
|
|
self.sv[v1].alpha[i] = self.c + diff;
|
|
}
|
|
} else {
|
|
let delta = (self.sv[v1].grad[i] - self.sv[v2].grad[j]) / curv;
|
|
let sum = self.sv[v1].alpha[i] + self.sv[v2].alpha[j];
|
|
self.sv[v1].alpha[i] -= delta;
|
|
self.sv[v2].alpha[j] += delta;
|
|
|
|
if sum > self.c {
|
|
if self.sv[v1].alpha[i] > self.c {
|
|
self.sv[v1].alpha[i] = self.c;
|
|
self.sv[v2].alpha[j] = sum - self.c;
|
|
}
|
|
} else if self.sv[v2].alpha[j] < T::zero() {
|
|
self.sv[v2].alpha[j] = T::zero();
|
|
self.sv[v1].alpha[i] = sum;
|
|
}
|
|
|
|
if sum > self.c {
|
|
if self.sv[v2].alpha[j] > self.c {
|
|
self.sv[v2].alpha[j] = self.c;
|
|
self.sv[v1].alpha[i] = sum - self.c;
|
|
}
|
|
} else if self.sv[v1].alpha[i] < T::zero() {
|
|
self.sv[v1].alpha[i] = T::zero();
|
|
self.sv[v2].alpha[j] = sum;
|
|
}
|
|
}
|
|
|
|
let delta_alpha_i = self.sv[v1].alpha[i] - old_alpha_i;
|
|
let delta_alpha_j = self.sv[v2].alpha[j] - old_alpha_j;
|
|
|
|
let si = T::two() * T::from_usize(i).unwrap() - T::one();
|
|
let sj = T::two() * T::from_usize(j).unwrap() - T::one();
|
|
for v in self.sv.iter_mut() {
|
|
v.grad[0] -= si * k1[v.index] * delta_alpha_i + sj * k2[v.index] * delta_alpha_j;
|
|
v.grad[1] += si * k1[v.index] * delta_alpha_i + sj * k2[v.index] * delta_alpha_j;
|
|
}
|
|
|
|
self.find_min_max_gradient();
|
|
}
|
|
|
|
let b = -(self.gmax + self.gmin) / T::two();
|
|
|
|
let mut support_vectors: Vec<M::RowVector> = Vec::new();
|
|
let mut w: Vec<T> = Vec::new();
|
|
|
|
for v in self.sv {
|
|
if v.alpha[0] != v.alpha[1] {
|
|
support_vectors.push(v.x);
|
|
w.push(v.alpha[1] - v.alpha[0]);
|
|
}
|
|
}
|
|
|
|
(support_vectors, w, b)
|
|
}
|
|
}
|
|
|
|
impl<T: Clone> Cache<T> {
|
|
fn new(n: usize) -> Cache<T> {
|
|
Cache {
|
|
data: vec![RefCell::new(None); n],
|
|
}
|
|
}
|
|
|
|
fn get<F: Fn() -> Vec<T>>(&self, i: usize, or: F) -> Ref<'_, Vec<T>> {
|
|
if self.data[i].borrow().is_none() {
|
|
self.data[i].replace(Some(or()));
|
|
}
|
|
Ref::map(self.data[i].borrow(), |v| v.as_ref().unwrap())
|
|
}
|
|
}
|
|
|
|
#[cfg(test)]
|
|
mod tests {
|
|
use super::*;
|
|
use crate::linalg::naive::dense_matrix::*;
|
|
use crate::metrics::mean_squared_error;
|
|
use crate::svm::*;
|
|
|
|
#[test]
|
|
fn svr_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 = SVR::fit(&x, &y, SVRParameters::default().with_eps(2.0).with_c(10.0))
|
|
.and_then(|lr| lr.predict(&x))
|
|
.unwrap();
|
|
|
|
assert!(mean_squared_error(&y_hat, &y) < 2.5);
|
|
}
|
|
|
|
#[test]
|
|
fn svr_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<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 svr = SVR::fit(&x, &y, Default::default()).unwrap();
|
|
|
|
let deserialized_svr: SVR<f64, DenseMatrix<f64>, LinearKernel> =
|
|
serde_json::from_str(&serde_json::to_string(&svr).unwrap()).unwrap();
|
|
|
|
assert_eq!(svr, deserialized_svr);
|
|
}
|
|
}
|