04: Základní algoritmy strojového učení - úvod do scikit-learn¶

Lineární regrese¶

Generování dat¶

In [1]:

import numpy as np
np.random.seed(0)

# Scikit-learn
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
from sklearn.metrics import mean_squared_error

import matplotlib.pyplot as plt
%matplotlib inline

import numpy as np np.random.seed(0) # Scikit-learn from sklearn.linear_model import LinearRegression from sklearn.preprocessing import PolynomialFeatures from sklearn.metrics import mean_squared_error import matplotlib.pyplot as plt %matplotlib inline

In [2]:

# funkce pocitajici data a vnasejici do nich sum (noise) 
def funkce(x, noise):
    return .6 *  x + (x ** .8) * noise

# funkce pocitajici data a vnasejici do nich sum (noise) def funkce(x, noise): return .6 * x + (x ** .8) * noise

In [3]:

# generovani trenovacich dat 
pocet = 20
mnozstvi_sumu = 0.9
# prvky
X_train = np.sort(np.random.rand(pocet))
# zanesme sum
sum_train = np.random.rand(pocet) * mnozstvi_sumu

# cile (reference, labely, targets)
y_train = funkce(X_train, sum_train) 
X_train = X_train.reshape(-1, 1)  # sloupcovy vektor

# vytvorme testovaci data z tez funkce 
pocet_test = 20
# testovaci prvky
X_test = np.sort(np.random.rand(pocet_test))

# cile (reference, labely, targets)
sum_test = np.random.rand(pocet_test) * mnozstvi_sumu
y_test = funkce(X_test, sum_test)
X_test = X_test.reshape(-1, 1)

# generovani trenovacich dat pocet = 20 mnozstvi_sumu = 0.9 # prvky X_train = np.sort(np.random.rand(pocet)) # zanesme sum sum_train = np.random.rand(pocet) * mnozstvi_sumu # cile (reference, labely, targets) y_train = funkce(X_train, sum_train) X_train = X_train.reshape(-1, 1) # sloupcovy vektor # vytvorme testovaci data z tez funkce pocet_test = 20 # testovaci prvky X_test = np.sort(np.random.rand(pocet_test)) # cile (reference, labely, targets) sum_test = np.random.rand(pocet_test) * mnozstvi_sumu y_test = funkce(X_test, sum_test) X_test = X_test.reshape(-1, 1)

In [4]:

# podivejme se na data skrze rozptylovy diagram
plt.scatter(X_train, y_train, edgecolor="b", s=20, label="Trenovaci data")
plt.scatter(X_test, y_test, edgecolor="g", color="g", s=20, label="Testovaci data")
plt.xlabel("x")
plt.ylabel("y")
plt.legend(loc="best")

# podivejme se na data skrze rozptylovy diagram plt.scatter(X_train, y_train, edgecolor="b", s=20, label="Trenovaci data") plt.scatter(X_test, y_test, edgecolor="g", color="g", s=20, label="Testovaci data") plt.xlabel("x") plt.ylabel("y") plt.legend(loc="best")

Out[4]:

<matplotlib.legend.Legend at 0x736634a6b0a0>

Lineární regrese v scikit-learn¶

In [5]:

# vytvorme model
linear_regression = LinearRegression()
# trenujme jej na trenovacich datech 
linear_regression.fit(X_train, y_train)

# vytvorme model linear_regression = LinearRegression() # trenujme jej na trenovacich datech linear_regression.fit(X_train, y_train)

Out[5]:

LinearRegression()

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In [6]:

linear_regression.fit_intercept

linear_regression.fit_intercept

Out[6]:

True

In [7]:

linear_regression.coef_

linear_regression.coef_

Out[7]:

array([1.14988114])

In [8]:

linear_regression.intercept_

linear_regression.intercept_

Out[8]:

np.float64(-0.006760181988206382)

In [9]:

y_train_pred = linear_regression.predict(X_train)
MSE_train = mean_squared_error(y_train, y_train_pred)
print(f'MSE training: {round(MSE_train, 3)}')

y_train_pred = linear_regression.predict(X_train) MSE_train = mean_squared_error(y_train, y_train_pred) print(f'MSE training: {round(MSE_train, 3)}')

MSE training: 0.024

In [10]:

y_test_pred = linear_regression.predict(X_test)
MSE_test = mean_squared_error(y_test, y_test_pred)
print(f'MSE training: {round(MSE_test, 3)}')

y_test_pred = linear_regression.predict(X_test) MSE_test = mean_squared_error(y_test, y_test_pred) print(f'MSE training: {round(MSE_test, 3)}')

MSE training: 0.031

In [11]:

# podivejme se na data skrze rozptylovy diagram
plt.scatter(X_train, y_train, edgecolor="b", s=20, label="Trenovaci data")
plt.scatter(X_test, y_test, edgecolor="g", color="g", s=20, label="Testovaci data")
plt.xlabel("x")
plt.ylabel("y")
plt.legend(loc="best")

X_plot = np.linspace(0, 1, 100)
y_plot = linear_regression.predict(X_plot.reshape(-1, 1))
plt.plot(X_plot, y_plot)

# podivejme se na data skrze rozptylovy diagram plt.scatter(X_train, y_train, edgecolor="b", s=20, label="Trenovaci data") plt.scatter(X_test, y_test, edgecolor="g", color="g", s=20, label="Testovaci data") plt.xlabel("x") plt.ylabel("y") plt.legend(loc="best") X_plot = np.linspace(0, 1, 100) y_plot = linear_regression.predict(X_plot.reshape(-1, 1)) plt.plot(X_plot, y_plot)

Out[11]:

[<matplotlib.lines.Line2D at 0x73660f63f7f0>]

In [12]:

X_funkce = np.linspace(0, 1, 100)
sum_hodnoty = np.ones(100) / 2. * mnozstvi_sumu
y_fun = funkce(X_funkce, sum_hodnoty)

# podivejme se na data skrze rozptylovy diagram
plt.scatter(X_train, y_train, edgecolor="b", s=20, label="Trenovaci data")
plt.scatter(X_test, y_test, edgecolor="g", color="g", s=20, label="Testovaci data")
plt.xlabel("x")
plt.ylabel("y")
plt.legend(loc="best")

X_plot = np.linspace(0, 1, 100)
y_plot = linear_regression.predict(X_plot.reshape(-1, 1))
plt.plot(X_plot, y_plot)

plt.plot(X_funkce, y_fun, color="k",  label="Underlying function")

X_funkce = np.linspace(0, 1, 100) sum_hodnoty = np.ones(100) / 2. * mnozstvi_sumu y_fun = funkce(X_funkce, sum_hodnoty) # podivejme se na data skrze rozptylovy diagram plt.scatter(X_train, y_train, edgecolor="b", s=20, label="Trenovaci data") plt.scatter(X_test, y_test, edgecolor="g", color="g", s=20, label="Testovaci data") plt.xlabel("x") plt.ylabel("y") plt.legend(loc="best") X_plot = np.linspace(0, 1, 100) y_plot = linear_regression.predict(X_plot.reshape(-1, 1)) plt.plot(X_plot, y_plot) plt.plot(X_funkce, y_fun, color="k", label="Underlying function")

Out[12]:

[<matplotlib.lines.Line2D at 0x73660f6fc2b0>]

Polynomická regrese¶

Generování dat¶

In [13]:

# funkce pocitajici data a vnasejici do nich sum (noise) 
def funkce(x, noise):
    return .6 *  np.sin(x) + x + (x ** .8) * noise

# funkce pocitajici data a vnasejici do nich sum (noise) def funkce(x, noise): return .6 * np.sin(x) + x + (x ** .8) * noise

In [14]:

# generovani trenovacich dat 
pocet = 20
mnozstvi_sumu = 0.7
# prvky
X_train = np.sort(np.random.rand(pocet))
# zanesme sum
sum_train = np.random.rand(pocet) * mnozstvi_sumu

# cile (reference, labely, targets)
y_train = funkce(X_train, sum_train) 
X_train = X_train.reshape(-1, 1)  # sloupcovy vektor

# vytvorme testovaci data z tez funkce 
pocet_test = 20
# testovaci prvky
X_test = np.sort(np.random.rand(pocet_test))

# cile (reference, labely, targets)
sum_test = np.random.rand(pocet_test) * mnozstvi_sumu
y_test = funkce(X_test, sum_test)
X_test = X_test.reshape(-1, 1)

# generovani trenovacich dat pocet = 20 mnozstvi_sumu = 0.7 # prvky X_train = np.sort(np.random.rand(pocet)) # zanesme sum sum_train = np.random.rand(pocet) * mnozstvi_sumu # cile (reference, labely, targets) y_train = funkce(X_train, sum_train) X_train = X_train.reshape(-1, 1) # sloupcovy vektor # vytvorme testovaci data z tez funkce pocet_test = 20 # testovaci prvky X_test = np.sort(np.random.rand(pocet_test)) # cile (reference, labely, targets) sum_test = np.random.rand(pocet_test) * mnozstvi_sumu y_test = funkce(X_test, sum_test) X_test = X_test.reshape(-1, 1)

In [15]:

# podivejme se na data skrze rozptylovy diagram
plt.scatter(X_train, y_train, edgecolor="b", s=20, label="Trenovaci data")
plt.scatter(X_test, y_test, edgecolor="g", color="g", s=20, label="Testovaci data")
plt.xlabel("x")
plt.ylabel("y")
plt.legend(loc="best")

# podivejme se na data skrze rozptylovy diagram plt.scatter(X_train, y_train, edgecolor="b", s=20, label="Trenovaci data") plt.scatter(X_test, y_test, edgecolor="g", color="g", s=20, label="Testovaci data") plt.xlabel("x") plt.ylabel("y") plt.legend(loc="best")

Out[15]:

<matplotlib.legend.Legend at 0x73660cf3f880>

In [16]:

# Transformujme vstupni data na polynomialni
stupne = 10
# definujme prvky
poly = PolynomialFeatures(degree=stupne, include_bias=False)
# transformujme trenovaci data
polynomial_features = poly.fit_transform(X_train.reshape(-1, 1))

# Transformujme vstupni data na polynomialni stupne = 10 # definujme prvky poly = PolynomialFeatures(degree=stupne, include_bias=False) # transformujme trenovaci data polynomial_features = poly.fit_transform(X_train.reshape(-1, 1))

In [17]:

# vytvorme model
linear_regression = LinearRegression()
# trenujme model na trenovacich datech
linear_regression.fit(polynomial_features, y_train)

# vytvorme model linear_regression = LinearRegression() # trenujme model na trenovacich datech linear_regression.fit(polynomial_features, y_train)

Out[17]:

LinearRegression()

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In [18]:

# spustme predikci
y_train_pred = linear_regression.predict(polynomial_features)
MSE_train = mean_squared_error(y_train, y_train_pred)
print(f'MSE training: {round(MSE_train, 3)}')

# spustme predikci y_train_pred = linear_regression.predict(polynomial_features) MSE_train = mean_squared_error(y_train, y_train_pred) print(f'MSE training: {round(MSE_train, 3)}')

MSE training: 0.005

In [19]:

# zhodnotme model na testovacich datech
test_features = poly.fit_transform(X_test.reshape(-1, 1))
y_pred = linear_regression.predict(test_features)
MSE_test = mean_squared_error(y_test, y_pred)
print(f'MSE testing: {round(MSE_test, 3)}')

# zhodnotme model na testovacich datech test_features = poly.fit_transform(X_test.reshape(-1, 1)) y_pred = linear_regression.predict(test_features) MSE_test = mean_squared_error(y_test, y_pred) print(f'MSE testing: {round(MSE_test, 3)}')

MSE testing: 0.384

In [20]:

X_funkce = np.linspace(0, 1, 100)
sum_hodnoty = np.ones(100) / 2. * mnozstvi_sumu
y_fun = funkce(X_funkce, sum_hodnoty)

# podivejme se na data skrze rozptylovy diagram
plt.scatter(X_train, y_train, edgecolor="b", s=20, label="Trenovaci data")
plt.scatter(X_test, y_test, edgecolor="g", color="g", s=20, label="Testovaci data")
plt.xlabel("x")
plt.ylabel("y")
plt.legend(loc="best")
plt.ylim(-0.5)

X_plot = np.linspace(0, 1, 100)
plot_polynomial_features = poly.fit_transform(X_plot.reshape(-1, 1))
y_plot = linear_regression.predict(plot_polynomial_features)
plt.plot(X_plot, y_plot)

plt.plot(X_funkce, y_fun, color="k",  label="Underlying function")

X_funkce = np.linspace(0, 1, 100) sum_hodnoty = np.ones(100) / 2. * mnozstvi_sumu y_fun = funkce(X_funkce, sum_hodnoty) # podivejme se na data skrze rozptylovy diagram plt.scatter(X_train, y_train, edgecolor="b", s=20, label="Trenovaci data") plt.scatter(X_test, y_test, edgecolor="g", color="g", s=20, label="Testovaci data") plt.xlabel("x") plt.ylabel("y") plt.legend(loc="best") plt.ylim(-0.5) X_plot = np.linspace(0, 1, 100) plot_polynomial_features = poly.fit_transform(X_plot.reshape(-1, 1)) y_plot = linear_regression.predict(plot_polynomial_features) plt.plot(X_plot, y_plot) plt.plot(X_funkce, y_fun, color="k", label="Underlying function")

Out[20]:

[<matplotlib.lines.Line2D at 0x73660ce11e10>]