How to feed previous time-stamp prediction as additional input to the next time-stamp? - time-series

Question

This question might have been asked, but I got confused.
I am trying to apply one of RNN types, e.g. LSTM for time-series forecasting. I have inputs, y (stock returns). For each timestamp, I'd like to get the predictions. Q1 - Am I correct choosing seq2seq approach?
I also want to use predictions from previous timestamp (initializing initial values with some constant) as additional (still using my existing inputs) input in the form of squared residuals, i.e. using
eps_{t-1} = (y_{t-1} - y^_{t-1})^2 as additional input at t (as well as previous inputs).
So, how can I do this in tensorflow or in pytorch?
I tried to depict what I want on the attached graph. The graph
p.s. Sorry, it the question is poorly formulated

Answer 1

Let say your input if of dimension (32,10,1) with batch_size 32, time steps of length 10 and dimension of 1. Same for your target (stock return). This code make use of the tf.scan function, which is usefull when implementing custom recurrent networks (it will iterate over the timesteps). It remains to use the residual of t-1 in t somewhere, as you would like to.
ps: it is a very basic implementation of lstm from scratch, without any bias or output activation.
import tensorflow as tf
import numpy as np
tf.reset_default_graph()
BS = 32
TS = 10
inputs_dim = 1
target_dim = 1
inputs = tf.placeholder(shape=[BS, TS, inputs_dim], dtype=tf.float32)
stock_returns = tf.placeholder(shape=[BS, TS, target_dim], dtype=tf.float32)
state_size = 16
# initial hidden state
init_state = tf.placeholder(shape=[2, BS, state_size],
dtype=tf.float32, name='initial_state')
# initializer
xav_init = tf.contrib.layers.xavier_initializer
# params
W = tf.get_variable('W', shape=[4, state_size, state_size],
initializer=xav_init())
U = tf.get_variable('U', shape=[4, inputs_dim, state_size],
initializer=xav_init())
W_out = tf.get_variable('W_out', shape=[state_size, target_dim],
initializer=xav_init())
#the function to feed tf.scan with
def step(prev, inputs_):
#unpack all inputs and previous outputs
st_1, ct_1 = prev[0][0], prev[0][1]
x = inputs_[0]
target = inputs_[1]
#get previous squared residual
eps = prev[1]
"""
here do whatever you want with eps_t-1
like x += eps if x if of the same dimension
or include it somewhere in your graph
"""
# lstm gates (add bias if needed)
#
# input gate
i = tf.sigmoid(tf.matmul(x,U[0]) + tf.matmul(st_1,W[0]))
# forget gate
f = tf.sigmoid(tf.matmul(x,U[1]) + tf.matmul(st_1,W[1]))
# output gate
o = tf.sigmoid(tf.matmul(x,U[2]) + tf.matmul(st_1,W[2]))
# gate weights
g = tf.tanh(tf.matmul(x,U[3]) + tf.matmul(st_1,W[3]))
ct = ct_1*f + g*i
st = tf.tanh(ct)*o
"""
make prediction, compute residual in t
and pass it to t+1
Normaly, we would compute prediction outside the scan function,
but as we need it here, we could just keep it and return it back
as an output of the scan function
"""
prediction_t = tf.matmul(st, W_out) # + bias
eps = (target - prediction_t)**2
return [tf.stack((st, ct), axis=0), eps, prediction_t]
states, eps, preds = tf.scan(step, [tf.transpose(inputs, [1,0,2]),
tf.transpose(stock_returns, [1,0,2])], initializer=[init_state,
tf.zeros((32,1), dtype=tf.float32),
tf.zeros((32,1),dtype=tf.float32)])
with tf.Session() as sess:
sess.run(tf.global_variables_initializer())
out = sess.run(preds, feed_dict=
{inputs:np.random.rand(BS,TS,inputs_dim),
stock_returns:np.random.rand(BS,TS,target_dim),
init_state:np.zeros((2,BS,state_size))})
out = tf.transpose(out,[1,0,2])
print(out)
And the output :
Tensor("transpose_2:0", shape=(32, 10, 1), dtype=float32)
Base code from here