[人工智能]九、过拟合

九、过拟合

内容参考来自https://github.com/dragen1860/Deep-Learning-with-TensorFlow-book开源书籍《TensorFlow2深度学习》，这只是我做的简单的学习笔记，方便以后复习

1.模型的容量

通俗地讲，模型的容量或表达能力，是指模型拟合复杂函数的能力。

2.过拟合与欠拟合

过拟合(Overfitting)：当模型的容量过大时，网络模型除了学习到训练集数据的模态之外，还把额外的观测
误差也学习进来，导致学习的模型在训练集上面表现较好，但是在未见的样本上表现不
佳，也就是模型泛化能力偏弱。

欠拟合(Underfitting)：当模型的容量过小时，模型不能够很好地学习到训练集数据的模态，导致训练集上表现不佳，同时在未见的样本上表现也不佳。

3.正则化

常用的正则化方式有 L0、L1、L2 正则化。

实例

import  tensorflow as tf
from    tensorflow.keras import datasets, layers, optimizers, Sequential, metrics


def preprocess(x, y):

    x = tf.cast(x, dtype=tf.float32) / 255.
    y = tf.cast(y, dtype=tf.int32)

    return x,y


batchsz = 128
(x, y), (x_val, y_val) = datasets.mnist.load_data()
print('datasets:', x.shape, y.shape, x.min(), x.max())



db = tf.data.Dataset.from_tensor_slices((x,y))
db = db.map(preprocess).shuffle(60000).batch(batchsz).repeat(10)

ds_val = tf.data.Dataset.from_tensor_slices((x_val, y_val))
ds_val = ds_val.map(preprocess).batch(batchsz) 




network = Sequential([layers.Dense(256, activation='relu'),
                     layers.Dense(128, activation='relu'),
                     layers.Dense(64, activation='relu'),
                     layers.Dense(32, activation='relu'),
                     layers.Dense(10)])
network.build(input_shape=(None, 28*28))
network.summary()

optimizer = optimizers.Adam(lr=0.01)



for step, (x,y) in enumerate(db):

    with tf.GradientTape() as tape:
        # [b, 28, 28] => [b, 784]
        x = tf.reshape(x, (-1, 28*28))
        # [b, 784] => [b, 10]
        out = network(x)
        # [b] => [b, 10]
        y_onehot = tf.one_hot(y, depth=10) 
        # [b]
        loss = tf.reduce_mean(tf.losses.categorical_crossentropy(y_onehot, out, from_logits=True))


        loss_regularization = []
        for p in network.trainable_variables:
            loss_regularization.append(tf.nn.l2_loss(p))
        loss_regularization = tf.reduce_sum(tf.stack(loss_regularization))

        loss = loss + 0.0001 * loss_regularization
 

    grads = tape.gradient(loss, network.trainable_variables)
    optimizer.apply_gradients(zip(grads, network.trainable_variables))


    if step % 100 == 0:

        print(step, 'loss:', float(loss), 'loss_regularization:', float(loss_regularization)) 


    # evaluate
    if step % 500 == 0:
        total, total_correct = 0., 0

        for step, (x, y) in enumerate(ds_val): 
            # [b, 28, 28] => [b, 784]
            x = tf.reshape(x, (-1, 28*28))
            # [b, 784] => [b, 10]
            out = network(x) 
            # [b, 10] => [b] 
            pred = tf.argmax(out, axis=1) 
            pred = tf.cast(pred, dtype=tf.int32)
            # bool type 
            correct = tf.equal(pred, y)
            # bool tensor => int tensor => numpy
            total_correct += tf.reduce_sum(tf.cast(correct, dtype=tf.int32)).numpy()
            total += x.shape[0]

        print(step, 'Evaluate Acc:', total_correct/total)

4.Dropout

Dropout 通过随机断开神经网络的连接，减少每次训练时实际参与计算的模型的参数量；但是在测试时，Dropout 会恢
复所有的连接，保证模型测试时获得最好的性能。

# 添加 dropout 操作，断开概率为 0.5
x = tf.nn.dropout(x, rate=0.5)

# 添加 Dropout 层，断开概率为 0.5
model.add(layers.Dropout(rate=0.5))

5.数据增强

数据增强(DataAugmentation)是指在维持样本标签不变的条件下，根据先验知识改变样本的特征，使得新产生的样本也符合或者近似符合数据的真实分布。

旋转

# 图片逆时针旋转 180 度
x = tf.image.rot90(x,2)

翻转

# 随机水平翻转
x = tf.image.random_flip_left_right(x)
# 随机竖直翻转
x = tf.image.random_flip_up_down(x)

裁剪

# 图片先缩放到稍大尺寸
x = tf.image.resize(x, [244, 244])
# 再随机裁剪到合适尺寸
x = tf.image.random_crop(x, [224,224,3])

6.过拟合问题实战

import matplotlib.pyplot as plt
# 导入数据集生成工具
import numpy as np
import seaborn as sns
from sklearn.datasets import make_moons
from sklearn.model_selection import train_test_split
from tensorflow.keras import layers, Sequential, regularizers
from mpl_toolkits.mplot3d import Axes3D

plt.rcParams['font.size'] = 16
plt.rcParams['font.family'] = ['STKaiti']
plt.rcParams['axes.unicode_minus'] = False

OUTPUT_DIR = 'output_dir'
N_EPOCHS = 500


def load_dataset():
    # 采样点数
    N_SAMPLES = 1000
    # 测试数量比率
    TEST_SIZE = None

    # 从 moon 分布中随机采样 1000 个点，并切分为训练集-测试集
    X, y = make_moons(n_samples=N_SAMPLES, noise=0.25, random_state=100)
    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=TEST_SIZE, random_state=42)
    return X, y, X_train, X_test, y_train, y_test


def make_plot(X, y, plot_name, file_name, XX=None, YY=None, preds=None, dark=False, output_dir=OUTPUT_DIR):
    # 绘制数据集的分布， X 为 2D 坐标， y 为数据点的标签
    if dark:
        plt.style.use('dark_background')
    else:
        sns.set_style("whitegrid")
    axes = plt.gca()
    axes.set_xlim([-2, 3])
    axes.set_ylim([-1.5, 2])
    axes.set(xlabel="$x_1$", ylabel="$x_2$")
    plt.title(plot_name, fontsize=20, fontproperties='SimHei')
    plt.subplots_adjust(left=0.20)
    plt.subplots_adjust(right=0.80)
    if XX is not None and YY is not None and preds is not None:
        plt.contourf(XX, YY, preds.reshape(XX.shape), 25, alpha=0.08, cmap=plt.cm.Spectral)
        plt.contour(XX, YY, preds.reshape(XX.shape), levels=[.5], cmap="Greys", vmin=0, vmax=.6)
    # 绘制散点图，根据标签区分颜色m=markers
    markers = ['o' if i == 1 else 's' for i in y.ravel()]
    mscatter(X[:, 0], X[:, 1], c=y.ravel(), s=20, cmap=plt.cm.Spectral, edgecolors='none', m=markers, ax=axes)
    # 保存矢量图
    plt.savefig(output_dir + '/' + file_name)
    plt.show()
    plt.close()


def mscatter(x, y, ax=None, m=None, **kw):
    import matplotlib.markers as mmarkers
    if not ax: ax = plt.gca()
    sc = ax.scatter(x, y, **kw)
    if (m is not None) and (len(m) == len(x)):
        paths = []
        for marker in m:
            if isinstance(marker, mmarkers.MarkerStyle):
                marker_obj = marker
            else:
                marker_obj = mmarkers.MarkerStyle(marker)
            path = marker_obj.get_path().transformed(
                marker_obj.get_transform())
            paths.append(path)
        sc.set_paths(paths)
    return sc


def network_layers_influence(X_train, y_train):
    # 构建 5 种不同层数的网络
    for n in range(5):
        # 创建容器
        model = Sequential()
        # 创建第一层
        model.add(layers.Dense(8, input_dim=2, activation='relu'))
        # 添加 n 层，共 n+2 层
        for _ in range(n):
            model.add(layers.Dense(32, activation='relu'))
        # 创建最末层
        model.add(layers.Dense(1, activation='sigmoid'))
        # 模型装配与训练
        model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])
        model.fit(X_train, y_train, epochs=N_EPOCHS, verbose=1)
        # 绘制不同层数的网络决策边界曲线
        # 可视化的 x 坐标范围为[-2, 3]
        xx = np.arange(-2, 3, 0.01)
        # 可视化的 y 坐标范围为[-1.5, 2]
        yy = np.arange(-1.5, 2, 0.01)
        # 生成 x-y 平面采样网格点，方便可视化
        XX, YY = np.meshgrid(xx, yy)
        preds = model.predict_classes(np.c_[XX.ravel(), YY.ravel()])
        title = "网络层数：{0}".format(2 + n)
        file = "网络容量_%i.png" % (2 + n)
        make_plot(X_train, y_train, title, file, XX, YY, preds, output_dir=OUTPUT_DIR + '/network_layers')


def dropout_influence(X_train, y_train):
    # 构建 5 种不同数量 Dropout 层的网络
    for n in range(5):
        # 创建容器
        model = Sequential()
        # 创建第一层
        model.add(layers.Dense(8, input_dim=2, activation='relu'))
        counter = 0
        # 网络层数固定为 5
        for _ in range(5):
            model.add(layers.Dense(64, activation='relu'))
        # 添加 n 个 Dropout 层
        if counter < n:
            counter += 1
            model.add(layers.Dropout(rate=0.5))

        # 输出层
        model.add(layers.Dense(1, activation='sigmoid'))
        # 模型装配
        model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])
        # 训练
        model.fit(X_train, y_train, epochs=N_EPOCHS, verbose=1)
        # 绘制不同 Dropout 层数的决策边界曲线
        # 可视化的 x 坐标范围为[-2, 3]
        xx = np.arange(-2, 3, 0.01)
        # 可视化的 y 坐标范围为[-1.5, 2]
        yy = np.arange(-1.5, 2, 0.01)
        # 生成 x-y 平面采样网格点，方便可视化
        XX, YY = np.meshgrid(xx, yy)
        preds = model.predict_classes(np.c_[XX.ravel(), YY.ravel()])
        title = "无Dropout层" if n == 0 else "{0}层 Dropout层".format(n)
        file = "Dropout_%i.png" % n
        make_plot(X_train, y_train, title, file, XX, YY, preds, output_dir=OUTPUT_DIR + '/dropout')


def build_model_with_regularization(_lambda):
    # 创建带正则化项的神经网络
    model = Sequential()
    model.add(layers.Dense(8, input_dim=2, activation='relu'))  # 不带正则化项
    # 2-4层均是带 L2 正则化项
    model.add(layers.Dense(256, activation='relu', kernel_regularizer=regularizers.l2(_lambda)))
    model.add(layers.Dense(256, activation='relu', kernel_regularizer=regularizers.l2(_lambda)))
    model.add(layers.Dense(256, activation='relu', kernel_regularizer=regularizers.l2(_lambda)))
    # 输出层
    model.add(layers.Dense(1, activation='sigmoid'))
    model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])  # 模型装配
    return model


def plot_weights_matrix(model, layer_index, plot_name, file_name, output_dir=OUTPUT_DIR):
    # 绘制权值范围函数
    # 提取指定层的权值矩阵
    weights = model.layers[layer_index].get_weights()[0]
    shape = weights.shape
    # 生成和权值矩阵等大小的网格坐标
    X = np.array(range(shape[1]))
    Y = np.array(range(shape[0]))
    X, Y = np.meshgrid(X, Y)
    # 绘制3D图
    fig = plt.figure()
    ax = fig.gca(projection='3d')
    ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
    plt.title(plot_name, fontsize=20, fontproperties='SimHei')
    # 绘制权值矩阵范围
    ax.plot_surface(X, Y, weights, cmap=plt.get_cmap('rainbow'), linewidth=0)
    # 设置坐标轴名
    ax.set_xlabel('网格x坐标', fontsize=16, rotation=0, fontproperties='SimHei')
    ax.set_ylabel('网格y坐标', fontsize=16, rotation=0, fontproperties='SimHei')
    ax.set_zlabel('权值', fontsize=16, rotation=90, fontproperties='SimHei')
    # 保存矩阵范围图
    plt.savefig(output_dir + "/" + file_name + ".svg")
    plt.close(fig)


def regularizers_influence(X_train, y_train):
    for _lambda in [1e-5, 1e-3, 1e-1, 0.12, 0.13]:  # 设置不同的正则化系数
        # 创建带正则化项的模型
        model = build_model_with_regularization(_lambda)
        # 模型训练
        model.fit(X_train, y_train, epochs=N_EPOCHS, verbose=1)
        # 绘制权值范围
        layer_index = 2
        plot_title = "正则化系数：{}".format(_lambda)
        file_name = "正则化网络权值_" + str(_lambda)
        # 绘制网络权值范围图
        plot_weights_matrix(model, layer_index, plot_title, file_name, output_dir=OUTPUT_DIR + '/regularizers')
        # 绘制不同正则化系数的决策边界线
        # 可视化的 x 坐标范围为[-2, 3]
        xx = np.arange(-2, 3, 0.01)
        # 可视化的 y 坐标范围为[-1.5, 2]
        yy = np.arange(-1.5, 2, 0.01)
        # 生成 x-y 平面采样网格点，方便可视化
        XX, YY = np.meshgrid(xx, yy)
        preds = model.predict_classes(np.c_[XX.ravel(), YY.ravel()])
        title = "正则化系数：{}".format(_lambda)
        file = "正则化_%g.svg" % _lambda
        make_plot(X_train, y_train, title, file, XX, YY, preds, output_dir=OUTPUT_DIR + '/regularizers')


def main():
    X, y, X_train, X_test, y_train, y_test = load_dataset()
    # 绘制数据集分布
    make_plot(X, y, None, "月牙形状二分类数据集分布.svg")
    # 网络层数的影响
    network_layers_influence(X_train, y_train)
    # Dropout的影响
    dropout_influence(X_train, y_train)
    # 正则化的影响
    regularizers_influence(X_train, y_train)


if __name__ == '__main__':
    main()

图太多就不展示了，可以自己试试

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