deep-learning-from-scratch/ch06 at master · oreilly-japan/deep-learning-from-scratch · GitHub
「ゼロから作るDeep Learning ① (Pythonで学ぶディープラーニングの理論と実装)」 p.193～195 の写経です。
過学習の主な原因
- パラメータを大量に持ち、表現力の高いモデルであること
- 訓練データが少ないこと
上記が原因で、重みパラメータが大きくなり、 結果として、過学習となることが多いらしい。
Weight decay (荷重減衰)とは
重みの2乗ノルム(L2ノルム)を損失関数に加算し、 重みが大きくなることを抑えること
ただし
Weight decay の python 実装
# coding: utf-8 import os import sys sys.path.append(os.pardir) # 親ディレクトリのファイルをインポートするための設定 import numpy as np import matplotlib.pyplot as plt import urllib.request import gzip from collections import OrderedDict def main(): max_epochs = 201 mymnist = MyMnist() train_test_data = mymnist.load_mnist() markers = {'train': 'o', 'test': 's'} # weight decayは荷重減衰で、0はweight decayを使用しない場合 for i, weight_decay_lambda in enumerate([0, 0.1]): (train_acc_list,test_acc_list) = \ my_train(train_test_data, weight_decay_lambda, max_epochs ) plt.subplot(1,2,i+1) x = np.arange(max_epochs) plt.plot(x, train_acc_list,marker='o',label='train',markevery=10) plt.plot(x, test_acc_list, marker='s',label='test', markevery=10) plt.xlabel("epochs") plt.ylabel("accuracy") plt.ylim(0, 1.0) plt.legend(loc='lower right') plt.show() def my_train(train_test_data, weight_decay_lambda, # 荷重減衰の設定 max_epochs): (x_train, t_train, x_test, t_test) = train_test_data # 過学習を再現するために、学習データを削減 x_train = x_train[:300] t_train = t_train[:300] network = MultiLayerNet(input_size=784, hidden_size_list=[100,100,100,100,100,100], output_size=10, weight_decay_lambda=weight_decay_lambda) optimizer = SGD(lr=0.01) train_size = x_train.shape[0] batch_size = 100 train_acc_list = [] test_acc_list = [] iter_per_epoch = max(train_size / batch_size, 1) epoch_cnt = 0 for i in range(1000000000): batch_mask = np.random.choice(train_size, batch_size) x_batch = x_train[batch_mask] t_batch = t_train[batch_mask] grads = network.gradient(x_batch, t_batch) optimizer.update(network.params, grads) if i % iter_per_epoch == 0: train_acc = network.accuracy(x_train, t_train) test_acc = network.accuracy(x_test, t_test) train_acc_list.append(train_acc) test_acc_list.append(test_acc) print("epoch:" , str(epoch_cnt) , "train acc:",str(train_acc) , "test acc:", str(test_acc)) epoch_cnt += 1 if epoch_cnt >= max_epochs: break return (train_acc_list, test_acc_list) class MyMnist: def __init__(self): pass def load_mnist(self): data_files = self.download_mnist() # convert numpy dataset = {} dataset['train_img'] = self.load_img( data_files['train_img'] ) dataset['train_label'] = self.load_label(data_files['train_label']) dataset['test_img'] = self.load_img( data_files['test_img'] ) dataset['test_label'] = self.load_label(data_files['test_label']) for key in ('train_img', 'test_img'): dataset[key] = dataset[key].astype(np.float32) dataset[key] /= 255.0 for key in ('train_label','test_label'): dataset[key]=self.change_one_hot_label( dataset[key] ) return (dataset['train_img'], dataset['train_label'], dataset['test_img'], dataset['test_label'] ) def change_one_hot_label(self,X): T = np.zeros((X.size, 10)) for idx, row in enumerate(T): row[X[idx]] = 1 return T def download_mnist(self): url_base = 'http://yann.lecun.com/exdb/mnist/' key_file = {'train_img' :'train-images-idx3-ubyte.gz', 'train_label':'train-labels-idx1-ubyte.gz', 'test_img' :'t10k-images-idx3-ubyte.gz', 'test_label' :'t10k-labels-idx1-ubyte.gz' } data_files = {} dataset_dir = os.path.dirname(os.path.abspath(__file__)) for data_name, file_name in key_file.items(): req_url = url_base+file_name file_path = dataset_dir + "/" + file_name request = urllib.request.Request( req_url ) response = urllib.request.urlopen(request).read() with open(file_path, mode='wb') as f: f.write(response) data_files[data_name] = file_path return data_files def load_img( self,file_path): img_size = 784 # = 28*28 with gzip.open(file_path, 'rb') as f: data = np.frombuffer(f.read(), np.uint8, offset=16) data = data.reshape(-1, img_size) return data def load_label(self,file_path): with gzip.open(file_path, 'rb') as f: labels = np.frombuffer(f.read(), np.uint8, offset=8) return labels # 全結合による多層ニューラルネットワーク class MultiLayerNet: def __init__(self, input_size, # 入力size (MNISTの場合は784) hidden_size_list, # 隠れ層のneuron数list 例[100,100,100] output_size, # shuturyoku 出力size (MNISTの場合は10) activation='relu', # 活性化関数 relu or sigmoid weight_init_std='relu',# ※ weight_decay_lambda=0):# Weight Decay (L2ノルム)の強さ # weight_init_std : 重みの標準偏差 ( 例 0.01 ) # 'relu'または'he'を指定した場合は「Heの初期値」 # 'sigmoid'または'xavier'を指定した場合は「Xavierの初期値」 self.input_size = input_size self.output_size = output_size self.hidden_size_list = hidden_size_list self.hidden_layer_num = len(hidden_size_list) self.weight_decay_lambda = weight_decay_lambda self.params = {} self.__init_weight(weight_init_std) # 重み初期化 # レイヤの生成 activation_layer = {'sigmoid': Sigmoid, 'relu': Relu} self.layers = OrderedDict() for idx in range(1, self.hidden_layer_num+1): self.layers['Affine' + str(idx)] = Affine(self.params['W' + str(idx)], self.params['b' + str(idx)]) self.layers['Activation_function' + str(idx)] = \ activation_layer[activation]() idx = self.hidden_layer_num + 1 self.layers['Affine' + str(idx)] = Affine(self.params['W' + str(idx)], self.params['b' + str(idx)]) self.last_layer = SoftmaxWithLoss() # 重みの初期値設定 # weight_init_std : 重みの標準偏差を指定（e.g. 0.01） # 'relu'または'he'を指定した場合は「Heの初期値」を設定 # 'sigmoid'または'xavier'を指定した場合は「Xavierの初期値」を設定 def __init_weight(self, weight_init_std): all_size_list = \ [self.input_size] + self.hidden_size_list + [self.output_size] for idx in range(1, len(all_size_list)): scale = weight_init_std # ReLUを使う場合 if str(weight_init_std).lower() in ('relu', 'he'): scale = np.sqrt(2.0 / all_size_list[idx - 1]) # sigmoidを使う場合 elif str(weight_init_std).lower() in ('sigmoid', 'xavier'): scale = np.sqrt(1.0 / all_size_list[idx - 1]) self.params['W' + str(idx)] = \ scale * np.random.randn(all_size_list[idx-1], all_size_list[idx]) self.params['b' + str(idx)] = np.zeros(all_size_list[idx]) def predict(self, x): for layer in self.layers.values(): x = layer.forward(x) return x # 損失関数。x:入力データ、t:教師ラベル def loss(self, x, t): y = self.predict(x) weight_decay = 0 for idx in range(1, self.hidden_layer_num + 2): W = self.params['W' + str(idx)] weight_decay += 0.5 * self.weight_decay_lambda * np.sum(W ** 2) return self.last_layer.forward(y, t) + weight_decay def accuracy(self, x, t): y = self.predict(x) y = np.argmax(y, axis=1) if t.ndim != 1 : t = np.argmax(t, axis=1) accuracy = np.sum(y == t) / float(x.shape[0]) return accuracy # 勾配(数値微分)。x:入力データ、t:教師ラベル def numerical_gradient(self, x, t): loss_W = lambda W: self.loss(x, t) grads = {} for idx in range(1, self.hidden_layer_num+2): grads['W' + str(idx)] = \ numerical_gradient(loss_W, self.params['W' + str(idx)]) grads['b' + str(idx)] = \ numerical_gradient(loss_W, self.params['b' + str(idx)]) return grads # 勾配(誤差逆伝搬法)。x:入力データ、t:教師ラベル def gradient(self, x, t): # forward self.loss(x, t) # backward dout = 1 dout = self.last_layer.backward(dout) layers = list(self.layers.values()) layers.reverse() for layer in layers: dout = layer.backward(dout) # 設定 grads = {} for idx in range(1, self.hidden_layer_num+2): grads['W' + str(idx)] = \ self.layers['Affine' + str(idx)].dW + \ self.weight_decay_lambda * self.layers['Affine' + str(idx)].W grads['b' + str(idx)] = self.layers['Affine' + str(idx)].db return grads class Affine: def __init__(self, W, b): self.W =W self.b = b self.x = None self.original_x_shape = None # 重み・バイアスパラメータの微分 self.dW = None self.db = None def forward(self, x): # テンソル対応 self.original_x_shape = x.shape x = x.reshape(x.shape[0], -1) self.x = x out = np.dot(self.x, self.W) + self.b return out def backward(self, dout): dx = np.dot(dout, self.W.T) self.dW = np.dot(self.x.T, dout) self.db = np.sum(dout, axis=0) dx = dx.reshape(*self.original_x_shape) return dx class Relu: def __init__(self): self.mask = None def forward(self, x): self.mask = (x <= 0) out = x.copy() out[self.mask] = 0 return out def backward(self, dout): dout[self.mask] = 0 dx = dout return dx class Sigmoid: def __init__(self): self.out = None def forward(self, x): out = sigmoid(x) self.out = out return out def backward(self, dout): dx = dout * (1.0 - self.out) * self.out return dx class SoftmaxWithLoss: def __init__(self): self.loss = None self.y = None # softmaxの出力 self.t = None # 教師データ def forward(self, x, t): self.t = t self.y = self.softmax(x) self.loss = self.cross_entropy_error(self.y, self.t) return self.loss def backward(self, dout=1): batch_size = self.t.shape[0] if self.t.size == self.y.size: # 教師データがone-hot-vectorの場合 dx = (self.y - self.t) / batch_size else: dx = self.y.copy() dx[np.arange(batch_size), self.t] -= 1 dx = dx / batch_size return dx def softmax(self,x): x = x - np.max(x, axis=-1, keepdims=True) # オーバーフロー対策 return np.exp(x) / np.sum(np.exp(x), axis=-1, keepdims=True) def cross_entropy_error(self, y, t): if y.ndim == 1: t = t.reshape(1, t.size) y = y.reshape(1, y.size) # 教師データがone-hot-vectorの場合、正解ラベルのインデックスに変換 if t.size == y.size: t = t.argmax(axis=1) batch_size = y.shape[0] return -np.sum(np.log(y[np.arange(batch_size), t] + 1e-7)) / batch_size # 確率的勾配降下法（Stochastic Gradient Descent） class SGD: def __init__(self, lr=0.01): self.lr = lr def update(self, params, grads): for key in params.keys(): params[key] -= self.lr * grads[key] if __name__ == '__main__': main()
上記を実行すると、以下のように表示されます。
右側がWeight decayありで、 教師dataとテストdataでの精度の差が少ないようです。 また、教師dataが100%に至ってないことから、 過学習が防げているらしい。
