小姐姐帶你一起學：如何用Python實現7種機器學習演算法（附程式碼）

import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
np.random.seed(123)

# We will use a simple training set
X = 2 * np.random.rand(500, 1)
y = 5 + 3 * X + np.random.randn(500, 1)
fig = plt.figure(figsize=(8,6))
plt.scatter(X, y)
plt.title("Dataset")
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.show()

# Split the data into a training and test set
X_train, X_test, y_train, y_test = train_test_split(X, y)
print(f'Shape X_train: {X_train.shape}')
print(f'Shape y_train: {y_train.shape}')
print(f'Shape X_test: {X_test.shape}')
print(f'Shape y_test: {y_test.shape}')

class LinearRegression:
    
    def __init__(self):
        pass
    
    def train_gradient_descent(self, X, y, learning_rate=0.01, n_iters=100):
        """
        Trains a linear regression model using gradient descent
        """
        # Step 0: Initialize the parameters
        n_samples, n_features = X.shape
        self.weights = np.zeros(shape=(n_features,1))
        self.bias = 0
        costs = []
        
        for i in range(n_iters):
            # Step 1: Compute a linear combination of the input features and weights
            y_predict = np.dot(X, self.weights) + self.bias
           
            # Step 2: Compute cost over training set
            cost = (1 / n_samples) * np.sum((y_predict - y)**2)
            costs.append(cost)
           
            if i % 100 == 0:
                print(f"Cost at iteration {i}: {cost}")
            
            # Step 3: Compute the gradients
            dJ_dw = (2 / n_samples) * np.dot(X.T, (y_predict - y))
            dJ_db = (2 / n_samples) * np.sum((y_predict - y)) 
            
            # Step 4: Update the parameters
            self.weights = self.weights - learning_rate * dJ_dw
            self.bias = self.bias - learning_rate * dJ_db
        
        return self.weights, self.bias, costs
   
    def train_normal_equation(self, X, y):
        """
        Trains a linear regression model using the normal equation
        """
        self.weights = np.dot(np.dot(np.linalg.inv(np.dot(X.T, X)), X.T), y)
        self.bias = 0
        
        return self.weights, self.bias
        
    def predict(self, X):
        return np.dot(X, self.weights) + self.bias

regressor = LinearRegression()
w_trained, b_trained, costs = regressor.train_gradient_descent(X_train, y_train, learning_rate=0.005, n_iters=600)
fig = plt.figure(figsize=(8,6))
plt.plot(np.arange(n_iters), costs)
plt.title("Development of cost during training")
plt.xlabel("Number of iterations")
plt.ylabel("Cost")
plt.show()

n_samples, _ = X_train.shape
n_samples_test, _ = X_test.shape

y_p_train = regressor.predict(X_train)
y_p_test = regressor.predict(X_test)

error_train =  (1 / n_samples) * np.sum((y_p_train - y_train) ** 2)
error_test =  (1 / n_samples_test) * np.sum((y_p_test - y_test) ** 2)

print(f"Error on training set: {np.round(error_train, 4)}")
print(f"Error on test set: {np.round(error_test)}")

# To compute the parameters using the normal equation, we add a bias value of 1 to each input example
X_b_train = np.c_[np.ones((n_samples)), X_train]
X_b_test = np.c_[np.ones((n_samples_test)), X_test]

reg_normal = LinearRegression()
w_trained = reg_normal.train_normal_equation(X_b_train, y_train)

y_p_train = reg_normal.predict(X_b_train)
y_p_test = reg_normal.predict(X_b_test)

error_train =  (1 / n_samples) * np.sum((y_p_train - y_train) ** 2)
error_test =  (1 / n_samples_test) * np.sum((y_p_test - y_test) ** 2)

print(f"Error on training set: {np.round(error_train, 4)}")
print(f"Error on test set: {np.round(error_test, 4)}")

# Plot the test predictions


fig = plt.figure(figsize=(8,6))
plt.scatter(X_train, y_train)
plt.scatter(X_test, y_p_test)
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.show()

import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.datasets import make_blobs
import matplotlib.pyplot as plt
np.random.seed(123)

% matplotlib inline

# We will perform logistic regression using a simple toy dataset of two classes
X, y_true = make_blobs(n_samples= 1000, centers=2)

fig = plt.figure(figsize=(8,6))
plt.scatter(X[:,0], X[:,1], c=y_true)
plt.title("Dataset")
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.show()

# Reshape targets to get column vector with shape (n_samples, 1)
y_true = y_true[:, np.newaxis]
# Split the data into a training and test set
X_train, X_test, y_train, y_test = train_test_split(X, y_true)
print(f'Shape X_train: {X_train.shape}')
print(f'Shape y_train: {y_train.shape}')
print(f'Shape X_test: {X_test.shape}')
print(f'Shape y_test: {y_test.shape}')

class LogisticRegression:
   
    def __init__(self):
        pass

    def sigmoid(self, a):
        return 1 / (1 + np.exp(-a))

    def train(self, X, y_true, n_iters, learning_rate):
        """
        Trains the logistic regression model on given data X and targets y
        """
        # Step 0: Initialize the parameters
        n_samples, n_features = X.shape
        self.weights = np.zeros((n_features, 1))
        self.bias = 0
        costs = []
    
        for i in range(n_iters):
            # Step 1 and 2: Compute a linear combination of the input features and weights, 
            # apply the sigmoid activation function
            y_predict = self.sigmoid(np.dot(X, self.weights) + self.bias)
       
            # Step 3: Compute the cost over the whole training set.
            cost = (- 1 / n_samples) * np.sum(y_true * np.log(y_predict) + (1 - y_true) * (np.log(1 - y_predict)))

            # Step 4: Compute the gradients
            dw = (1 / n_samples) * np.dot(X.T, (y_predict - y_true))
            db = (1 / n_samples) * np.sum(y_predict - y_true)

            # Step 5: Update the parameters
            self.weights = self.weights - learning_rate * dw
            self.bias = self.bias - learning_rate * db

            costs.append(cost)
            if i % 100 == 0:
                print(f"Cost after iteration {i}: {cost}")

        return self.weights, self.bias, costs

    def predict(self, X):
        """
        Predicts binary labels for a set of examples X.
        """
        y_predict = self.sigmoid(np.dot(X, self.weights) + self.bias)
        y_predict_labels = [1 if elem > 0.5 else 0 for elem in y_predict]

        return np.array(y_predict_labels)[:, np.newaxis]

regressor = LogisticRegression()
w_trained, b_trained, costs = regressor.train(X_train, y_train, n_iters=600, learning_rate=0.009)

fig = plt.figure(figsize=(8,6))
plt.plot(np.arange(600), costs)
plt.title("Development of cost over training")
plt.xlabel("Number of iterations")
plt.ylabel("Cost")
plt.show()

y_p_train = regressor.predict(X_train)
y_p_test = regressor.predict(X_test)

print(f"train accuracy: {100 - np.mean(np.abs(y_p_train - y_train)) * 100}%")
print(f"test accuracy: {100 - np.mean(np.abs(y_p_test - y_test))}%")

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
from sklearn.model_selection import train_test_split
np.random.seed(123)

% matplotlib inline

X, y = make_blobs(n_samples=1000, centers=2)
fig = plt.figure(figsize=(8,6))
plt.scatter(X[:,0], X[:,1], c=y)
plt.title("Dataset")
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.show()

y_true = y[:, np.newaxis]

X_train, X_test, y_train, y_test = train_test_split(X, y_true)
print(f'Shape X_train: {X_train.shape}')
print(f'Shape y_train: {y_train.shape})')
print(f'Shape X_test: {X_test.shape}')
print(f'Shape y_test: {y_test.shape}')

class Perceptron():

    def __init__(self):
        pass

    def train(self, X, y, learning_rate=0.05, n_iters=100):
        n_samples, n_features = X.shape

        # Step 0: Initialize the parameters
        self.weights = np.zeros((n_features,1))
        self.bias = 0

        for i in range(n_iters):
            # Step 1: Compute the activation
            a = np.dot(X, self.weights) + self.bias

            # Step 2: Compute the output
            y_predict = self.step_function(a)

            # Step 3: Compute weight updates
            delta_w = learning_rate * np.dot(X.T, (y - y_predict))
            delta_b = learning_rate * np.sum(y - y_predict)

            # Step 4: Update the parameters
            self.weights += delta_w
            self.bias += delta_b

        return self.weights, self.bias

    def step_function(self, x):
        return np.array([1 if elem >= 0 else 0 for elem in x])[:, np.newaxis]

    def predict(self, X):
        a = np.dot(X, self.weights) + self.bias
        return self.step_function(a)

p = Perceptron()
w_trained, b_trained = p.train(X_train, y_train,learning_rate=0.05, n_iters=500)

y_p_train = p.predict(X_train)
y_p_test = p.predict(X_test)

print(f"training accuracy: {100 - np.mean(np.abs(y_p_train - y_train)) * 100}%")
print(f"test accuracy: {100 - np.mean(np.abs(y_p_test - y_test)) * 100}%")

def plot_hyperplane(X, y, weights, bias):
    """
    Plots the dataset and the estimated decision hyperplane
    """
    slope = - weights[0]/weights[1]
    intercept = - bias/weights[1]
    x_hyperplane = np.linspace(-10,10,10)
    y_hyperplane = slope * x_hyperplane + intercept
    fig = plt.figure(figsize=(8,6))
    plt.scatter(X[:,0], X[:,1], c=y)
    plt.plot(x_hyperplane, y_hyperplane, '-')
    plt.title("Dataset and fitted decision hyperplane")
    plt.xlabel("First feature")
    plt.ylabel("Second feature")
    plt.show()

plot_hyperplane(X, y, w_trained, b_trained)

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split
np.random.seed(123)

% matplotlib inline

# We will use the digits dataset as an example. It consists of the 1797 images of hand-written digits. Each digit is
# represented by a 64-dimensional vector of pixel values.


digits = load_digits()
X, y = digits.data, digits.target

X_train, X_test, y_train, y_test = train_test_split(X, y)
print(f'X_train shape: {X_train.shape}')
print(f'y_train shape: {y_train.shape}')
print(f'X_test shape: {X_test.shape}')
print(f'y_test shape: {y_test.shape}')

# Example digits
fig = plt.figure(figsize=(10,8))
for i in range(10):
    ax = fig.add_subplot(2, 5, i+1)
    plt.imshow(X[i].reshape((8,8)), cmap='gray')

class kNN():
    def __init__(self):
        pass

    def fit(self, X, y):
        self.data = X
        self.targets = y

    def euclidean_distance(self, X):
        """
        Computes the euclidean distance between the training data and
        a new input example or matrix of input examples X
        """
        # input: single data point
        if X.ndim == 1:
            l2 = np.sqrt(np.sum((self.data - X)**2, axis=1))

        # input: matrix of data points
        if X.ndim == 2:
            n_samples, _ = X.shape
            l2 = [np.sqrt(np.sum((self.data - X[i])**2, axis=1)) for i in range(n_samples)]

        return np.array(l2)

    def predict(self, X, k=1):
        """
        Predicts the classification for an input example or matrix of input examples X
        """
        # step 1: compute distance between input and training data
        dists = self.euclidean_distance(X)

        # step 2: find the k nearest neighbors and their classifications
        if X.ndim == 1:
            if k == 1:
                nn = np.argmin(dists)
                return self.targets[nn]
            else:
                knn = np.argsort(dists)[:k]
                y_knn = self.targets[knn]
                max_vote = max(y_knn, key=list(y_knn).count)
                return max_vote

        if X.ndim == 2:
            knn = np.argsort(dists)[:, :k]
            y_knn = self.targets[knn]
            if k == 1:
                return y_knn.T
            else:
                n_samples, _ = X.shape
                max_votes = [max(y_knn[i], key=list(y_knn[i]).count) for i in range(n_samples)]
                return max_votes

knn = kNN()
knn.fit(X_train, y_train)

print("Testing one datapoint, k=1")
print(f"Predicted label: {knn.predict(X_test[0], k=1)}")
print(f"True label: {y_test[0]}")
print()
print("Testing one datapoint, k=5")
print(f"Predicted label: {knn.predict(X_test[20], k=5)}")
print(f"True label: {y_test[20]}")
print()
print("Testing 10 datapoint, k=1")
print(f"Predicted labels: {knn.predict(X_test[5:15], k=1)}")
print(f"True labels: {y_test[5:15]}")
print()
print("Testing 10 datapoint, k=4")
print(f"Predicted labels: {knn.predict(X_test[5:15], k=4)}")
print(f"True labels: {y_test[5:15]}")
print()

# Compute accuracy on test set
y_p_test1 = knn.predict(X_test, k=1)
test_acc1= np.sum(y_p_test1[0] == y_test)/len(y_p_test1[0]) * 100
print(f"Test accuracy with k = 1: {format(test_acc1)}")

y_p_test8 = knn.predict(X_test, k=5)
test_acc8= np.sum(y_p_test8 == y_test)/len(y_p_test8) * 100
print(f"Test accuracy with k = 8: {format(test_acc8)}")

import numpy as np
import matplotlib.pyplot as plt
import random
from sklearn.datasets import make_blobs
np.random.seed(123)

% matplotlib inline

X, y = make_blobs(centers=4, n_samples=1000)
print(f'Shape of dataset: {X.shape}')

fig = plt.figure(figsize=(8,6))
plt.scatter(X[:,0], X[:,1], c=y)
plt.title("Dataset with 4 clusters")
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.show()

class KMeans():
    def __init__(self, n_clusters=4):
        self.k = n_clusters

    def fit(self, data):
        """
        Fits the k-means model to the given dataset
        """
        n_samples, _ = data.shape
        # initialize cluster centers
        self.centers = np.array(random.sample(list(data), self.k))
        self.initial_centers = np.copy(self.centers)

        # We will keep track of whether the assignment of data points
        # to the clusters has changed. If it stops changing, we are 
        # done fitting the model
        old_assigns = None
        n_iters = 0

        while True:
            new_assigns = [self.classify(datapoint) for datapoint in data]

            if new_assigns == old_assigns:
                print(f"Training finished after {n_iters} iterations!")
                return

            old_assigns = new_assigns
            n_iters += 1

            # recalculate centers
            for id_ in range(self.k):
                points_idx = np.where(np.array(new_assigns) == id_)
                datapoints = data[points_idx]
                self.centers[id_] = datapoints.mean(axis=0)

    def l2_distance(self, datapoint):
        dists = np.sqrt(np.sum((self.centers - datapoint)**2, axis=1))
        return dists

    def classify(self, datapoint):
        """
        Given a datapoint, compute the cluster closest to the
        datapoint. Return the cluster ID of that cluster.
        """
        dists = self.l2_distance(datapoint)
        return np.argmin(dists)

    def plot_clusters(self, data):
        plt.figure(figsize=(12,10))
        plt.title("Initial centers in black, final centers in red")
        plt.scatter(data[:, 0], data[:, 1], marker='.', c=y)
        plt.scatter(self.centers[:, 0], self.centers[:,1], c='r')
        plt.scatter(self.initial_centers[:, 0], self.initial_centers[:,1], c='k')
        plt.show()

kmeans = KMeans(n_clusters=4)
kmeans.fit(X)

kmeans.plot_clusters(X)

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.datasets import make_circles
from sklearn.model_selection import train_test_split
np.random.seed(123)
% matplotlib inline

X, y = make_circles(n_samples=1000, factor=0.5, noise=.1)
fig = plt.figure(figsize=(8,6))
plt.scatter(X[:,0], X[:,1], c=y)
plt.xlim([-1.5, 1.5])
plt.ylim([-1.5, 1.5])
plt.title("Dataset")
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.show()

# reshape targets to get column vector with shape (n_samples, 1)
y_true = y[:, np.newaxis]
# Split the data into a training and test set
X_train, X_test, y_train, y_test = train_test_split(X, y_true)
print(f'Shape X_train: {X_train.shape}')
print(f'Shape y_train: {y_train.shape}')
print(f'Shape X_test: {X_test.shape}')
print(f'Shape y_test: {y_test.shape}')

class NeuralNet():
    def __init__(self, n_inputs, n_outputs, n_hidden):
        self.n_inputs = n_inputs
        self.n_outputs = n_outputs
        self.hidden = n_hidden
        # Initialize weight matrices and bias vectors
        self.W_h = np.random.randn(self.n_inputs, self.hidden)
        self.b_h = np.zeros((1, self.hidden))
        self.W_o = np.random.randn(self.hidden, self.n_outputs)
        self.b_o = np.zeros((1, self.n_outputs))
    def sigmoid(self, a):
        return 1 / (1 + np.exp(-a))
    def forward_pass(self, X):
        """
        Propagates the given input X forward through the net.
        Returns:
            A_h: matrix with activations of all hidden neurons for all input examples
            O_h: matrix with outputs of all hidden neurons for all input examples
            A_o: matrix with activations of all output neurons for all input examples
            O_o: matrix with outputs of all output neurons for all input examples
        """
        # Compute activations and outputs of hidden units
        A_h = np.dot(X, self.W_h) + self.b_h
        O_h = np.tanh(A_h)
        # Compute activations and outputs of output units
        A_o = np.dot(O_h, self.W_o) + self.b_o
        O_o = self.sigmoid(A_o)
        outputs = {
                "A_h": A_h,
                "A_o": A_o,
                "O_h": O_h,
                "O_o": O_o,
                }
        return outputs
    def cost(self, y_true, y_predict, n_samples):
        """
        Computes and returns the cost over all examples
        """
        # same cost function as in logistic regression
        cost = (- 1 / n_samples) * np.sum(y_true * np.log(y_predict) + (1 - y_true) * (np.log(1 - y_predict)))
        cost = np.squeeze(cost)
        assert isinstance(cost, float)
        return cost
    def backward_pass(self,  X, Y, n_samples, outputs):
        """
        Propagates the errors backward through the net.
        Returns:
            dW_h: partial derivatives of loss function w.r.t hidden weights
            db_h: partial derivatives of loss function w.r.t hidden bias
            dW_o: partial derivatives of loss function w.r.t output weights
            db_o: partial derivatives of loss function w.r.t output bias
        """
        dA_o = (outputs["O_o"] - Y)
        dW_o = (1 / n_samples) * np.dot(outputs["O_h"].T, dA_o)
        db_o = (1 / n_samples) * np.sum(dA_o)
        dA_h = (np.dot(dA_o, self.W_o.T)) * (1 - np.power(outputs["O_h"], 2))
        dW_h = (1 / n_samples) * np.dot(X.T, dA_h)
        db_h = (1 / n_samples) * np.sum(dA_h)
        gradients = {
                "dW_o": dW_o,
                "db_o": db_o,
                "dW_h": dW_h,
                "db_h": db_h,
                }
        return gradients
    def update_weights(self, gradients, eta):
        """
        Updates the model parameters using a fixed learning rate
        """
        self.W_o = self.W_o - eta * gradients["dW_o"]
        self.W_h = self.W_h - eta * gradients["dW_h"]
        self.b_o = self.b_o - eta * gradients["db_o"]
        self.b_h = self.b_h - eta * gradients["db_h"]
    def train(self, X, y, n_iters=500, eta=0.3):
        """
        Trains the neural net on the given input data
        """
        n_samples, _ = X.shape
        for i in range(n_iters):
            outputs = self.forward_pass(X)
            cost = self.cost(y, outputs["O_o"], n_samples=n_samples)
            gradients = self.backward_pass(X, y, n_samples, outputs)
            if i % 100 == 0:
                print(f'Cost at iteration {i}: {np.round(cost, 4)}')
            self.update_weights(gradients, eta)
    def predict(self, X):
        """
        Computes and returns network predictions for given dataset
        """
        outputs = self.forward_pass(X)
        y_pred = [1 if elem >= 0.5 else 0 for elem in outputs["O_o"]]
        return np.array(y_pred)[:, np.newaxis]

nn = NeuralNet(n_inputs=2, n_hidden=6, n_outputs=1)
print("Shape of weight matrices and bias vectors:")
print(f'W_h shape: {nn.W_h.shape}')
print(f'b_h shape: {nn.b_h.shape}')
print(f'W_o shape: {nn.W_o.shape}')
print(f'b_o shape: {nn.b_o.shape}')
print()
print("Training:")
nn.train(X_train, y_train, n_iters=2000, eta=0.7)

n_test_samples, _ = X_test.shape
y_predict = nn.predict(X_test)
print(f"Classification accuracy on test set: {(np.sum(y_predict == y_test)/n_test_samples)*100} %")

X_temp, y_temp = make_circles(n_samples=60000, noise=.5)
y_predict_temp = nn.predict(X_temp)
y_predict_temp = np.ravel(y_predict_temp)

fig = plt.figure(figsize=(8,12))
ax = fig.add_subplot(2,1,1)
plt.scatter(X[:,0], X[:,1], c=y)
plt.xlim([-1.5, 1.5])
plt.ylim([-1.5, 1.5])
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.title("Training and test set")
ax = fig.add_subplot(2,1,2)
plt.scatter(X_temp[:,0], X_temp[:,1], c=y_predict_temp)
plt.xlim([-1.5, 1.5])
plt.ylim([-1.5, 1.5])
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.title("Decision boundary")

from sklearn.datasets import load_iris
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.datasets import make_blobs
import matplotlib.pyplot as plt
np.random.seed(13)

X, y_true = make_blobs(centers=4, n_samples = 5000)
fig = plt.figure(figsize=(8,6))
plt.scatter(X[:,0], X[:,1], c=y_true)
plt.title("Dataset")
plt.xlabel("First feature")
plt.ylabel("Second feature")
plt.show()

# reshape targets to get column vector with shape (n_samples, 1)
y_true = y_true[:, np.newaxis]
# Split the data into a training and test set
X_train, X_test, y_train, y_test = train_test_split(X, y_true)
print(f'Shape X_train: {X_train.shape}')
print(f'Shape y_train: {y_train.shape}')
print(f'Shape X_test: {X_test.shape}')
print(f'Shape y_test: {y_test.shape}')

class SoftmaxRegressor:
    def __init__(self):
        pass
    def train(self, X, y_true, n_classes, n_iters=10, learning_rate=0.1):
        """
        Trains a multinomial logistic regression model on given set of training data
        """
        self.n_samples, n_features = X.shape
        self.n_classes = n_classes
        self.weights = np.random.rand(self.n_classes, n_features)
        self.bias = np.zeros((1, self.n_classes))
        all_losses = []
        for i in range(n_iters):
            scores = self.compute_scores(X)
            probs = self.softmax(scores)
            y_predict = np.argmax(probs, axis=1)[:, np.newaxis]
            y_one_hot = self.one_hot(y_true)
            loss = self.cross_entropy(y_one_hot, probs)
            all_losses.append(loss)
            dw = (1 / self.n_samples) * np.dot(X.T, (probs - y_one_hot))
            db = (1 / self.n_samples) * np.sum(probs - y_one_hot, axis=0)
            self.weights = self.weights - learning_rate * dw.T
            self.bias = self.bias - learning_rate * db
            if i % 100 == 0:
                print(f'Iteration number: {i}, loss: {np.round(loss, 4)}')
        return self.weights, self.bias, all_losses
    def predict(self, X):
        """
        Predict class labels for samples in X.
        Args:
            X: numpy array of shape (n_samples, n_features)
        Returns:
            numpy array of shape (n_samples, 1) with predicted classes
        """
        scores = self.compute_scores(X)
        probs = self.softmax(scores)
        return np.argmax(probs, axis=1)[:, np.newaxis]
    def softmax(self, scores):
        """
        Tranforms matrix of predicted scores to matrix of probabilities
        Args:
            scores: numpy array of shape (n_samples, n_classes)
            with unnormalized scores
        Returns:
            softmax: numpy array of shape (n_samples, n_classes)
            with probabilities
        """
        exp = np.exp(scores)
        sum_exp = np.sum(np.exp(scores), axis=1, keepdims=True)
        softmax = exp / sum_exp
        return softmax
    def compute_scores(self, X):
        """
        Computes class-scores for samples in X
        Args:
            X: numpy array of shape (n_samples, n_features)
        Returns:
            scores: numpy array of shape (n_samples, n_classes)
        """
        return np.dot(X, self.weights.T) + self.bias
    def cross_entropy(self, y_true, scores):
        loss = - (1 / self.n_samples) * np.sum(y_true * np.log(scores))
        return loss
    def one_hot(self, y):
        """
        Tranforms vector y of labels to one-hot encoded matrix
        """
        one_hot = np.zeros((self.n_samples, self.n_classes))
        one_hot[np.arange(self.n_samples), y.T] = 1
        return one_hot

regressor = SoftmaxRegressor()
w_trained, b_trained, loss = regressor.train(X_train, y_train, learning_rate=0.1, n_iters=800, n_classes=4)
fig = plt.figure(figsize=(8,6))
plt.plot(np.arange(800), loss)
plt.title("Development of loss during training")
plt.xlabel("Number of iterations")
plt.ylabel("Loss")
plt.show()Iteration number: 0, loss: 1.393

n_test_samples, _ = X_test.shape
y_predict = regressor.predict(X_test)
print(f"Classification accuracy on test set: {(np.sum(y_predict == y_test)/n_test_samples) * 100}%")