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```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
df = pd.read_csv("iris_basic.csv")
print(df.head())
```
sl sw pl pw target tNames
0 5.1 3.5 1.4 0.2 0 setosa
1 4.9 3.0 1.4 0.2 0 setosa
2 4.7 3.2 1.3 0.2 0 setosa
3 4.6 3.1 1.5 0.2 0 setosa
4 5.0 3.6 1.4 0.2 0 setosa
```python
x = df["pw"].to_numpy().reshape(-1, 1) # (150,1)
x
```
array([[0.2],
[0.2],
[0.2],
[0.2],
[0.2],
[0.4],
[0.3],
[0.2],
[0.2],
[0.1],
[0.2],
[0.2],
[0.1],
[0.1],
[0.2],
[0.4],
[0.4],
[0.3],
[0.3],
[0.3],
[0.2],
[0.4],
[0.2],
[0.5],
[0.2],
[0.2],
[0.4],
[0.2],
[0.2],
[0.2],
[0.2],
[0.4],
[0.1],
[0.2],
[0.2],
[0.2],
[0.2],
[0.1],
[0.2],
[0.2],
[0.3],
[0.3],
[0.2],
[0.6],
[0.4],
[0.3],
[0.2],
[0.2],
[0.2],
[0.2],
[1.4],
[1.5],
[1.5],
[1.3],
[1.5],
[1.3],
[1.6],
[1. ],
[1.3],
[1.4],
[1. ],
[1.5],
[1. ],
[1.4],
[1.3],
[1.4],
[1.5],
[1. ],
[1.5],
[1.1],
[1.8],
[1.3],
[1.5],
[1.2],
[1.3],
[1.4],
[1.4],
[1.7],
[1.5],
[1. ],
[1.1],
[1. ],
[1.2],
[1.6],
[1.5],
[1.6],
[1.5],
[1.3],
[1.3],
[1.3],
[1.2],
[1.4],
[1.2],
[1. ],
[1.3],
[1.2],
[1.3],
[1.3],
[1.1],
[1.3],
[2.5],
[1.9],
[2.1],
[1.8],
[2.2],
[2.1],
[1.7],
[1.8],
[1.8],
[2.5],
[2. ],
[1.9],
[2.1],
[2. ],
[2.4],
[2.3],
[1.8],
[2.2],
[2.3],
[1.5],
[2.3],
[2. ],
[2. ],
[1.8],
[2.1],
[1.8],
[1.8],
[1.8],
[2.1],
[1.6],
[1.9],
[2. ],
[2.2],
[1.5],
[1.4],
[2.3],
[2.4],
[1.8],
[1.8],
[2.1],
[2.4],
[2.3],
[1.9],
[2.3],
[2.5],
[2.3],
[1.9],
[2. ],
[2.3],
[1.8]])
```python
y = df["target"].to_numpy().reshape(-1, 1) # (150,1)
y = (y == 0).astype(float)
y
```
array([[1.],
[1.],
[1.],
[1.],
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[1.],
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[1.],
[1.],
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[1.],
[1.],
[1.],
[1.],
[1.],
[1.],
[0.],
[0.],
[0.],
[0.],
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```python
def sigmoid(z):
z = np.clip(z, -500, 500)
sig = 1.0 / (1.0 + np.exp(-z))
return sig
```
```python
def log_loss(y, p, eps=1e-12):
p = np.clip(p, eps, 1 - eps)
return -np.mean(y*np.log(p) + (1-y)*np.log(1-p))
```
```python
lr=0.1
epochs=2000
l2=0.0,
X = np.column_stack([x, np.ones_like(x)])
m = X.shape[0]
theta = np.zeros((2,1))
theta
```
array([[0.],
[0.]])
```python
X.T
```
array([[0.2, 0.2, 0.2, 0.2, 0.2, 0.4, 0.3, 0.2, 0.2, 0.1, 0.2, 0.2, 0.1,
0.1, 0.2, 0.4, 0.4, 0.3, 0.3, 0.3, 0.2, 0.4, 0.2, 0.5, 0.2, 0.2,
0.4, 0.2, 0.2, 0.2, 0.2, 0.4, 0.1, 0.2, 0.2, 0.2, 0.2, 0.1, 0.2,
0.2, 0.3, 0.3, 0.2, 0.6, 0.4, 0.3, 0.2, 0.2, 0.2, 0.2, 1.4, 1.5,
1.5, 1.3, 1.5, 1.3, 1.6, 1. , 1.3, 1.4, 1. , 1.5, 1. , 1.4, 1.3,
1.4, 1.5, 1. , 1.5, 1.1, 1.8, 1.3, 1.5, 1.2, 1.3, 1.4, 1.4, 1.7,
1.5, 1. , 1.1, 1. , 1.2, 1.6, 1.5, 1.6, 1.5, 1.3, 1.3, 1.3, 1.2,
1.4, 1.2, 1. , 1.3, 1.2, 1.3, 1.3, 1.1, 1.3, 2.5, 1.9, 2.1, 1.8,
2.2, 2.1, 1.7, 1.8, 1.8, 2.5, 2. , 1.9, 2.1, 2. , 2.4, 2.3, 1.8,
2.2, 2.3, 1.5, 2.3, 2. , 2. , 1.8, 2.1, 1.8, 1.8, 1.8, 2.1, 1.6,
1.9, 2. , 2.2, 1.5, 1.4, 2.3, 2.4, 1.8, 1.8, 2.1, 2.4, 2.3, 1.9,
2.3, 2.5, 2.3, 1.9, 2. , 2.3, 1.8],
[1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. ,
1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. ,
1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. ,
1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. ,
1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. ,
1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. ,
1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. ,
1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. ,
1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. ,
1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. ,
1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. , 1. ,
1. , 1. , 1. , 1. , 1. , 1. , 1. ]])
```python
for i in range(epochs):
z = X @ theta # (m,1)
h = sigmoid(z) # (m,1)
grad = (X.T @ (h - y)) / m # (2,1) <-- from your formula
theta -= lr * grad
#if (i % 0 == 0 or t == epochs-1):
# print(f"{i:4d} loss={log_loss(y, h):.6f} w={theta[0,0]:.6f} b={theta[1,0]:.6f}")
w, b = theta[0,0], theta[1,0]
```
```python
def predict_proba(x, w, b):
x = np.asarray(x, float).reshape(-1)
return sigmoid(w*x + b)
def predict(x, w, b, thresh=0.5):
return (predict_proba(x, w, b) >= thresh).astype(int)
```
```python
rng = np.random.default_rng(0)
m = 120
xNew = np.linspace(-0.5, 2.5, m)
p = predict_proba(xNew, w, b)
print(f"\nLearned: w={w:.3f}, b={b:.3f}, loss={log_loss(p.reshape(-1,1), p.reshape(-1,1)):.4f}")
```
Learned: w=-5.989, b=4.279, loss=0.1812
```python
yJitter = y +np.random.uniform(-0.2, 0.2, size=y.shape)
plt.plot(x, yJitter, 'ok', alpha=0.1)
plt.plot(xNew,p)
```
[<matplotlib.lines.Line2D at 0x112e5cd70>]
![png](main_files/main_10_1.png)
```python
```
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