feat: refactors packages layout

2020-03-13 14:30:45 -07:00
parent 4f8318e933
commit 87b6fab795
12 changed files with 10 additions and 27 deletions
@@ -0,0 +1,398 @@
+use crate::math::NumericExt;
+use crate::linalg::Matrix;
+use crate::optimization::FunctionOrder;
+use crate::optimization::first_order::{FirstOrderOptimizer, OptimizerResult};
+use crate::optimization::line_search::Backtracking;
+use crate::optimization::first_order::lbfgs::LBFGS;
+
+#[derive(Debug)]
+pub struct LogisticRegression<M: Matrix> {    
+    weights: M,     
+    classes: Vec<f64>,
+    num_attributes: usize,
+    num_classes: usize
+}
+
+trait ObjectiveFunction<M: Matrix> {
+    fn f(&self, w_bias: &M) -> f64;
+    fn df(&self, g: &mut M, w_bias: &M);
+
+    fn partial_dot(w: &M, x: &M, v_col: usize, m_row: usize) -> f64 {
+        let mut sum = 0f64;
+        let p =  x.shape().1;
+        for i in 0..p {
+            sum += x.get(m_row, i) * w.get(0, i + v_col);
+        }
+    
+        sum + w.get(0, p + v_col)
+    }
+}
+
+struct BinaryObjectiveFunction<'a, M: Matrix> {
+    x: &'a M,
+    y: Vec<usize>    
+} 
+
+impl<'a, M: Matrix> ObjectiveFunction<M> for BinaryObjectiveFunction<'a, M> {    
+
+    fn f(&self, w_bias: &M) -> f64 {                
+        let mut f = 0.;        
+        let (n, _) = self.x.shape();   
+        
+        for i in 0..n {
+            let wx = BinaryObjectiveFunction::partial_dot(w_bias, self.x, 0, i);            
+            f += wx.ln_1pe() - (self.y[i] as f64) * wx;
+        }        
+        
+        f 
+    }
+
+    fn df(&self, g: &mut M, w_bias: &M) {
+        
+        g.copy_from(&M::zeros(1, g.shape().1));
+             
+        let (n, p) = self.x.shape();        
+                
+        for i in 0..n {            
+                       
+            let wx = BinaryObjectiveFunction::partial_dot(w_bias, self.x, 0, i);                        
+
+            let dyi = (self.y[i] as f64) - wx.sigmoid();
+            for j in 0..p {
+                g.set(0, j, g.get(0, j) - dyi * self.x.get(i, j));
+            }
+            g.set(0, p, g.get(0, p) - dyi);
+        }      
+        
+    }    
+
+}
+
+struct MultiClassObjectiveFunction<'a, M: Matrix> {
+    x: &'a M,
+    y: Vec<usize>,
+    k: usize
+}
+
+impl<'a, M: Matrix> ObjectiveFunction<M> for MultiClassObjectiveFunction<'a, M> {    
+
+    fn f(&self, w_bias: &M) -> f64 {                
+        let mut f = 0.;
+        let mut prob = M::zeros(1, self.k);
+        let (n, p) = self.x.shape();
+        for i in 0..n {            
+            for j in 0..self.k {                
+                prob.set(0, j, MultiClassObjectiveFunction::partial_dot(w_bias, self.x, j * (p + 1), i));
+            }
+            prob.softmax_mut();
+            f -= prob.get(0, self.y[i]).ln();
+        }        
+        
+        f 
+    }
+
+    fn df(&self, g: &mut M, w: &M) {
+        
+        g.copy_from(&M::zeros(1, g.shape().1));
+        
+        let mut prob = M::zeros(1, self.k);
+        let (n, p) = self.x.shape();        
+        
+        for i in 0..n {            
+            for j in 0..self.k {                
+                prob.set(0, j, MultiClassObjectiveFunction::partial_dot(w, self.x, j * (p + 1), i));
+            }            
+
+            prob.softmax_mut();            
+
+            for j in 0..self.k {
+                let yi =(if self.y[i] == j { 1.0 } else { 0.0 }) - prob.get(0, j);
+    
+                for l in 0..p {
+                    let pos = j * (p + 1);
+                    g.set(0, pos + l, g.get(0, pos + l) - yi * self.x.get(i, l));
+                }
+                g.set(0, j * (p + 1) + p, g.get(0, j * (p + 1) + p) - yi);                
+            }
+        }        
+        
+    }
+
+}
+
+impl<M: Matrix> LogisticRegression<M> {
+
+    pub fn fit(x: &M, y: &M::RowVector) -> LogisticRegression<M>{
+
+        let y_m = M::from_row_vector(y.clone());
+        let (x_nrows, num_attributes) = x.shape();
+        let (_, y_nrows) = y_m.shape();
+
+        if x_nrows != y_nrows {
+            panic!("Number of rows of X doesn't match number of rows of Y");
+        }
+        
+        let classes = y_m.unique();        
+
+        let k = classes.len();        
+
+        let mut yi: Vec<usize> = vec![0; y_nrows];
+
+        for i in 0..y_nrows {
+            let yc = y_m.get(0, i);             
+            yi[i] = classes.iter().position(|c| yc == *c).unwrap();
+        }
+
+        if k < 2 {
+
+            panic!("Incorrect number of classes: {}", k);
+
+        } else if k == 2 {
+
+            let x0 = M::zeros(1, num_attributes + 1);
+
+            let objective = BinaryObjectiveFunction{
+                x: x,
+                y: yi                
+            };             
+            
+            let result = LogisticRegression::minimize(x0, objective);
+            
+            LogisticRegression {
+                weights: result.x,                
+                classes: classes,
+                num_attributes: num_attributes,
+                num_classes: k,                
+            }  
+
+        } else {
+
+            let x0 = M::zeros(1, (num_attributes + 1) * k);
+
+            let objective = MultiClassObjectiveFunction{
+                x: x,
+                y: yi,
+                k: k
+            };                
+            
+            let result = LogisticRegression::minimize(x0, objective);
+
+            let weights = result.x.reshape(k, num_attributes + 1);
+
+            LogisticRegression {
+                weights: weights,                
+                classes: classes,
+                num_attributes: num_attributes,
+                num_classes: k                
+            }            
+        }        
+        
+        
+    }
+
+    pub fn predict(&self, x: &M) -> M::RowVector {
+        let n = x.shape().0;
+        let mut result = M::zeros(1, n);
+        if self.num_classes == 2 {            
+            let (nrows, _) = x.shape();
+            let x_and_bias = x.v_stack(&M::ones(nrows, 1));
+            let y_hat: Vec<f64> = x_and_bias.dot(&self.weights.transpose()).to_raw_vector();
+            for i in 0..n {
+                result.set(0, i, self.classes[if y_hat[i].sigmoid() > 0.5 { 1 } else { 0 }]);
+            }            
+
+        } else {
+            let (nrows, _) = x.shape();
+            let x_and_bias = x.v_stack(&M::ones(nrows, 1));        
+            let y_hat = x_and_bias.dot(&self.weights.transpose());            
+            let class_idxs = y_hat.argmax();
+            for i in 0..n {
+                result.set(0, i, self.classes[class_idxs[i]]);
+            }            
+        }
+        result.to_row_vector()
+    }
+
+    pub fn coefficients(&self) -> M {
+        self.weights.slice(0..self.num_classes, 0..self.num_attributes)
+    }
+
+    pub fn intercept(&self) -> M {
+        self.weights.slice(0..self.num_classes, self.num_attributes..self.num_attributes+1)
+    }    
+
+    fn minimize(x0: M, objective: impl ObjectiveFunction<M>) -> OptimizerResult<M> {
+        let f = |w: &M| -> f64 {                
+            objective.f(w)
+        };
+
+        let df = |g: &mut M, w: &M| {
+            objective.df(g, w)
+        };
+
+        let mut ls: Backtracking = Default::default();
+        ls.order = FunctionOrder::THIRD;
+        let optimizer: LBFGS = Default::default();              
+        
+        optimizer.optimize(&f, &df, &x0, &ls)
+    }
+
+}
+
+#[cfg(test)]
+mod tests {    
+    use super::*; 
+    use crate::linalg::naive::dense_matrix::*;       
+    use ndarray::{arr1, arr2};
+
+    #[test]
+    fn multiclass_objective_f() { 
+
+        let x = DenseMatrix::from_array(&[
+            &[1., -5.],
+            &[ 2.,  5.],
+            &[ 3., -2.],
+            &[ 1.,  2.],
+            &[ 2.,  0.],
+            &[ 6., -5.],
+            &[ 7.,  5.],
+            &[ 6., -2.],
+            &[ 7.,  2.],
+            &[ 6.,  0.],
+            &[ 8., -5.],
+            &[ 9.,  5.],
+            &[10., -2.],
+            &[ 8.,  2.],
+            &[ 9.,  0.]]);
+
+        let y = vec![0, 0, 1, 1, 2, 1, 1, 0, 0, 2, 1, 1, 0, 0, 1];
+
+        let objective = MultiClassObjectiveFunction{
+            x: &x,
+            y: y,
+            k: 3
+        };
+
+        let mut g = DenseMatrix::zeros(1, 9);                
+
+        objective.df(&mut g, &DenseMatrix::vector_from_array(&[1., 2., 3., 4., 5., 6., 7., 8., 9.]));
+        objective.df(&mut g, &DenseMatrix::vector_from_array(&[1., 2., 3., 4., 5., 6., 7., 8., 9.]));
+        
+        assert!((g.get(0, 0) + 33.000068218163484).abs() < std::f64::EPSILON); 
+
+        let f = objective.f(&DenseMatrix::vector_from_array(&[1., 2., 3., 4., 5., 6., 7., 8., 9.]));
+
+        assert!((f -  408.0052230582765).abs() < std::f64::EPSILON);        
+    }
+
+    #[test]
+    fn binary_objective_f() { 
+
+        let x = DenseMatrix::from_array(&[
+            &[1., -5.],
+            &[ 2.,  5.],
+            &[ 3., -2.],
+            &[ 1.,  2.],
+            &[ 2.,  0.],
+            &[ 6., -5.],
+            &[ 7.,  5.],
+            &[ 6., -2.],
+            &[ 7.,  2.],
+            &[ 6.,  0.],
+            &[ 8., -5.],
+            &[ 9.,  5.],
+            &[10., -2.],
+            &[ 8.,  2.],
+            &[ 9.,  0.]]);
+
+        let y = vec![0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1];
+
+        let objective = BinaryObjectiveFunction{
+            x: &x,
+            y: y            
+        };
+
+        let mut g = DenseMatrix::zeros(1, 3);                
+
+        objective.df(&mut g, &DenseMatrix::vector_from_array(&[1., 2., 3.]));
+        objective.df(&mut g, &DenseMatrix::vector_from_array(&[1., 2., 3.]));        
+        
+        assert!((g.get(0, 0) - 26.051064349381285).abs() < std::f64::EPSILON); 
+        assert!((g.get(0, 1) - 10.239000702928523).abs() < std::f64::EPSILON); 
+        assert!((g.get(0, 2) - 3.869294270156324).abs() < std::f64::EPSILON); 
+
+        let f = objective.f(&DenseMatrix::vector_from_array(&[1., 2., 3.]));        
+
+        assert!((f -  59.76994756647412).abs() < std::f64::EPSILON);   
+    }
+
+    #[test]
+    fn lr_fit_predict() {             
+
+        let x = DenseMatrix::from_array(&[
+            &[1., -5.],
+            &[ 2.,  5.],
+            &[ 3., -2.],
+            &[ 1.,  2.],
+            &[ 2.,  0.],
+            &[ 6., -5.],
+            &[ 7.,  5.],
+            &[ 6., -2.],
+            &[ 7.,  2.],
+            &[ 6.,  0.],
+            &[ 8., -5.],
+            &[ 9.,  5.],
+            &[10., -2.],
+            &[ 8.,  2.],
+            &[ 9.,  0.]]);
+        let y = vec![0., 0., 1., 1., 2., 1., 1., 0., 0., 2., 1., 1., 0., 0., 1.];
+
+        let lr = LogisticRegression::fit(&x, &y);
+
+        assert_eq!(lr.coefficients().shape(), (3, 2));
+        assert_eq!(lr.intercept().shape(), (3, 1));
+        
+        assert!((lr.coefficients().get(0, 0) - 0.0435).abs() < 1e-4);
+        assert!((lr.intercept().get(0, 0) - 0.1250).abs() < 1e-4);        
+
+        let y_hat = lr.predict(&x);                
+
+        assert_eq!(y_hat, vec![0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]);
+        
+
+    }    
+
+    #[test]
+    fn lr_fit_predict_iris() { 
+        let x = arr2(&[
+            [5.1, 3.5, 1.4, 0.2],
+            [4.9, 3.0, 1.4, 0.2],
+            [4.7, 3.2, 1.3, 0.2],
+            [4.6, 3.1, 1.5, 0.2],
+            [5.0, 3.6, 1.4, 0.2],
+            [5.4, 3.9, 1.7, 0.4],
+            [4.6, 3.4, 1.4, 0.3],
+            [5.0, 3.4, 1.5, 0.2],
+            [4.4, 2.9, 1.4, 0.2],
+            [4.9, 3.1, 1.5, 0.1],
+            [7.0, 3.2, 4.7, 1.4],
+            [6.4, 3.2, 4.5, 1.5],
+            [6.9, 3.1, 4.9, 1.5],
+            [5.5, 2.3, 4.0, 1.3],
+            [6.5, 2.8, 4.6, 1.5],
+            [5.7, 2.8, 4.5, 1.3],
+            [6.3, 3.3, 4.7, 1.6],
+            [4.9, 2.4, 3.3, 1.0],
+            [6.6, 2.9, 4.6, 1.3],
+            [5.2, 2.7, 3.9, 1.4]]);
+        let y = arr1(&[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]);        
+
+        let lr = LogisticRegression::fit(&x, &y);         
+
+        let y_hat = lr.predict(&x);                        
+
+        assert_eq!(y_hat, arr1(&[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]));
+        
+    }
+
+}