tensorflow实现线性模型和sklearn的线性模型比较

自己用tensorflow实现了linear模型，但是和sklearn提供的模型效果相比，实验结果差了很多，所以尝试了修改优化算法，正则化，损失函数和归一化，记录尝试的所有过程和自己的实验心得。

import numpy as np
import tensorflow as tf
import sklearn
import pandas as pd
class Model:
    def __init__(self, sess, feature_size, step, learning_rate, regulation):
        self.sess = sess
        self.feature_size = feature_size
        self.step = step
        self.learning_rate = learning_rate
        self.regulation = regulation

        self.build_model()
        self.add_loss()
        self.add_optimizer()

        self.sess.run(tf.global_variables_initializer())
        self.sess.run(tf.local_variables_initializer())

    def build_model(self):
        self.x = tf.placeholder(shape=[None, self.feature_size], dtype=tf.float32)
        self.y_true = tf.placeholder(shape=[None, 1], dtype=tf.float32)

        with tf.name_scope('linear_model'):
            l2_reg = tf.contrib.layers.l2_regularizer(0.1)
            self.w = tf.get_variable(name='w', shape=[self.feature_size, 1],
                                     initializer=tf.truncated_normal_initializer(), regularizer=l2_reg)
            self.b = tf.get_variable(name='b', shape=[1],
                                     initializer=tf.truncated_normal_initializer(stddev=1, seed=1))
            self.y_pred = tf.matmul(self.x, self.w) + self.b

    def add_loss(self, loss='l2'):
        reg_variables = tf.get_collection(tf.GraphKeys.REGULARIZATION_LOSSES)
        if loss == 'l2':
            self.loss = tf.reduce_mean(tf.square(self.y_true - self.y_pred))
        if loss == 'l1':
            self.loss = tf.reduce_mean(tf.abs(self.y_true - self.y_pred))
        if loss == 'huber':
            delta = tf.constant(0.25)  # delta越大两边线性部分越陡峭，损失越大
            self.loss = tf.multiply(tf.square(delta), tf.sqrt(1. + tf.square((self.y_true - self.y_pred) / delta)) - 1.)
        self.loss += tf.add_n(reg_variables)

    def add_optimizer(self):
        self.optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate)
        self.train_step = self.optimizer.minimize(self.loss)

    def predict(self, x_test):
        self.pred_test = tf.matmul(tf.cast(x_test, tf.float32), self.w) + self.b

        pred_test = self.sess.run([self.pred_test])

        return pred_test

    def train(self, train_data, train_label):
        loss, y_pred = self.sess.run([self.loss, self.y_pred], feed_dict={self.x: train_data, self.y_true: train_label})
        return loss, y_pred
if __name__ == '__main__':
    feature_size, step, learning_rate, regulation = 100, 1000, 0.0001, 'L2'
    sample_size = 30
    x = [list(np.random.rand(feature_size)) for _ in range(sample_size)]
    y = [np.random.rand(1) for _ in range(sample_size)]

    x = pd.DataFrame(x).apply(lambda x: (x - np.mean(x)) / (np.max(x) - np.min(x))).values

    with tf.Session() as sess:
        model = Model(sess, feature_size, step, learning_rate, regulation)
        _, _ = model.train(x, y)
        # print('loss is ', loss)

        pred_test = model.predict(x)
        # print('pred label\tture label')
        # for each in zip(pred, y):
        #     print(round(each[0][0], 6), '\t', round(each[1][0], 6))
        loss = sum([(each[0][0] - each[1][0]) ** 2 for each in zip(pred_test, y)])
        print('LR net loss ', loss)

    from sklearn import linear_model

    reg = linear_model.LinearRegression()
    reg.fit(x, y)
    pred_test1 = reg.predict(x)
    loss = sum([(each[0][0] - each[1][0]) ** 2 for each in zip(pred_test1, y)])
    print('sklearn loss ', loss)

    import matplotlib.pyplot as plt

    fig = plt.figure()
    x = [i for i in range(len(x))]

    plt.plot(x, y, 'k*-', markersize=12)
    plt.plot(x, [each[0] for each in pred_test[0]], 'r.-', markersize=12)
    plt.plot(x, [each[0] for each in pred_test1], 'b.-', markersize=12)
    plt.legend(('true', 'my', 'Linear Fit'), loc='lower right')
    plt.title('regression compare')
    plt.show()

以下是实验记录：
权重的初始化很重要，初始化成为为0，结果全为0，初始化阶段的正太分布，结果全为负数

1. GradientDescentOptimizer
   LR net loss [74.816734]
   sklearn loss 4.22780141391886e-30

2. MomentumOptimizer
   LR net loss [1.5802944]
   sklearn loss 2.1308488904700377e-30

如果数据是稀疏的，用以下四种算法，同时保证可以更快的退出鞍点，用Adam算法，加入动量。
https://segmentfault.com/a/1190000012668819

1. AdagradOptimizer 对稀疏数据很友好
   LR net loss [19.184008]
   sklearn loss 1.1571757477856268e-29

2. RMSPropOptimizer
   LR net loss [1.3790985]
   sklearn loss 5.1738182026018704e-30

3. AdadeltaOptimizer 结果会非常不稳定
   LR net loss [16.51035]
   sklearn loss 7.90786835165399e-30

4. AdamOptimizer
   LR net loss [0.98462635]
   sklearn loss 5.571330143123396e-30

5. AdamOptimizer + 加入L2正则化项
   LR net loss [0.0768552]
   sklearn loss 4.7639803104362666e-30

6. AdamOptimizer + 加入L1正则化项
   LR net loss [5.0768552]
   sklearn loss 4.7639803104362666e-30

7. AdamOptimizer + 加入L2正则化项 + huber 损失（之前默认L2损失）
   LR net loss [0.58679754]
   sklearn loss 3.3163743270370446e-29

8. AdamOptimizer + 加入L2正则化项 + L2 损失 + 归一化
   LR net loss [0.989549]
   sklearn loss 1.8846380063795735e-29

9. AdamOptimizer + 加入L2正则化项 + L2 损失 + 归一化 + 修改infer的方式
   LR net loss [1.4737219]
   sklearn loss 8.079969451484434e-29