線性迴歸，Tensorflow，非線性方程，tf.contrib.learn

Question

作爲一個練習，我嘗試使用tf.contrib.learn.LinearRegressor來爲方程建模y = 3 * x1^2 + 4 * x2^2。代碼運行，但我對結果的準確性有點失望。這個結果對於線性方程如y = 3 * x1 + 4 * x2是很好的。我認爲tf.contrib.learn可以很好地處理平方條款。是否有可用於獲得更好結果的設置，如不同的優化器？

from __future__ import absolute_import 
    from __future__ import division 
    from __future__ import print_function 

    import argparse 
    import sys 
    import tempfile 

    from six.moves import urllib 

    import pandas as pd 
    import tensorflow as tf 
    import numpy as np 
    import matplotlib.pyplot as plt 
    import math 

    FLAGS = None 

    myImportedDatax1_np = np.empty((100, 1)) 
    myImportedDatax2_np = np.empty((100, 1)) 
    myImportedDatay_np = np.empty((100, 1)) 

    def trueOutput(x1, x2): 
     return [3 * math.pow(x1, 2) + 4 * math.pow(x2, 2)] 

    count = 0 
# Create data, using true equation, in range x1= 0 to 9, and x2=0 to 9 
    for a in range(0, 10): 
     for b in range(0, 10): 
     myImportedDatax1_np[count] = a 
     myImportedDatax2_np[count] = b 
     myImportedDatay_np[count] = trueOutput(myImportedDatax1_np[count], myImportedDatax2_np[count]) 
     print(myImportedDatay_np[count]) 
     count = count + 1 

    combined_Imported_Data_x = np.append(myImportedDatax1_np, myImportedDatax2_np, axis=1) 

    def build_estimator(model_dir, model_type): 
     x1 = tf.contrib.layers.real_valued_column("x1") 
     x2 = tf.contrib.layers.real_valued_column("x2") 

     wide_columns = [x1, x2] 
     m = tf.contrib.learn.LinearRegressor(model_dir=model_dir, feature_columns=wide_columns) 
     return m 

    def input_fn(input_batch, output_batch): 
     inputs = {"x1": tf.constant(input_batch[:,0]), "x2": tf.constant(input_batch[:,1])} 
     output = tf.constant(output_batch) 
     return inputs, output 

    def input_fn_predict(x1, x2): 
     inputs = {"x1": tf.constant([[x1]]), "x2": tf.constant([[x2]])} 
     return inputs 

    def train_and_eval(model_dir, model_type, train_steps, train_data, test_data): 
     model_dir = tempfile.mkdtemp() if not model_dir else model_dir 
     print("model directory = %s" % model_dir) 
     m = build_estimator(model_dir, model_type) 
     m.fit(input_fn=lambda: input_fn(combined_Imported_Data_x, myImportedDatay_np), steps=train_steps) 

     my_x1 = 2 
     my_x2 = 6 
     prediction = list(m.predict(input_fn=lambda: input_fn_predict(my_x1, my_x2))) 
     print("Prediction value is: ") 
     print(prediction) 
     print("Actual value is: ") 
     true_y = trueOutput(my_x1, my_x2) 
     print(true_y) 

    def main(_): 
     train_and_eval(FLAGS.model_dir, FLAGS.model_type, FLAGS.train_steps, 
        FLAGS.train_data, FLAGS.test_data) 

    if __name__ == "__main__": 
     parser = argparse.ArgumentParser() 
     parser.register("type", "bool", lambda v: v.lower() == "true") 
     parser.add_argument(
      "--model_dir", 
      type=str, 
      default="", 
      help="Base directory for output models." 
    ) 
     parser.add_argument(
      "--model_type", 
      type=str, 
      default="wide_n_deep", 
      help="Valid model types: {'wide', 'deep', 'wide_n_deep'}." 
    ) 
     parser.add_argument(
      "--train_steps", 
      type=int, 
      default=10000, 
      help="Number of training steps." 
    ) 
     parser.add_argument(
      "--train_data", 
      type=str, 
      default="", 
      help="Path to the training data." 
    ) 
     parser.add_argument(
      "--test_data", 
      type=str, 
      default="", 
      help="Path to the test data." 
    ) 
     FLAGS, unparsed = parser.parse_known_args() 
     tf.app.run(main=main, argv=[sys.argv[0]] + unparsed) 

Answer 1

tf.contrib.learn.LinearRegressor用於模擬線性迴歸。方程y = 3 * x1^2 + 4 * x2^2不是x1和x2中的線性迴歸，因此tf.contrib.learn.LinearRegressor將無法​​建模。您可以創建新功能x1^2和x2^2，然後使用tf.contrib.learn.LinearRegressor來訓練模型。此外，看到這裏的討論關於利用神經網絡預測平方函數： neural-network-to-predict-nth-square