Week 7 Videos

Linear data with an outlier

import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng()

type(rng)

numpy.random._generator.Generator

rng.random(5)

array([0.71766176, 0.67084367, 0.3629894 , 0.63571399, 0.2977128 ])

30*rng.random(5) - 20

array([ -4.40385734,  -6.41524188,   1.36656718, -19.49290652,
        -0.85800345])

m,b = 30*rng.random(2) - 20

x = np.arange(0, 10, 0.5)

x

array([0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5, 5. , 5.5, 6. ,
       6.5, 7. , 7.5, 8. , 8.5, 9. , 9.5])

y = m*x+b

fig, ax = plt.subplots()
ax.scatter(x, y)

<matplotlib.collections.PathCollection at 0x7fa719099a60>

noise = rng.normal(loc=0, scale=10, size=y.shape)

y2 = y+noise

fig, ax = plt.subplots()
ax.scatter(x, y2)

<matplotlib.collections.PathCollection at 0x7fa735291b20>

y2[5] = 500

fig, ax = plt.subplots()
ax.scatter(x, y2)

<matplotlib.collections.PathCollection at 0x7fa7359da3a0>

Line of best fit using Mean Squared Error

from sklearn.linear_model import LinearRegression

reg = LinearRegression()

x.shape

(20,)

X = x.reshape(-1,1)

reg.fit(X, y2)

LinearRegression()

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ypred = reg.predict(X)

fig, ax = plt.subplots()
ax.scatter(x, y2)
ax.plot(x, ypred, 'r')

[<matplotlib.lines.Line2D at 0x7fa717972460>]

Line of best fit using Mean Absolute Error

Reference: Stack Overflow

from sklearn.linear_model import SGDRegressor

sgdreg = SGDRegressor(loss="epsilon_insensitive", epsilon=0)

sgdreg.fit(X, y2)

SGDRegressor(epsilon=0, loss='epsilon_insensitive')

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ypred2 = sgdreg.predict(X)

fig, ax = plt.subplots()
ax.scatter(x, y2)
ax.plot(x, ypred, 'r')
ax.plot(x, ypred2, 'k')

[<matplotlib.lines.Line2D at 0x7fa7018b3130>]

Computing Mean Squared Error and Mean Absolute Error in scikit-learn

from sklearn.metrics import mean_absolute_error, mean_squared_error

mean_squared_error(y2, ypred)

13823.74709827255

mean_squared_error(y2, ypred2)

14622.352062657656

mean_absolute_error(y2, ypred)

51.65405629230766

mean_absolute_error(y2, ypred2)

35.41119321144292

((y2-ypred)**2).mean()

13823.74709827255

((y2-ypred)**2).sum()/len(y2)

13823.74709827255

(abs(y2-ypred)).mean()

51.65405629230766

Created in Deepnote