In [2]:

    

import numpy as np


    

In [3]:

    

import matplotlib.pyplot as plt
%matplotlib inline


    

In [4]:

    

n_samples = 10000


    

In [5]:

    

x = np.zeros(n_samples)


    

In [6]:

    

x[1] = 1
alpha = -0.001

a_0 = 2*np.exp(alpha) * np.cos(2*np.pi*0.005)
a_1 = - np.exp(2*alpha)


    

In [7]:

    

for i in range(2,n_samples):
    x[i]= a_0 * x[i-1] + a_1 * x[i-2] + np.random.randn()


    

In [8]:

    

plt.plot(x)


    

    
Out[8]:





[<matplotlib.lines.Line2D at 0x7f224ae4f470>]






    

In [9]:

    

X = np.array([[x[i-1],x[i-2]] for i in range(2,1000)])
Y = np.array([x[i] for i in range(2,1000)])


    

In [10]:

    

a_true = np.array([a_0, a_1]).reshape(-1,1)


    

In [11]:

    

a_true


    

    
Out[11]:





array([[ 1.99701511],
       [-0.998002  ]])

In [12]:

    

import tensorflow as tf


    

In [13]:

    

X_tf = tf.placeholder(dtype=tf.float32, shape=[None,2], name="X_tf")
Y_tf = tf.placeholder(dtype=tf.float32, shape=[None,1], name="Y_tf")


    

In [14]:

    

epsilon_tf = tf.Variable(tf.random_normal([2,1], stddev=1.0, dtype=tf.float32), name="epsilon_tf")
a_tf = tf.Variable(tf.random_normal([2,1], stddev=1.0, dtype=tf.float32))
# a_tf = tf.Variable(initial_value=coeffs_true)


    

In [15]:

    

#for i in range(2:1000)
#    Y_tf[i] = tf.matmul(a_tf, X_tf) +


    

In [36]:

    

loss = tf.reduce_mean(
    tf.square(
        tf.subtract(
            tf.matmul(X_tf,a_tf), Y_tf
        )
    )
)


    

In [37]:

    

train_op = tf.train.AdamOptimizer(learning_rate=0.01, epsilon=1E-12).minimize(loss)


    

In [38]:

    

# train_op = tf.train.MomentumOptimizer(learning_rate=0.01,momentum=0).minimize(loss)


    

In [39]:

    

# train_op = tf.train.ProximalAdagradOptimizer(learning_rate=0.5).minimize(loss)


    

In [40]:

    

sess = tf.InteractiveSession()
sess.run(tf.global_variables_initializer())


    

In [41]:

    

loss_list = []


    

In [42]:

    

sess.run(a_tf, feed_dict={X_tf:X, Y_tf:Y.reshape(-1,1)})


    

    
Out[42]:





array([[-0.36336908],
       [-0.63079107]], dtype=float32)

In [43]:

    

for i in range(100000):
    sess.run(train_op, feed_dict={X_tf:X, Y_tf:Y.reshape(-1,1)})
    loss_val = sess.run(loss, feed_dict={X_tf:X, Y_tf:Y.reshape(-1,1)})
    loss_list.append(loss_val)


    

In [44]:

    

plt.plot(np.log10(loss_list))


    

    
Out[44]:





[<matplotlib.lines.Line2D at 0x7f223c1fda58>]






    

In [47]:

    

sess.run(a_tf, feed_dict={X_tf:X, Y_tf:Y.reshape(-1,1)})


    

    
Out[47]:





array([[ 1.98685229],
       [-0.9880107 ]], dtype=float32)

In [48]:

    

a_true


    

    
Out[48]:





array([[ 1.99701511],
       [-0.998002  ]])

In [ ]: