def gradient_descent_experiment(true_rdm=None, num_reads=100000):
#genome = get_ecoli_genome(at_lab=False)
G = len(genome)
w = 10
mfl = 250
lamb = 1.0/mfl
simulating_data = False
if true_rdm is None:
simulating_data = True
true_matrix = [[-2, 0, 0, 0] for i in range(w)]
true_mu = -20
true_eps = score_genome_np(true_matrix, genome)
true_ps = fd_solve_np(true_eps, true_mu)
true_reads = reads_from_ps(true_ps, mfl, min_seq_len=75, num_reads=num_reads)
true_rdm = density_from_reads(true_reads, G)
true_state = ((true_matrix, true_mu), true_eps)
true_ll = logf(true_state) if simulating_data else None
matrix = random_energy_matrix(w)
mu = -20
eps = score_genome_np(matrix, genome)
init_state = ((matrix, mu), eps)
logf = lambda state:timestamp(complete_log_likelihood(state, true_rdm, lamb, num_reads=num_reads))
dw = 0.1
dmu = 0.1
old_ll = 0
print "true_ll:", true_ll
cur_ll = logf(init_state)
eta = 10**-7 # learning rate
iterations = 0
while cur_ll > old_ll or iterations == 0:
old_ll = cur_ll
dmat = [[0]*4 for i in range(w)]
for i in range(w):
for j in range(4):
print "i, j:", i, j
new_mat = [row[:] for row in matrix]
new_mat[i][j] += dw
fwd_eps, rev_eps = eps
new_eps = update_scores_np(fwd_eps, rev_eps, i, j, dw, w, genome)
new_state = ((new_mat, mu), new_eps)
new_ll = logf(new_state)
print "cur ll, new_ll:", cur_ll, new_ll, "(improvement)" if new_ll > cur_ll else "(worsening)"
delta_w = (new_ll - cur_ll)/dw * eta
print "delta_w:", delta_w
dmat[i][j] = delta_w
new_mu = mu + dmu
new_state = ((matrix, new_mu), eps)
new_ll = logf(new_state)
print "mu:"
print "cur ll, new_ll:", cur_ll, new_ll, "(improvement)" if new_ll > cur_ll else "(worsening)"
delta_mu = (new_ll - cur_ll)/dmu * eta
print "delta_mu:", delta_mu
old_matrix = [row[:] for row in matrix]
for i in range(w):
for j in range(4):
matrix[i][j] += dmat[i][j]
old_eps = np.array(eps)
eps = score_genome_np(matrix, genome)
old_mu = mu
mu += delta_mu
cur_state = ((matrix, mu), eps)
cur_ll = logf(cur_state)
print "\nresults of iteration %s:" % iterations
pprint(matrix)
print mu
print "likelihood:", old_ll, "->", cur_ll
iterations += 1
return ((old_matrix, old_mu), old_eps)
MU_SIGMA = 0.1
def complete_rprop(((mat,mu),(fwd_eps,rev_eps)),genome):
"""Propose a new matrix and new mu, given mat,mu. Return updated
scores for convenience"""
pprint(mat)
print "mu:",mu
w = len(mat)
new_mat = [row[:] for row in mat] # make a copy of the matrix
new_mu = mu
if random.random() < 0.5: # flip a coin and update weight matrix or mu
altered_col = random.randrange(w) # pick a column to alter
altered_row = random.randrange(4) # pick a row to alter
dw = random.gauss(0,MAT_SIGMA) # add N(0,2) noise
new_mat[altered_col][altered_row] += dw
new_fwd_eps,new_rev_eps = update_scores_np(fwd_eps,rev_eps,altered_col,altered_row,dw,w,genome)
else:
new_mu += random.gauss(0,MU_SIGMA)
new_fwd_eps,new_rev_eps = fwd_eps,rev_eps # careful about returning copy...?
return ((new_mat,new_mu),(new_fwd_eps,new_rev_eps))
def log_dprop(((matp,mup),epsp),((mat,mu),eps)):
dmat = sum([xp - x for (rowp,row) in zip(matp,mat) for (xp,x) in zip(rowp,row)])
dmu = mup - mu
if dmat != 0:
return log(1/2.0 * dnorm(dmat,0,MAT_SIGMA))
else:
return log(1/2.0 * dnorm(dmu,0,MAT_SIGMA))
#return log(dnorm(dmat,0,MAT_SIGMA)) + log(dnorm(dmu,0,MU_SIGMA))
def capture_state((mat_and_mu,site_scores)):
