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NonlinearVAR.py
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NonlinearVAR.py
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from nlTools import *
import numpy as np
import pdb
from projection_simplex import projection_simplex_sort as proj_simplex
import torch
import pickle
class NonlinearVAR:
def __init__(self, N, M, P, filename_tosave = 'model.nlv'):
self.A = np.zeros([N, N, P])
self.nnl = [NodalNonlinearity(M) for m in range(M)]
self.filename_tosave = filename_tosave
@staticmethod
def from_pickle(filename):
infile = open(filename,'rb')
new_obj = pickle.load(infile)
assert type(new_obj) is NonlinearVAR
infile.close()
return new_obj
def to_pickle(self, filename=None):
if filename is None:
filename = self.filename_tosave
outfile = open(filename,'wb')
pickle.dump(self, outfile)
outfile.close()
def forward(self, m_z_previous):
# m_z_previous: {z[t-p]}, p=1..P
N, P = m_z_previous.shape
assert(N == self.A.shape[0])
assert(P == self.A.shape[2])
m_y_tilde = np.zeros([N, P])
for n in range(N):
for p in range(P):
m_y_tilde[n, p] = self.nnl[n].g(m_z_previous[n,p]) #!LEq(6)
v_y_hat = np.zeros(N)
for p in range(P):
v_y_hat = v_y_hat + self.A[:,:, p] @ m_y_tilde[:,p] #!LEq(7)
v_z_hat = np.zeros(N)
for n in range(N):
v_z_hat[n]= self.nnl[n].f(v_y_hat[n]) #!LEq(8)
return v_z_hat, v_y_hat, m_y_tilde
def compute_cost(self, v_z_hat, v_z_t): #could be static
v_cost = (v_z_t - v_z_hat)**2
total_cost = sum(v_cost) #!LEq(9)
return total_cost
def backward(self, m_z_previous, v_z_t, v_z_hat, v_y_hat, m_y_tilde): #kevin changed funciton signature
N, P = m_z_previous.shape # from tuple_in to v_z_hat, v_y_hat, m_y_tilde
assert(N == self.A.shape[0])
assert(P == self.A.shape[2])
assert(N == v_z_t.shape[0])
#v_z_hat, v_y_hat, m_y_tilde = tuple_in
v_s = 2*(v_z_hat - v_z_t) #LEq(10b)
# Gradients with respect to nonlinearity parameters:
dc_dalpha = N*[[]]
dc_dk = N*[[]]
dc_dw = N*[[]]
dc_db = N*[[]]
for i in range(N):
df_dalpha_i, df_dk_i, df_dw_i, df_db_i = self.nnl[i].gradients_f(v_y_hat[i])
dc_dalpha[i] = v_s[i]* df_dalpha_i
dc_dk[i] = v_s[i]* df_dk_i
dc_dw[i] = v_s[i]* df_dw_i
dc_db[i] = v_s[i]* df_db_i
for p in range(P):
dg_dalpha, dg_dk, dg_dw, dg_db = self.nnl[i].gradients_g(m_z_previous[i, p])
for n in range(N):
my_f_prime_n = self.nnl[n].f_prime(v_y_hat[n])
dc_dalpha[i] = dc_dalpha[i] + v_s[n]*my_f_prime_n*self.A[n, i, p]*dg_dalpha
dc_dk[i] = dc_dk[i] + v_s[n]*my_f_prime_n*self.A[n, i, p]*dg_dk
dc_dw[i] = dc_dw[i] + v_s[n]*my_f_prime_n*self.A[n, i, p]*dg_dw
dc_db[i] = dc_db[i] + v_s[n]*my_f_prime_n*self.A[n, i, p]*dg_db #!LEq(16)
# Gradient with respect to A matrices (3-way tensor form):
dc_dA = np.zeros(self.A.shape)
for i in range(N):
my_f_prime_i = self.nnl[i].f_prime(v_y_hat[i])
for p in range(P):
dc_dA[i,:,p] = v_s[i]*my_f_prime_i*m_y_tilde[:,p] #!LEq(25)
return dc_dalpha, dc_dk, dc_dw, dc_db, dc_dA
@staticmethod
def learn(m_z_train, P, M, nEpochs, zl_desired, zu_desired, eta, \
m_z_test, optimizer_handle = torch.optim.Adam, filename_prefix=''):
return learn_nonlinearVAR(m_z_train, P, M, nEpochs, \
zl_desired, zu_desired, eta, m_z_test, optimizer_handle, filename_prefix=filename_prefix)
# will not be used directly
def learn_nonlinearVAR(m_z_train, P, M, nEpochs, \
zl_desired, zu_desired, eta, m_z_test, optimizer_handle = torch.optim.Adam, filename_prefix=''):
#b_torch_optim = 1
N, T = m_z_train.shape
Nt, Tt = m_z_test.shape; assert(Nt == N)
A_initial = np.zeros([N, N, P])
nnl_initial = [nnl_randomInit(M, zl_desired[n], zu_desired[n])\
for n in range(N)] # TODO: different initializations
nlv = NonlinearVAR(N, M, P, filename_prefix)
nlv.A = A_initial
nlv.nnl = nnl_initial
cost_train = np.zeros(nEpochs)
cost_test = np.zeros(nEpochs)
# conforming Pytorch tensors
ttg = lambda array: torch.tensor(array, requires_grad = True)
t_A = ttg(nlv.A)
t_alpha = [ttg(nlv.nnl[i].alpha) for i in range(N)]
t_k = [ttg(nlv.nnl[i].k) for i in range(N)]
t_w = [ttg(nlv.nnl[i].w) for i in range(N)]
t_b = [ttg(nlv.nnl[i].b) for i in range(N)]
my_parameters = [t_A] + t_alpha + t_k + t_w + t_b
optimizer = optimizer_handle(my_parameters, lr=eta) #TODO: try rmsprop
for epoch in range(nEpochs):
print('Epoch ', epoch)
cost_test[epoch], cost_train[epoch] = \
run_an_epoch(nlv, m_z_train, m_z_test, optimizer, \
t_A, t_alpha, t_k, t_w, t_b, zl_desired, zu_desired)
nlv.to_pickle(nlv.filename_tosave+str(epoch)+'.nlv')
return nlv, cost_train, cost_test
def run_an_epoch(nlv, m_z_train, m_z_test, optimizer, \
t_A, t_alpha, t_k, t_w, t_b, zl_desired, zu_desired):
N, T = m_z_train.shape
Nt, Tt = m_z_test.shape; assert(Nt == N)
P = nlv.A.shape[2]
cost_thisEpoch_t = np.zeros(T)
#TEST (forward only)
if m_z_test is not None:
for tt in range(P, Tt): #TODO: reduce code repetition
v_z_tt = m_z_test[:, tt]
m_z_previous_t = np.zeros([N, P])
for p in range(P):
m_z_previous_t[:,p] = m_z_test[:,tt-1-p]
v_z_hat_t = nlv.forward(m_z_previous_t)[0]
cost_thisEpoch_t[tt] = nlv.compute_cost(v_z_hat_t, v_z_tt)/N
cost_test_out = np.mean(cost_thisEpoch_t)
#TRAIN (forward, backward, and SGD)
cost_thisEpoch = np.zeros(T)
for t in range(P, T):
v_z_t = m_z_train[:, t]
m_z_previous = np.zeros([N, P])
for p in range(P):
m_z_previous[:,p] = m_z_train[:,t-1-p]
#
v_z_hat, v_y_hat, m_y_tilde = nlv.forward(m_z_previous)
tuple_bInfo = (v_z_hat, v_y_hat, m_y_tilde)
cost_thisEpoch[t] = nlv.compute_cost(v_z_hat, v_z_t)/N
dc_dalpha, dc_dk, dc_dw, dc_db, dc_dA = \
nlv.backward(m_z_previous, v_z_t, tuple_bInfo)
assert (not(np.isnan(dc_dalpha).any()))
# Gradient step
#if b_torch_optim:
t_A.grad = torch.tensor(dc_dA)
for i in range(N):
t_alpha[i].grad = torch.tensor(dc_dalpha[i])
t_k[i].grad = torch.tensor(dc_dk[i])
t_w[i].grad = torch.tensor(dc_dw[i])
t_b[i].grad = torch.tensor(dc_db[i])
optimizer.step()
nlv.A = t_A.detach().numpy()
for i in range(N):
nlv.nnl[i].alpha = t_alpha[i].detach().numpy()
nlv.nnl[i].k = t_k[i].detach().numpy()
nlv.nnl[i].w = t_w[i].detach().numpy()
nlv.nnl[i].b = t_b[i].detach().numpy()
#Projection
for i in range(N):
nlv.nnl[i].b = zl_desired[i]
nlv.nnl[i].alpha = proj_simplex(nlv.nnl[i].alpha, \
zu_desired[i]-zl_desired[i])
if (abs(nlv.nnl[i].zu() - zu_desired[i])>1e-5).any() \
or(abs(nlv.nnl[i].zl() - zl_desired[i])>1e-5).any():
print('projection failed!'); pdb.set_trace()
nlv.nnl[i].w = np.maximum(0.01, nlv.nnl[i].w)
cost_train_out = np.mean(cost_thisEpoch)
return cost_test_out, cost_train_out