​

​

import numpy as np
from keras.datasets import mnist
from keras.models import Sequential
from keras.layers import Dense, Flatten, Conv2D, MaxPooling2D
from keras.utils import np_utils

# 加载MNIST数据集并进行预处理
(X_train, y_train), (X_test, y_test) = mnist.load_data()
X_train = X_train.reshape(X_train.shape[0], 28, 28, 1).astype('float32') / 255
X_test = X_test.reshape(X_test.shape[0], 28, 28, 1).astype('float32') / 255
y_train = np_utils.to_categorical(y_train)
y_test = np_utils.to_categorical(y_test)

# 构建深度学习模型
model = Sequential()
model.add(Conv2D(32, (3, 3), activation='relu', input_shape=(28, 28, 1)))
model.add(MaxPooling2D((2, 2)))
model.add(Conv2D(64, (3, 3), activation='relu'))
model.add(MaxPooling2D((2, 2)))
model.add(Flatten())
model.add(Dense(128, activation='relu'))
model.add(Dense(10, activation='softmax'))

# 编译模型
model.compile(optimizer='adam', loss='categorical_crossentropy', metrics=['accuracy'])

# 训练模型并评估性能
model.fit(X_train, y_train, epochs=10, batch_size=32, verbose=1)
score = model.evaluate(X_test, y_test, verbose=0)
print('Test loss:', score[0])
print('Test accuracy:', score[1])

​

import numpy as np

class NaiveBayes:
    def __init__(self, n_classes):
        self.n_classes = n_classes
        self.priors = None
        self.posteriors = None
    
    def fit(self, X, y):
        n_samples, n_features = X.shape
        self.priors = np.zeros(self.n_classes)
        self.posteriors = np.zeros((self.n_classes, n_features))
        for c in range(self.n_classes):
            X_c = X[y == c]
            self.priors[c] = len(X_c) / n_samples
            self.posteriors[c] = (X_c.sum(axis=0) + 1) / (len(X_c) + 1)
    
    def predict(self, X):
        y_pred = []
        for x in X:
            posteriors = []
            for c in range(self.n_classes):
                prior = np.log(self.priors[c])
                likelihood = np.sum(np.log(self.posteriors[c]) * x)
                posterior = prior + likelihood
                posteriors.append(posterior)
            y_pred.append(np.argmax(posteriors))
        return y_pred

import numpy as np

# 输入数据和标签
x = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([[0], [0], [0], [1]])

# 定义神经网络
class NeuralNetwork:
    def __init__(self):
        np.random.seed(1)
        self.weights = 2 * np.random.random((2, 1)) - 1

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

    def sigmoid_derivative(self, x):
        return x * (1 - x)

    def train(self, x, y, iterations):
        for i in range(iterations):
            output = self.predict(x)
            error = y - output
            adjustment = np.dot(x.T, error * self.sigmoid_derivative(output))
            self.weights += adjustment

    def predict(self, x):
        return self.sigmoid(np.dot(x, self.weights))

# 训练神经网络
neural_network = NeuralNetwork()
neural_network.train(x, y, 10000)

# 预测
print(neural_network.predict(np.array([0, 0])))
print(neural_network.predict(np.array([0, 1])))
print(neural_network.predict(np.array([1, 0])))
print(neural_network.predict(np.array([1, 1])))

[0.5]
[0.2689864]
[0.2689864]
[0.11738518]