Multi-parametric binary classifier

Readme.md

@@ -469,7 +469,182 @@ plt.plot(xNew,p)
     
 
 
+# Multi-Parametric Binary Classifier
+
+
+```python
+x1 = df["sl"].to_numpy()
+x2 = df["sw"].to_numpy()
+X = np.column_stack([ np.ones_like(x1), x1, x2])
+```
+
+
+```python
+y = df["target"].to_numpy()
+#y = (y == 2).astype(float) 
+```
+
+
+```python
+plt.plot(x1[y==0], x2[y==0],'.g' ,label='Set')
+plt.plot(x1[y==1], x2[y==1],'.r', label='Ver')
+plt.plot(x1[y==2], x2[y==2],'.b', label='Vir')
+plt.legend()
+plt.show()
+```
+
+
+    
+![png](main_files/main_14_0.png)
+    
+
+
+
+```python
+y = df["target"].to_numpy()
+y = (y == 2).astype(float) 
+```
+
+
+```python
+def predict_proba(X, theta):
+    z = X@theta
+    return sigmoid(z)
+```
+
 
 ```python
+lr=0.01
+epochs=5000
+m = X.shape[0]
+theta = np.random.randn(3)
+theta
+```
+
+
+    array([ 0.68799477,  0.14542591, -0.00438461])
+
 
+
+```python
+for i in range(epochs):
+    z = X @ theta               # (m,1)
+    h = 1/(1+np.exp(-z))              # (m,1)
+    grad = (X.T @ (h - y)) / m  # (2,1)  <-- from your formula
+    theta -= lr * grad
+
+    if (i % 100 == 0):
+        print(f"{i:4d}  loss={log_loss(y, h):.6f}")
+ 
+theta
+```
+
+       0  loss=1.178088
+     100  loss=0.647786
+     200  loss=0.630318
+     300  loss=0.615215
+     400  loss=0.602111
+     500  loss=0.590698
+     600  loss=0.580716
+     700  loss=0.571949
+     800  loss=0.564217
+     900  loss=0.557369
+    1000  loss=0.551279
+    1100  loss=0.545841
+    1200  loss=0.540968
+    1300  loss=0.536583
+    1400  loss=0.532624
+    1500  loss=0.529037
+    1600  loss=0.525776
+    1700  loss=0.522803
+    1800  loss=0.520083
+    1900  loss=0.517587
+    2000  loss=0.515291
+    2100  loss=0.513174
+    2200  loss=0.511214
+    2300  loss=0.509398
+    2400  loss=0.507709
+    2500  loss=0.506136
+    2600  loss=0.504667
+    2700  loss=0.503292
+    2800  loss=0.502002
+    2900  loss=0.500790
+    3000  loss=0.499649
+    3100  loss=0.498572
+    3200  loss=0.497554
+    3300  loss=0.496590
+    3400  loss=0.495676
+    3500  loss=0.494807
+    3600  loss=0.493980
+    3700  loss=0.493191
+    3800  loss=0.492438
+    3900  loss=0.491718
+    4000  loss=0.491028
+    4100  loss=0.490367
+    4200  loss=0.489731
+    4300  loss=0.489120
+    4400  loss=0.488532
+    4500  loss=0.487964
+    4600  loss=0.487416
+    4700  loss=0.486887
+    4800  loss=0.486374
+    4900  loss=0.485877
+
+
+
+    array([-0.45875015,  1.02970203, -2.10588172])
+
+
+
+```python
+x1New, x2New = np.meshgrid(
+    np.linspace(3,8,100).reshape(-1,1),
+    np.linspace(0,6,100).reshape(-1,1))
+XNew = np.column_stack([np.ones(x1New.size), x1New.ravel(), x2New.ravel()])
+
+z = XNew @ theta
+yPred = 1 / (1 + np.exp(-z))
+zz = yPred.reshape(x1New.shape)
+zz
+```
+
+
+    array([[9.32789869e-01, 9.35977755e-01, 9.39024319e-01, ...,
+            9.99535858e-01, 9.99559369e-01, 9.99581689e-01],
+           [9.24332755e-01, 9.27890766e-01, 9.31293909e-01, ...,
+            9.99472707e-01, 9.99499415e-01, 9.99524770e-01],
+           [9.14908551e-01, 9.18870810e-01, 9.22664164e-01, ...,
+            9.99400969e-01, 9.99431308e-01, 9.99460111e-01],
+           ...,
+           [5.83101559e-05, 6.14226291e-05, 6.47012289e-05, ...,
+            8.96718270e-03, 9.44134205e-03, 9.94032212e-03],
+           [5.13237738e-05, 5.40633488e-05, 5.69491493e-05, ...,
+            7.90122160e-03, 8.31948909e-03, 8.75970294e-03],
+           [4.51744213e-05, 4.75857700e-05, 5.01258268e-05, ...,
+            6.96108505e-03, 7.32995218e-03, 7.71821361e-03]], shape=(100, 100))
+
+
+
+```python
+plt.figure(figsize=(8,6))
+plt.plot(x1[y==0], x2[y==0],'or' ,label='No Virg')
+plt.plot(x1[y==1], x2[y==1],'g^',label='Virginica')
+contour = plt.contour(x1New,x2New,zz, linewidths=1)
+plt.clabel(contour, inline=1,fontsize=15)
+plt.xlabel("Sepal Length")
+plt.ylabel("Sepal Width")
+plt.legend()
+plt.show()
+
+```
+
+
+    
+![png](main_files/main_20_0.png)
+    
+
+
+
+```python
+# Softmax model ???
 ```