Add logistic regression & optimize the gradient descent algorithm (#832)

DIRECTORY.md

@@ -156,6 +156,7 @@
     * [Cholesky](https://github.com/TheAlgorithms/Rust/blob/master/src/machine_learning/cholesky.rs)
     * [K Means](https://github.com/TheAlgorithms/Rust/blob/master/src/machine_learning/k_means.rs)
     * [Linear Regression](https://github.com/TheAlgorithms/Rust/blob/master/src/machine_learning/linear_regression.rs)
+    * [Logistic Regression](https://github.com/TheAlgorithms/Rust/blob/master/src/machine_learning/logistic_regression.rs)
     * Loss Function
       * [Average Margin Ranking Loss](https://github.com/TheAlgorithms/Rust/blob/master/src/machine_learning/loss_function/average_margin_ranking_loss.rs)
       * [Hinge Loss](https://github.com/TheAlgorithms/Rust/blob/master/src/machine_learning/loss_function/hinge_loss.rs)

src/machine_learning/logistic_regression.rs

@@ -0,0 +1,92 @@
+use super::optimization::gradient_descent;
+use std::f64::consts::E;
+
+/// Returns the wieghts after performing Logistic regression on the input data points.
+pub fn logistic_regression(
+    data_points: Vec<(Vec<f64>, f64)>,
+    iterations: usize,
+    learning_rate: f64,
+) -> Option<Vec<f64>> {
+    if data_points.is_empty() {
+        return None;
+    }
+
+    let num_features = data_points[0].0.len() + 1;
+    let mut params = vec![0.0; num_features];
+
+    let derivative_fn = |params: &[f64]| derivative(params, &data_points);
+
+    gradient_descent(derivative_fn, &mut params, learning_rate, iterations as i32);
+
+    Some(params)
+}
+
+fn derivative(params: &[f64], data_points: &[(Vec<f64>, f64)]) -> Vec<f64> {
+    let num_features = params.len();
+    let mut gradients = vec![0.0; num_features];
+
+    for (features, y_i) in data_points {
+        let z = params[0]
+            + params[1..]
+                .iter()
+                .zip(features)
+                .map(|(p, x)| p * x)
+                .sum::<f64>();
+        let prediction = 1.0 / (1.0 + E.powf(-z));
+
+        gradients[0] += prediction - y_i;
+        for (i, x_i) in features.iter().enumerate() {
+            gradients[i + 1] += (prediction - y_i) * x_i;
+        }
+    }
+
+    gradients
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_logistic_regression_simple() {
+        let data = vec![
+            (vec![0.0], 0.0),
+            (vec![1.0], 0.0),
+            (vec![2.0], 0.0),
+            (vec![3.0], 1.0),
+            (vec![4.0], 1.0),
+            (vec![5.0], 1.0),
+        ];
+
+        let result = logistic_regression(data, 10000, 0.05);
+        assert!(result.is_some());
+
+        let params = result.unwrap();
+        assert!((params[0] + 17.65).abs() < 1.0);
+        assert!((params[1] - 7.13).abs() < 1.0);
+    }
+
+    #[test]
+    fn test_logistic_regression_extreme_data() {
+        let data = vec![
+            (vec![-100.0], 0.0),
+            (vec![-10.0], 0.0),
+            (vec![0.0], 0.0),
+            (vec![10.0], 1.0),
+            (vec![100.0], 1.0),
+        ];
+
+        let result = logistic_regression(data, 10000, 0.05);
+        assert!(result.is_some());
+
+        let params = result.unwrap();
+        assert!((params[0] + 6.20).abs() < 1.0);
+        assert!((params[1] - 5.5).abs() < 1.0);
+    }
+
+    #[test]
+    fn test_logistic_regression_no_data() {
+        let result = logistic_regression(vec![], 5000, 0.1);
+        assert_eq!(result, None);
+    }
+}

src/machine_learning/mod.rs

@@ -1,12 +1,14 @@
 mod cholesky;
 mod k_means;
 mod linear_regression;
+mod logistic_regression;
 mod loss_function;
 mod optimization;
 
 pub use self::cholesky::cholesky;
 pub use self::k_means::k_means;
 pub use self::linear_regression::linear_regression;
+pub use self::logistic_regression::logistic_regression;
 pub use self::loss_function::average_margin_ranking_loss;
 pub use self::loss_function::hng_loss;
 pub use self::loss_function::huber_loss;

src/machine_learning/optimization/gradient_descent.rs

@@ -23,7 +23,7 @@
 /// A reference to the optimized parameter vector `x`.
 
 pub fn gradient_descent(
-    derivative_fn: fn(&[f64]) -> Vec<f64>,
+    derivative_fn: impl Fn(&[f64]) -> Vec<f64>,
     x: &mut Vec<f64>,
     learning_rate: f64,
     num_iterations: i32,