def E_step(self, anneal, model_params, my_data):
""" MCA E_step
my_data variables used:
my_data['y'] Datapoints
my_data['can'] Candidate H's according to selection func.
Annealing variables used:
anneal['T'] Temperature for det. annealing AND softmax
anneal['N_cut_factor'] 0.: no truncation; 1. trunc. according to model
"""
comm = self.comm
my_y = my_data['y']
my_cand = my_data['candidates']
my_N, D = my_data['y'].shape
H = self.H
state_mtx = self.state_matrix # shape: (no_states, Hprime)
state_abs = self.state_abs # shape: (no_states,)
no_states = len(state_abs)
W = model_params['W']
pies = model_params['pi']
sigma = model_params['sigma']
# Precompute
T = anneal['T']
T_rho = np.maximum(T, self.rho_temp_bound)
rho = 1. / (1. - 1. / T_rho)
beta = 1. / T
pre1 = -1. / 2. / sigma / sigma
pil_bar = np.log(pies / (1. - pies))
Wl = np.log(W)
Wrho = np.exp(rho * Wl)
# Allocate return structures
F = np.empty([my_N, 1 + H + no_states])
# Iterate over all datapoints
for n in xrange(my_N):
tracing.tracepoint("E_step:iterating")
y = my_y[n, :]
cand = my_cand[n, :]
# Zero active hidden causes
log_prod_joint = pre1 * (y**2).sum()
F[n, 0] = log_prod_joint
# Hidden states with one active cause
log_prod_joint = pil_bar + pre1 * ((W - y)**2).sum(axis=1)
F[n, 1:H + 1] = log_prod_joint
# Handle hidden states with more than 1 active cause
log_prior = pil_bar * state_abs # is (no_states,)
Wrho_ = Wrho[cand] # is (Hprime x D)
Wbar = np.exp(np.log(np.dot(state_mtx, Wrho_)) / rho)
log_prod_joint = log_prior + pre1 * ((Wbar - y)**2).sum(axis=1)
F[n, 1 + H:] = log_prod_joint
assert np.isfinite(F).all()
return {'logpj': F}
def M_step(self, anneal, model_params, my_suff_stat, my_data):
""" MCA M_step
my_data variables used:
my_data['y'] Datapoints
my_data['candidates'] Candidate H's according to selection func.
Annealing variables used:
anneal['T'] Temperature for det. annealing AND softmax
anneal['N_cut_factor'] 0.: no truncation; 1. trunc. according to model
"""
comm = self.comm
H, Hprime = self.H, self.Hprime
gamma = self.gamma
W = model_params['W']
pies = model_params['pi']
sigma = model_params['sigma']
# Read in data:
my_y = my_data['y']
my_cand = my_data['candidates']
my_logpj = my_suff_stat['logpj']
my_N, D = my_y.shape
N = comm.allreduce(my_N)
state_mtx = self.state_matrix # shape: (no_states, Hprime)
state_abs = self.state_abs # shape: (no_states,)
no_states = len(state_abs)
# To compute et_loglike:
my_ldenom_sum = 0.0
ldenom_sum = 0.0
# Precompute
T = anneal['T']
T_rho = np.maximum(T, self.rho_temp_bound)
rho = 1. / (1. - 1. / T_rho)
beta = 1. / T
pre0 = (1. - rho) / rho
pre1 = -1. / 2. / sigma / sigma
pil_bar = np.log(pies / (1. - pies))
Wl = np.log(W)
Wrho = np.exp(rho * Wl)
Wsquared = W * W
# Some asserts
assert np.isfinite(pil_bar).all()
assert np.isfinite(Wl).all()
assert np.isfinite(Wrho).all()
assert (Wrho > 1e-86).all()
my_corr = beta * ((my_logpj).max(axis=1)) # shape: (my_N,)
my_pjb = np.exp(beta * my_logpj -
my_corr[:, None]) # shape: (my_N, no_states)
# Precompute factor for pi/gamma update
A_pi_gamma = 0.
B_pi_gamma = 0.
for gp in xrange(0, self.gamma + 1):
a = comb(H, gp, exact=1) * pies**gp * (1. - pies)**(H - gp)
A_pi_gamma += a
B_pi_gamma += gp * a
# Truncate data
if anneal['Ncut_factor'] > 0.0:
tracing.tracepoint("M_step:truncating")
my_denoms = np.log(my_pjb.sum(axis=1)) + my_corr
N_use = int(N * (1 - (1 - A_pi_gamma) * anneal['Ncut_factor']))
cut_denom = parallel.allsort(my_denoms)[-N_use]
which = np.array(my_denoms >= cut_denom)
my_y = my_y[which]
my_cand = my_cand[which]
my_logpj = my_logpj[which]
my_pjb = my_pjb[which]
my_corr = my_corr[which]
my_N, D = my_y.shape
N_use = comm.allreduce(my_N)
else:
N_use = N
dlog.append('N_use', N_use)
# Allocate suff-stat arrays
my_Wp = np.zeros_like(W) # shape (H, D)
my_Wq = np.zeros_like(W) # shape (H, D)
my_pi = 0.0 #
my_sigma = 0.0 #
# Iterate over all datapoints
for n in xrange(my_N):
tracing.tracepoint("M_step:iterating")
y = my_y[n, :] # shape (D,)
cand = my_cand[n, :] # shape (Hprime,)
logpj = my_logpj[n, :] # shape (no_states,)
pjb = my_pjb[n, :] # shape (no_states,)
corr = my_corr[n] # scalar
this_Wp = np.zeros_like(
W) # numerator for W (current datapoint) (H, D)
this_Wq = np.zeros_like(
W) # denominator for W (current datapoint) (H, D)
this_pi = 0.0 # numerator for pi update (current datapoint)
this_sigma = 0.0 # numerator for gamma update (current datapoint)
# Zero active hidden causes
# this_Wp += 0. # nothing to do
# this_Wq += 0. # nothing to do
# this_pi += 0. # nothing to do
this_sigma += pjb[0] * (y**2).sum()
# One active hidden cause
this_Wp += (pjb[1:(H + 1), None] * Wsquared[:, :]) * y[None, :]
this_Wq += (pjb[1:(H + 1), None] * Wsquared[:, :])
this_pi += pjb[1:(H + 1)].sum()
this_sigma += (pjb[1:(H + 1)] * ((W - y)**2).sum(axis=1)).sum()
# Handle hidden states with more than 1 active cause
W_ = W[cand] # is (Hprime, D)
Wl_ = Wl[cand] # is ( " ")
Wrho_ = Wrho[cand] # is ( " ")
Wlrhom1 = (rho - 1) * Wl_ # is (Hprime, D)
Wlbar = np.log(np.dot(state_mtx, Wrho_)) / rho # is (no_states, D)
Wbar = np.exp(Wlbar) # is (no_states, D)
blpj = beta * logpj[1 + H:] - corr # is (no_states,)
Aid = (state_mtx[:, :, None] *
np.exp(blpj[:, None, None] + (1 - rho) * Wlbar[:, None, :] +
Wlrhom1[None, :, :])).sum(axis=0)
assert np.isfinite(Wlbar).all()
assert np.isfinite(Wbar).all()
assert np.isfinite(pjb).all()
assert np.isfinite(Aid).all()
this_Wp[cand] += Aid * y[None, :]
this_Wq[cand] += Aid
this_pi += (pjb[1 + H:] * state_abs).sum()
this_sigma += (pjb[1 + H:] * ((Wbar - y)**2).sum(axis=1)).sum()
denom = pjb.sum()
my_Wp += this_Wp / denom
my_Wq += this_Wq / denom
my_pi += this_pi / denom
my_sigma += this_sigma / denom
my_ldenom_sum += np.log(np.sum(
np.exp(logpj))) #For loglike computation
# Calculate updated W
if 'W' in self.to_learn:
tracing.tracepoint("M_step:update W")
Wp = np.empty_like(my_Wp)
Wq = np.empty_like(my_Wq)
assert np.isfinite(my_Wp).all()
assert np.isfinite(my_Wq).all()
comm.Allreduce([my_Wp, MPI.DOUBLE], [Wp, MPI.DOUBLE])
comm.Allreduce([my_Wq, MPI.DOUBLE], [Wq, MPI.DOUBLE])
# Make sure wo do not devide by zero
tiny = np.finfo(Wq.dtype).tiny
Wp[Wq < tiny] = 0.
Wq[Wq < tiny] = tiny
W_new = Wp / Wq
else:
W_new = W
# Calculate updated pi
if 'pi' in self.to_learn:
tracing.tracepoint("M_step:update pi")
assert np.isfinite(my_pi).all()
pi_new = A_pi_gamma / B_pi_gamma * pies * comm.allreduce(
my_pi) / N_use
else:
pi_new = pies
# Calculate updated sigma
if 'sigma' in self.to_learn: # TODO: XXX see LinCA XXX (merge!)
tracing.tracepoint("M_step:update sigma")
assert np.isfinite(my_sigma).all()
sigma_new = np.sqrt(comm.allreduce(my_sigma) / D / N_use)
else:
sigma_new = sigma
#Put all together and compute (always) et_approx_likelihood
ldenom_sum = comm.allreduce(my_ldenom_sum)
lAi = (H * np.log(1. - pi_new)) - (
(D / 2) * np.log(2 * pi)) - (D * np.log(sigma_new))
#For practical and et approx reasons we use: sum of restected respons=1
loglike_et = (lAi * N_use) + ldenom_sum
return {'W': W_new, 'pi': pi_new, 'sigma': sigma_new, 'Q': loglike_et}
def E_step(self, anneal, model_params, my_data):
""" BSC E_step
my_data variables used:
my_data['y'] Datapoints
my_data['can'] Candidate H's according to selection func.
Annealing variables used:
anneal['T'] Temperature for det. annealing
anneal['N_cut_factor'] 0.: no truncation; 1. trunc. according to model
"""
comm = self.comm
my_y = my_data['y'].copy()
my_cand = my_data['candidates']
my_N, D = my_data['y'].shape
H = self.H
SM = self.state_matrix # shape: (no_states, Hprime)
state_abs = self.state_abs # shape: (no_states,)
W = model_params['W']
pies = model_params['pi']
sigma = model_params['sigma']
try:
mu = model_params['mu']
except:
mu = np.zeros(D)
model_params['mu'] = mu
# Precompute
beta = 1. / anneal['T']
pre1 = -1. / 2. / sigma / sigma
pil_bar = np.log(pies / (1. - pies))
# Allocate return structures
F = np.empty([my_N, 1 + H + self.no_states])
pre_F = np.empty([my_N, 1 + H + self.no_states])
denoms = np.zeros(my_N)
# Joerg's data noise idea
data_noise_scale = anneal['data_noise']
dlog.append('Data Noise', data_noise_scale)
if data_noise_scale > 0.:
my_data['data_noise'] = np.random.normal(scale=data_noise_scale,
size=my_y.shape)
my_y += my_data['data_noise']
# Pre-fill pre_F:
pre_F[:, 0] = 0.
pre_F[:, 1:H + 1] = pil_bar
pre_F[:, 1 + H:] = pil_bar * state_abs # is (no_states,)
# Iterate over all datapoints
tracing.tracepoint("E_step:iterating")
for n in xrange(my_N):
y = my_data['y'][n, :] - mu
cand = my_data['candidates'][n, :]
# Zero active hidden causes
log_prod_joint = pre1 * (y**2).sum()
F[n, 0] = log_prod_joint
# Hidden states with one active cause
log_prod_joint = pre1 * ((W - y)**2).sum(axis=1)
F[n, 1:H + 1] = log_prod_joint
# Handle hidden states with more than 1 active cause
W_ = W[cand] # is (Hprime x D)
Wbar = np.dot(SM, W_)
log_prod_joint = pre1 * ((Wbar - y)**2).sum(axis=1)
F[n, 1 + H:] = log_prod_joint
if anneal['anneal_prior']:
F = beta * (pre_F + F)
else:
F = pre_F + beta * F
return {'logpj': F}
def M_step(self, anneal, model_params, my_suff_stat, my_data):
""" MCA M_step
my_data variables used:
my_data['y'] Datapoints
my_data['candidates'] Candidate H's according to selection func.
Annealing variables used:
anneal['T'] Temperature for det. annealing AND softmax
anneal['N_cut_factor'] 0.: no truncation; 1. trunc. according to model
"""
comm = self.comm
H, Hprime = self.H, self.Hprime
gamma = self.gamma
W = model_params['W']
pies = model_params['pi']
sigma = model_params['sigma']
# Read in data:
my_y = my_data['y']
my_cand = my_data['candidates']
my_logpj = my_suff_stat['logpj']
my_N, D = my_y.shape
N = comm.allreduce(my_N)
state_mtx = self.state_matrix # shape: (no_states, Hprime)
state_abs = self.state_abs # shape: (no_states,)
no_states = len(state_abs)
# Disable some warnings
old_seterr = np.seterr(divide='ignore', under='ignore')
# To compute et_loglike:
my_ldenom_sum = 0.0
ldenom_sum = 0.0
# Precompute
T = anneal['T']
T_rho = np.maximum(T, self.rho_T_bound)
rho = 1. / (1. - 1. / T_rho)
rho = np.maximum(np.minimum(rho, self.rho_ubound), self.rho_lbound)
beta = 1. / T
pre1 = -1. / 2. / sigma / sigma
pil_bar = np.log(pies / (1. - pies))
Wl = accel.log(np.abs(W))
Wrho = accel.exp(rho * Wl)
Wrhos = np.sign(W) * Wrho
Wsquared = W * W
# Some asserts
assert np.isfinite(pil_bar).all()
assert np.isfinite(Wl).all()
assert np.isfinite(Wrho).all()
assert (Wrho > 1e-86).all()
my_corr = beta * ((my_logpj).max(axis=1)) # shape: (my_N,)
my_logpjb = beta * my_logpj - my_corr[:,
None] # shape: (my_N, no_states)
my_pj = accel.exp(my_logpj) # shape: (my_N, no_states)
my_pjb = accel.exp(my_logpjb) # shape: (my_N, no_states)
# Precompute factor for pi update and ET cutting
A_pi_gamma = 0.
B_pi_gamma = 0.
for gp in xrange(0, self.gamma + 1):
a = comb(H, gp) * pies**gp * (1. - pies)**(H - gp)
A_pi_gamma += a
B_pi_gamma += gp * a
# Truncate data
if anneal['Ncut_factor'] > 0.0:
tracing.tracepoint("M_step:truncating")
my_logdenoms = accel.log(my_pjb.sum(axis=1)) + my_corr
N_use = int(N * (1 - (1 - A_pi_gamma) * anneal['Ncut_factor']))
cut_denom = parallel.allsort(my_logdenoms)[-N_use]
my_sel, = np.where(my_logdenoms >= cut_denom)
my_N, = my_sel.shape
N_use = comm.allreduce(my_N)
else:
my_N, _ = my_y.shape
my_sel = np.arange(my_N)
N_use = N
# Allocate suff-stat arrays
my_Wp = np.zeros_like(W) # shape (H, D)
my_Wq = np.zeros_like(W) # shape (H, D)
my_pi = 0.0 #
my_sigma = 0.0 #
# Do reverse correlation if requested
if self.rev_corr:
my_y_rc = my_data['y_rc']
D_rev_corr = my_y_rc.shape[1]
my_rev_corr = np.zeros((H, D_rev_corr))
my_rev_corr_count = np.zeros(H)
# Iterate over all datapoints
tracing.tracepoint("M_step:iterating...")
dlog.append('N_use', N_use)
for n in my_sel:
y = my_y[n, :] # shape (D,)
cand = my_cand[n, :] # shape (Hprime,)
logpj = my_logpj[n, :] # shape (no_states,)
logpjb = my_logpjb[n, :] # shape (no_states,)
pj = my_pj[n, :] # shape (no_states,)
pjb = my_pjb[n, :] # shape (no_states,)
this_Wp = np.zeros_like(
W) # numerator for W (current datapoint) (H, D)
this_Wq = np.zeros_like(
W) # denominator for W (current datapoint) (H, D)
this_pi = 0.0 # numerator for pi update (current datapoint)
this_sigma = 0.0 # numerator for gamma update (current datapoint)
# Zero active hidden causes
# this_Wp += 0. # nothing to do
# this_Wq += 0. # nothing to do
# this_pi += 0. # nothing to do
this_sigma += pjb[0] * (y**2).sum()
# One active hidden cause
this_Wp += (pjb[1:(H + 1), None]) * y[None, :]
this_Wq += (pjb[1:(H + 1), None])
this_pi += pjb[1:(H + 1)].sum()
this_sigma += (pjb[1:(H + 1)] * ((W - y)**2).sum(axis=1)).sum()
# Handle hidden states with more than 1 active cause
W_ = W[cand] # is (Hprime, D)
Wl_ = Wl[cand] # is ( " ")
Wrho_ = Wrho[cand] # is ( " ")
Wrhos_ = Wrhos[cand] # is ( " ")
#Wbar = calc_Wbar(state_mtx, W_)
#Wlbar = np.log(np.abs(Wbar))
t0 = np.dot(state_mtx, Wrhos_)
Wlbar = accel.log(np.abs(t0)) / rho # is (no_states, D)
#Wlbar = np.maximum(Wlbar, -9.21)
Wbar = np.sign(t0) * accel.exp(Wlbar) # is (no_states, D)
t = Wlbar[:, None, :] - Wl_[None, :, :]
t = np.maximum(t, 0.)
Aid = state_mtx[:, :,
None] * accel.exp(logpjb[H + 1:, None, None] -
(rho - 1) * t)
Aid = Aid.sum(axis=0)
#Aid = calc_Aid(logpjb[H+1:], W_, Wl_, state_mtx, Wbar, Wlbar, rho)
#assert np.isfinite(Wlbar).all()
#assert np.isfinite(Wbar).all()
#assert np.isfinite(pjb).all()
#assert np.isfinite(Aid).all()
this_Wp[cand] += Aid * y[None, :]
this_Wq[cand] += Aid
this_pi += (pjb[1 + H:] * state_abs).sum()
this_sigma += (pjb[1 + H:] * ((Wbar - y)**2).sum(axis=1)).sum()
denom = pjb.sum()
my_Wp += this_Wp / denom
my_Wq += this_Wq / denom
my_pi += this_pi / denom
my_sigma += this_sigma / denom
#self.tbl.append("logpj", logpj)
#self.tbl.append("corr", my_corr[n])
#self.tbl.append("denom", denom)
#self.tbl.append("cand", cand)
#self.tbl.append("Aid", Aid)
my_ldenom_sum += accel.log(np.sum(
accel.exp(logpj))) #For loglike computation
# Estimate reverse correlation
if self.rev_corr:
pys = pjb / denom
if np.isfinite(pys).all():
my_rev_corr += pys[1:H + 1, None] * my_y_rc[n, None, :]
my_rev_corr_count += pys[1:H + 1]
my_rev_corr[cand] += np.sum(state_mtx[:, :, None] *
pys[H + 1:, None, None] *
my_y_rc[n, None, :],
axis=0)
my_rev_corr_count[cand] += np.sum(state_mtx[:, :] *
pys[H + 1, None],
axis=0)
else:
print "Not all finite rev_corr %d" % n
# Calculate updated W
if 'W' in self.to_learn:
tracing.tracepoint("M_step:update W")
Wp = np.empty_like(my_Wp)
Wq = np.empty_like(my_Wq)
assert np.isfinite(my_Wp).all()
assert np.isfinite(my_Wq).all()
comm.Allreduce([my_Wp, MPI.DOUBLE], [Wp, MPI.DOUBLE])
comm.Allreduce([my_Wq, MPI.DOUBLE], [Wq, MPI.DOUBLE])
# Make sure wo do not devide by zero
tiny = self.tol
Wq[Wq < tiny] = tiny
# Calculate updated W
W_new = Wp / Wq
# Add inertia depending on Wq
alpha = 2.5
inertia = np.maximum(1. - accel.exp(-Wq / alpha), 0.2)
W_new = inertia * W_new + (1 - inertia) * W
else:
W_new = W
# Calculate updated pi
if 'pi' in self.to_learn:
tracing.tracepoint("M_step:update pi")
assert np.isfinite(my_pi).all()
pi_new = A_pi_gamma / B_pi_gamma * pies * comm.allreduce(
my_pi) / N_use
else:
pi_new = pies
# Calculate updated sigma
if 'sigma' in self.to_learn: # TODO: XXX see LinCA XXX (merge!)
tracing.tracepoint("M_step:update sigma")
assert np.isfinite(my_sigma).all()
sigma_new = np.sqrt(comm.allreduce(my_sigma) / D / N_use)
else:
sigma_new = sigma
# Put all together and compute (always) et_approx_likelihood
ldenom_sum = comm.allreduce(my_ldenom_sum)
lAi = (H * np.log(1. - pi_new)) - (
(D / 2) * np.log(2 * pi)) - (D * np.log(sigma_new))
# For practical and et approx reasons we use: sum of restected respons=1
loglike_et = (lAi * N_use) + ldenom_sum
if self.rev_corr:
rev_corr = np.empty_like(my_rev_corr)
rev_corr_count = np.empty_like(my_rev_corr_count)
comm.Allreduce([my_rev_corr, MPI.DOUBLE], [rev_corr, MPI.DOUBLE])
comm.Allreduce([my_rev_corr_count, MPI.DOUBLE],
[rev_corr_count, MPI.DOUBLE])
rev_corr /= (1e-16 + rev_corr_count[:, None])
else:
rev_corr = np.zeros((H, D))
# Restore np.seterr
np.seterr(**old_seterr)
return {
'W': W_new,
'pi': pi_new,
'sigma': sigma_new,
'rev_corr': rev_corr,
'Q': loglike_et
}
def E_step(self, anneal, model_params, my_data):
""" BSC E_step
my_data variables used:
my_data['y'] Datapoints
my_data['can'] Candidate H's according to selection func.
Annealing variables used:
anneal['T'] Temperature for det. annealing
anneal['N_cut_factor'] 0.: no truncation; 1. trunc. according to model
"""
comm = self.comm
my_y = my_data['y'].copy()
my_cand = my_data['candidates']
my_N, D = my_data['y'].shape
H = self.H
SM = self.state_matrix # shape: (no_states, Hprime)
state_abs = self.state_abs # shape: (no_states,)
W = model_params['W']
pies = model_params['pi']
sigma = model_params['sigma']
try:
mu = model_params['mu']
except:
mu = np.zeros(D)
model_params['mu'] = mu
# Precompute
beta = 1./anneal['T']
pre1 = -1./2./sigma/sigma
pil_bar = np.log( pies/(1.-pies) )
# Allocate return structures
F = np.empty( [my_N, 1+H+self.no_states] )
pre_F = np.empty( [my_N, 1+H+ self.no_states] )
denoms = np.zeros(my_N)
# Joerg's data noise idea
data_noise_scale = anneal['data_noise']
dlog.append('Data Noise', data_noise_scale)
if data_noise_scale > 0.:
my_data['data_noise'] = np.random.normal(scale=data_noise_scale, size=my_y.shape)
my_y += my_data['data_noise']
# Pre-fill pre_F:
pre_F[:,0] = 0.
pre_F[:,1:H+1] = pil_bar
pre_F[:,1+H:] = pil_bar * state_abs # is (no_states,)
# Iterate over all datapoints
tracing.tracepoint("E_step:iterating")
for n in xrange(my_N):
y = my_data['y'][n,:] - mu
cand = my_data['candidates'][n,:]
# Zero active hidden causes
log_prod_joint = pre1 * (y**2).sum()
F[n,0] = log_prod_joint
# Hidden states with one active cause
log_prod_joint = pre1 * ((W-y)**2).sum(axis=1)
F[n,1:H+1] = log_prod_joint
# Handle hidden states with more than 1 active cause
W_ = W[cand] # is (Hprime x D)
Wbar = np.dot(SM,W_)
log_prod_joint = pre1 * ((Wbar-y)**2).sum(axis=1)
F[n,1+H:] = log_prod_joint
if anneal['anneal_prior']:
F = beta * (pre_F + F)
else:
F = pre_F + beta * F
return { 'logpj': F }
def M_step(self, anneal, model_params, my_suff_stat, my_data):
""" BSC M_step
my_data variables used:
my_data['y'] Datapoints
my_data['candidates'] Candidate H's according to selection func.
Annealing variables used:
anneal['T'] Temperature for det. annealing
anneal['N_cut_factor'] 0.: no truncation; 1. trunc. according to model
"""
comm = self.comm
H, Hprime = self.H, self.Hprime
gamma = self.gamma
W = model_params['W']
pies = model_params['pi']
sigma = model_params['sigma']
mu = model_params['mu']
# Read in data:
my_y = my_data['y'].copy()
candidates = my_data['candidates']
logpj_all = my_suff_stat['logpj']
all_denoms = np.exp(logpj_all).sum(axis=1)
my_N, D = my_y.shape
N = comm.allreduce(my_N)
# Joerg's data noise idea
data_noise_scale = anneal['data_noise']
if data_noise_scale > 0:
my_y += my_data['data_noise']
SM = self.state_matrix # shape: (no_states, Hprime)
# To compute et_loglike:
my_ldenom_sum = 0.0
ldenom_sum = 0.0
# Precompute factor for pi update
A_pi_gamma = 0
B_pi_gamma = 0
for gamma_p in range(gamma + 1):
A_pi_gamma += comb(H, gamma_p) * (pies**gamma_p) * (
(1 - pies)**(H - gamma_p))
B_pi_gamma += gamma_p * comb(H, gamma_p) * (pies**gamma_p) * (
(1 - pies)**(H - gamma_p))
E_pi_gamma = pies * H * A_pi_gamma / B_pi_gamma
# Truncate data
if anneal['Ncut_factor'] > 0.0:
tracing.tracepoint("M_step:truncating")
#alpha = 0.9 # alpha from ET paper
#N_use = int(alpha * (N * (1 - (1 - A_pi_gamma) * anneal['Ncut_factor'])))
N_use = int(N * (1 - (1 - A_pi_gamma) * anneal['Ncut_factor']))
cut_denom = parallel.allsort(all_denoms)[-N_use]
which = np.array(all_denoms >= cut_denom)
candidates = candidates[which]
logpj_all = logpj_all[which]
my_y = my_y[which]
my_N, D = my_y.shape
N_use = comm.allreduce(my_N)
else:
N_use = N
dlog.append('N', N_use)
# Calculate truncated Likelihood
L = H * np.log(1 - pies) - 0.5 * D * np.log(
2 * pi * sigma**2) - np.log(A_pi_gamma)
Fs = np.log(np.exp(logpj_all).sum(axis=1)).sum()
L += comm.allreduce(Fs) / N_use
dlog.append('L', L)
# Precompute
pil_bar = np.log(pies / (1. - pies))
corr_all = logpj_all.max(axis=1) # shape: (my_N,)
pjb_all = np.exp(logpj_all -
corr_all[:, None]) # shape: (my_N, no_states)
# Allocate
my_Wp = np.zeros_like(W) # shape (H, D)
my_Wq = np.zeros((H, H)) # shape (H, H)
my_pi = 0.0 #
my_sigma = 0.0 #
#my_mup = np.zeros_like(W) # shape (H, D)
#my_muq = np.zeros((H,H)) # shape (H, H)
my_mus = np.zeros(H) # shape D
data_sum = my_y.sum(axis=0) # sum over all data points for mu update
## Calculate mu
#for n in xrange(my_N):
#tracing.tracepoint("Calculationg offset")
#y = my_y[n,:] # length D
#cand = candidates[n,:] # length Hprime
#logpj = logpj_all[n,:] # length no_states
#corr = corr_all[n] # scalar
#pjb = pjb_all[n, :]
## Zero active hidden cause (do nothing for the W and pi case)
## this_Wp += 0. # nothing to do
## this_Wq += 0. # nothing to do
## this_pi += 0. # nothing to do
## One active hidden cause
#this_mup = np.outer(pjb[1:(H+1)],y)
#this_muq = pjb[1:(H+1)] * np.identity(H)
#this_mus = pjb[1:(H+1)]
## Handle hidden states with more than 1 active cause
#this_mup[cand] += np.dot(np.outer(y,pjb[(1+H):]),SM).T
#this_muq_tmp = np.zeros_like(my_muq[cand])
#this_muq_tmp[:,cand] = np.dot(pjb[(1+H):] * SM.T,SM)
#this_muq[cand] += this_muq_tmp
#this_mus[cand] += np.inner(SM.T,pjb[(1+H):])
#denom = pjb.sum()
#my_mup += this_mup / denom
#my_muq += this_muq / denom
#my_mus += this_mus / denom
## Calculate updated mu
#if 'mu' in self.to_learn:
#tracing.tracepoint("M_step:update mu")
#mup = np.empty_like(my_mup)
#muq = np.empty_like(my_muq)
#mus = np.empty_like(my_mus)
#all_data_sum = np.empty_like(data_sum)
#comm.Allreduce( [my_mup, MPI.DOUBLE], [mup, MPI.DOUBLE] )
#comm.Allreduce( [my_muq, MPI.DOUBLE], [muq, MPI.DOUBLE] )
#comm.Allreduce( [my_mus, MPI.DOUBLE], [mus, MPI.DOUBLE] )
#comm.Allreduce( [data_sum, MPI.DOUBLE], [all_data_sum, MPI.DOUBLE] )
#mu_numer = all_data_sum - np.dot(mus,np.dot(np.linalg.inv(muq), mup))
#mu_denom = my_N - np.dot(mus,np.dot(np.linalg.inv(muq), mus))
#mu_new = mu_numer/ mu_denom
#else:
#mu_new = mu
# Iterate over all datapoints
tracing.tracepoint("M_step:iterating")
for n in xrange(my_N):
y = my_y[n, :] - mu # length D
cand = candidates[n, :] # length Hprime
pjb = pjb_all[n, :]
this_Wp = np.zeros_like(
my_Wp) # numerator for current datapoint (H, D)
this_Wq = np.zeros_like(
my_Wq) # denominator for current datapoint (H, H)
this_pi = 0.0 # numerator for pi update (current datapoint)
# Zero active hidden cause (do nothing for the W and pi case)
# this_Wp += 0. # nothing to do
# this_Wq += 0. # nothing to do
# this_pi += 0. # nothing to do
# One active hidden cause
this_Wp = np.outer(pjb[1:(H + 1)], y)
this_Wq = pjb[1:(H + 1)] * np.identity(H)
this_pi = pjb[1:(H + 1)].sum()
this_mus = pjb[1:(H + 1)].copy()
# Handle hidden states with more than 1 active cause
this_Wp[cand] += np.dot(np.outer(y, pjb[(1 + H):]), SM).T
this_Wq_tmp = np.zeros_like(my_Wq[cand])
this_Wq_tmp[:, cand] = np.dot(pjb[(1 + H):] * SM.T, SM)
this_Wq[cand] += this_Wq_tmp
this_pi += np.inner(pjb[(1 + H):], SM.sum(axis=1))
this_mus[cand] += np.inner(SM.T, pjb[(1 + H):])
denom = pjb.sum()
my_Wp += this_Wp / denom
my_Wq += this_Wq / denom
my_pi += this_pi / denom
my_mus += this_mus / denom
# Calculate updated W
if 'W' in self.to_learn:
tracing.tracepoint("M_step:update W")
Wp = np.empty_like(my_Wp)
Wq = np.empty_like(my_Wq)
comm.Allreduce([my_Wp, MPI.DOUBLE], [Wp, MPI.DOUBLE])
comm.Allreduce([my_Wq, MPI.DOUBLE], [Wq, MPI.DOUBLE])
W_new = np.dot(np.linalg.inv(Wq), Wp)
# W_new = np.linalg.lstsq(Wq, Wp)
else:
W_new = W
# Calculate updated pi
if 'pi' in self.to_learn:
tracing.tracepoint("M_step:update pi")
pi_new = E_pi_gamma * comm.allreduce(my_pi) / H / N_use
else:
pi_new = pies
# Calculate updated sigma
if 'sigma' in self.to_learn:
tracing.tracepoint("M_step:update sigma")
# Loop for sigma update:
for n in xrange(my_N):
y = my_y[n, :] - mu # length D
cand = candidates[n, :] # length Hprime
logpj = logpj_all[n, :] # length no_states
corr = logpj.max() # scalar
pjb = np.exp(logpj - corr)
# Zero active hidden causes
this_sigma = pjb[0] * (y**2).sum()
# Hidden states with one active cause
this_sigma += (pjb[1:(H + 1)] * ((W - y)**2).sum(axis=1)).sum()
# Handle hidden states with more than 1 active cause
SM = self.state_matrix # is (no_states, Hprime)
W_ = W[cand] # is (Hprime x D)
Wbar = np.dot(SM, W_)
this_sigma += (pjb[(H + 1):] *
((Wbar - y)**2).sum(axis=1)).sum()
denom = pjb.sum()
my_sigma += this_sigma / denom
sigma_new = np.sqrt(comm.allreduce(my_sigma) / D / N_use)
else:
sigma_new = sigma
# Calculate updated mu:
if 'mu' in self.to_learn:
tracing.tracepoint("M_step:update mu")
mus = np.empty_like(my_mus)
all_data_sum = np.empty_like(data_sum)
comm.Allreduce([my_mus, MPI.DOUBLE], [mus, MPI.DOUBLE])
comm.Allreduce([data_sum, MPI.DOUBLE], [all_data_sum, MPI.DOUBLE])
mu_new = all_data_sum / my_N - np.inner(W_new.T / my_N, mus)
else:
mu_new = mu
for param in anneal.crit_params:
exec('this_param = ' + param)
anneal.dyn_param(param, this_param)
dlog.append('N_use', N_use)
return {'W': W_new, 'pi': pi_new, 'sigma': sigma_new, 'mu': mu_new}
def M_step(self, anneal, model_params, my_suff_stat, my_data):
""" MCA M_step
my_data variables used:
my_data['y'] Datapoints
my_data['candidates'] Candidate H's according to selection func.
Annealing variables used:
anneal['T'] Temperature for det. annealing AND softmax
anneal['N_cut_factor'] 0.: no truncation; 1. trunc. according to model
"""
comm = self.comm
H, Hprime = self.H, self.Hprime
gamma = self.gamma
W = model_params["W"]
pies = model_params["pi"]
sigma = model_params["sigma"]
# Read in data:
my_y = my_data["y"]
my_cand = my_data["candidates"]
my_logpj = my_suff_stat["logpj"]
my_N, D = my_y.shape
N = comm.allreduce(my_N)
state_mtx = self.state_matrix # shape: (no_states, Hprime)
state_abs = self.state_abs # shape: (no_states,)
no_states = len(state_abs)
# To compute et_loglike:
my_ldenom_sum = 0.0
ldenom_sum = 0.0
# Precompute
T = anneal["T"]
T_rho = np.maximum(T, self.rho_temp_bound)
rho = 1.0 / (1.0 - 1.0 / T_rho)
beta = 1.0 / T
pre0 = (1.0 - rho) / rho
pre1 = -1.0 / 2.0 / sigma / sigma
pil_bar = np.log(pies / (1.0 - pies))
Wl = np.log(W)
Wrho = np.exp(rho * Wl)
Wsquared = W * W
# Some asserts
assert np.isfinite(pil_bar).all()
assert np.isfinite(Wl).all()
assert np.isfinite(Wrho).all()
assert (Wrho > 1e-86).all()
my_corr = beta * ((my_logpj).max(axis=1)) # shape: (my_N,)
my_pjb = np.exp(beta * my_logpj - my_corr[:, None]) # shape: (my_N, no_states)
# Precompute factor for pi/gamma update
A_pi_gamma = 0.0
B_pi_gamma = 0.0
for gp in xrange(0, self.gamma + 1):
a = comb(H, gp, exact=1) * pies ** gp * (1.0 - pies) ** (H - gp)
A_pi_gamma += a
B_pi_gamma += gp * a
# Truncate data
if anneal["Ncut_factor"] > 0.0:
tracing.tracepoint("M_step:truncating")
my_denoms = np.log(my_pjb.sum(axis=1)) + my_corr
N_use = int(N * (1 - (1 - A_pi_gamma) * anneal["Ncut_factor"]))
cut_denom = parallel.allsort(my_denoms)[-N_use]
which = np.array(my_denoms >= cut_denom)
my_y = my_y[which]
my_cand = my_cand[which]
my_logpj = my_logpj[which]
my_pjb = my_pjb[which]
my_corr = my_corr[which]
my_N, D = my_y.shape
N_use = comm.allreduce(my_N)
else:
N_use = N
dlog.append("N_use", N_use)
# Allocate suff-stat arrays
my_Wp = np.zeros_like(W) # shape (H, D)
my_Wq = np.zeros_like(W) # shape (H, D)
my_pi = 0.0 #
my_sigma = 0.0 #
# Iterate over all datapoints
for n in xrange(my_N):
tracing.tracepoint("M_step:iterating")
y = my_y[n, :] # shape (D,)
cand = my_cand[n, :] # shape (Hprime,)
logpj = my_logpj[n, :] # shape (no_states,)
pjb = my_pjb[n, :] # shape (no_states,)
corr = my_corr[n] # scalar
this_Wp = np.zeros_like(W) # numerator for W (current datapoint) (H, D)
this_Wq = np.zeros_like(W) # denominator for W (current datapoint) (H, D)
this_pi = 0.0 # numerator for pi update (current datapoint)
this_sigma = 0.0 # numerator for gamma update (current datapoint)
# Zero active hidden causes
# this_Wp += 0. # nothing to do
# this_Wq += 0. # nothing to do
# this_pi += 0. # nothing to do
this_sigma += pjb[0] * (y ** 2).sum()
# One active hidden cause
this_Wp += (pjb[1 : (H + 1), None] * Wsquared[:, :]) * y[None, :]
this_Wq += pjb[1 : (H + 1), None] * Wsquared[:, :]
this_pi += pjb[1 : (H + 1)].sum()
this_sigma += (pjb[1 : (H + 1)] * ((W - y) ** 2).sum(axis=1)).sum()
# Handle hidden states with more than 1 active cause
W_ = W[cand] # is (Hprime, D)
Wl_ = Wl[cand] # is ( " ")
Wrho_ = Wrho[cand] # is ( " ")
Wlrhom1 = (rho - 1) * Wl_ # is (Hprime, D)
Wlbar = np.log(np.dot(state_mtx, Wrho_)) / rho # is (no_states, D)
Wbar = np.exp(Wlbar) # is (no_states, D)
blpj = beta * logpj[1 + H :] - corr # is (no_states,)
Aid = (
state_mtx[:, :, None]
* np.exp(blpj[:, None, None] + (1 - rho) * Wlbar[:, None, :] + Wlrhom1[None, :, :])
).sum(axis=0)
assert np.isfinite(Wlbar).all()
assert np.isfinite(Wbar).all()
assert np.isfinite(pjb).all()
assert np.isfinite(Aid).all()
this_Wp[cand] += Aid * y[None, :]
this_Wq[cand] += Aid
this_pi += (pjb[1 + H :] * state_abs).sum()
this_sigma += (pjb[1 + H :] * ((Wbar - y) ** 2).sum(axis=1)).sum()
denom = pjb.sum()
my_Wp += this_Wp / denom
my_Wq += this_Wq / denom
my_pi += this_pi / denom
my_sigma += this_sigma / denom
my_ldenom_sum += np.log(np.sum(np.exp(logpj))) # For loglike computation
# Calculate updated W
if "W" in self.to_learn:
tracing.tracepoint("M_step:update W")
Wp = np.empty_like(my_Wp)
Wq = np.empty_like(my_Wq)
assert np.isfinite(my_Wp).all()
assert np.isfinite(my_Wq).all()
comm.Allreduce([my_Wp, MPI.DOUBLE], [Wp, MPI.DOUBLE])
comm.Allreduce([my_Wq, MPI.DOUBLE], [Wq, MPI.DOUBLE])
# Make sure wo do not devide by zero
tiny = np.finfo(Wq.dtype).tiny
Wp[Wq < tiny] = 0.0
Wq[Wq < tiny] = tiny
W_new = Wp / Wq
else:
W_new = W
# Calculate updated pi
if "pi" in self.to_learn:
tracing.tracepoint("M_step:update pi")
assert np.isfinite(my_pi).all()
pi_new = A_pi_gamma / B_pi_gamma * pies * comm.allreduce(my_pi) / N_use
else:
pi_new = pies
# Calculate updated sigma
if "sigma" in self.to_learn: # TODO: XXX see LinCA XXX (merge!)
tracing.tracepoint("M_step:update sigma")
assert np.isfinite(my_sigma).all()
sigma_new = np.sqrt(comm.allreduce(my_sigma) / D / N_use)
else:
sigma_new = sigma
# Put all together and compute (always) et_approx_likelihood
ldenom_sum = comm.allreduce(my_ldenom_sum)
lAi = (H * np.log(1.0 - pi_new)) - ((D / 2) * np.log(2 * pi)) - (D * np.log(sigma_new))
# For practical and et approx reasons we use: sum of restected respons=1
loglike_et = (lAi * N_use) + ldenom_sum
return {"W": W_new, "pi": pi_new, "sigma": sigma_new, "Q": loglike_et}
def M_step(self, anneal, model_params, my_suff_stat, my_data):
""" BSC M_step
my_data variables used:
my_data['y'] Datapoints
my_data['candidates'] Candidate H's according to selection func.
Annealing variables used:
anneal['T'] Temperature for det. annealing
anneal['N_cut_factor'] 0.: no truncation; 1. trunc. according to model
"""
comm = self.comm
H, Hprime = self.H, self.Hprime
gamma = self.gamma
W = model_params['W']
pies = model_params['pi']
sigma = model_params['sigma']
mu = model_params['mu']
# Read in data:
my_y = my_data['y'].copy()
candidates = my_data['candidates']
logpj_all = my_suff_stat['logpj']
all_denoms = np.exp(logpj_all).sum(axis=1)
my_N, D = my_y.shape
N = comm.allreduce(my_N)
# Joerg's data noise idea
data_noise_scale = anneal['data_noise']
if data_noise_scale > 0:
my_y += my_data['data_noise']
SM = self.state_matrix # shape: (no_states, Hprime)
# To compute et_loglike:
my_ldenom_sum = 0.0
ldenom_sum = 0.0
# Precompute factor for pi update
A_pi_gamma = 0
B_pi_gamma = 0
for gamma_p in range(gamma+1):
A_pi_gamma += comb(H,gamma_p) * (pies**gamma_p) * ((1-pies)**(H-gamma_p))
B_pi_gamma += gamma_p * comb(H,gamma_p) * (pies**gamma_p) * ((1-pies)**(H-gamma_p))
E_pi_gamma = pies * H * A_pi_gamma / B_pi_gamma
# Truncate data
if anneal['Ncut_factor'] > 0.0:
tracing.tracepoint("M_step:truncating")
#alpha = 0.9 # alpha from ET paper
#N_use = int(alpha * (N * (1 - (1 - A_pi_gamma) * anneal['Ncut_factor'])))
N_use = int(N * (1 - (1 - A_pi_gamma) * anneal['Ncut_factor']))
cut_denom = parallel.allsort(all_denoms)[-N_use]
which = np.array(all_denoms >= cut_denom)
candidates = candidates[which]
logpj_all = logpj_all[which]
my_y = my_y[which]
my_N, D = my_y.shape
N_use = comm.allreduce(my_N)
else:
N_use = N
dlog.append('N', N_use)
# Calculate truncated Likelihood
L = H * np.log(1-pies) - 0.5 * D * np.log(2*pi*sigma**2) - np.log(A_pi_gamma)
Fs = np.log(np.exp(logpj_all).sum(axis=1)).sum()
L += comm.allreduce(Fs)/N_use
dlog.append('L',L)
# Precompute
pil_bar = np.log( pies/(1.-pies) )
corr_all = logpj_all.max(axis=1) # shape: (my_N,)
pjb_all = np.exp(logpj_all - corr_all[:, None]) # shape: (my_N, no_states)
# Allocate
my_Wp = np.zeros_like(W) # shape (H, D)
my_Wq = np.zeros((H,H)) # shape (H, H)
my_pi = 0.0 #
my_sigma = 0.0 #
#my_mup = np.zeros_like(W) # shape (H, D)
#my_muq = np.zeros((H,H)) # shape (H, H)
my_mus = np.zeros(H) # shape D
data_sum = my_y.sum(axis=0) # sum over all data points for mu update
## Calculate mu
#for n in xrange(my_N):
#tracing.tracepoint("Calculationg offset")
#y = my_y[n,:] # length D
#cand = candidates[n,:] # length Hprime
#logpj = logpj_all[n,:] # length no_states
#corr = corr_all[n] # scalar
#pjb = pjb_all[n, :]
## Zero active hidden cause (do nothing for the W and pi case)
## this_Wp += 0. # nothing to do
## this_Wq += 0. # nothing to do
## this_pi += 0. # nothing to do
## One active hidden cause
#this_mup = np.outer(pjb[1:(H+1)],y)
#this_muq = pjb[1:(H+1)] * np.identity(H)
#this_mus = pjb[1:(H+1)]
## Handle hidden states with more than 1 active cause
#this_mup[cand] += np.dot(np.outer(y,pjb[(1+H):]),SM).T
#this_muq_tmp = np.zeros_like(my_muq[cand])
#this_muq_tmp[:,cand] = np.dot(pjb[(1+H):] * SM.T,SM)
#this_muq[cand] += this_muq_tmp
#this_mus[cand] += np.inner(SM.T,pjb[(1+H):])
#denom = pjb.sum()
#my_mup += this_mup / denom
#my_muq += this_muq / denom
#my_mus += this_mus / denom
## Calculate updated mu
#if 'mu' in self.to_learn:
#tracing.tracepoint("M_step:update mu")
#mup = np.empty_like(my_mup)
#muq = np.empty_like(my_muq)
#mus = np.empty_like(my_mus)
#all_data_sum = np.empty_like(data_sum)
#comm.Allreduce( [my_mup, MPI.DOUBLE], [mup, MPI.DOUBLE] )
#comm.Allreduce( [my_muq, MPI.DOUBLE], [muq, MPI.DOUBLE] )
#comm.Allreduce( [my_mus, MPI.DOUBLE], [mus, MPI.DOUBLE] )
#comm.Allreduce( [data_sum, MPI.DOUBLE], [all_data_sum, MPI.DOUBLE] )
#mu_numer = all_data_sum - np.dot(mus,np.dot(np.linalg.inv(muq), mup))
#mu_denom = my_N - np.dot(mus,np.dot(np.linalg.inv(muq), mus))
#mu_new = mu_numer/ mu_denom
#else:
#mu_new = mu
# Iterate over all datapoints
tracing.tracepoint("M_step:iterating")
for n in xrange(my_N):
y = my_y[n,:]-mu # length D
cand = candidates[n,:] # length Hprime
pjb = pjb_all[n, :]
this_Wp = np.zeros_like(my_Wp) # numerator for current datapoint (H, D)
this_Wq = np.zeros_like(my_Wq) # denominator for current datapoint (H, H)
this_pi = 0.0 # numerator for pi update (current datapoint)
# Zero active hidden cause (do nothing for the W and pi case)
# this_Wp += 0. # nothing to do
# this_Wq += 0. # nothing to do
# this_pi += 0. # nothing to do
# One active hidden cause
this_Wp = np.outer(pjb[1:(H+1)],y)
this_Wq = pjb[1:(H+1)] * np.identity(H)
this_pi = pjb[1:(H+1)].sum()
this_mus = pjb[1:(H+1)].copy()
# Handle hidden states with more than 1 active cause
this_Wp[cand] += np.dot(np.outer(y,pjb[(1+H):]),SM).T
this_Wq_tmp = np.zeros_like(my_Wq[cand])
this_Wq_tmp[:,cand] = np.dot(pjb[(1+H):] * SM.T,SM)
this_Wq[cand] += this_Wq_tmp
this_pi += np.inner(pjb[(1+H):], SM.sum(axis=1))
this_mus[cand] += np.inner(SM.T,pjb[(1+H):])
denom = pjb.sum()
my_Wp += this_Wp / denom
my_Wq += this_Wq / denom
my_pi += this_pi / denom
my_mus += this_mus / denom
# Calculate updated W
if 'W' in self.to_learn:
tracing.tracepoint("M_step:update W")
Wp = np.empty_like(my_Wp)
Wq = np.empty_like(my_Wq)
comm.Allreduce( [my_Wp, MPI.DOUBLE], [Wp, MPI.DOUBLE] )
comm.Allreduce( [my_Wq, MPI.DOUBLE], [Wq, MPI.DOUBLE] )
W_new = np.dot(np.linalg.inv(Wq), Wp)
# W_new = np.linalg.lstsq(Wq, Wp)
else:
W_new = W
# Calculate updated pi
if 'pi' in self.to_learn:
tracing.tracepoint("M_step:update pi")
pi_new = E_pi_gamma * comm.allreduce(my_pi) / H / N_use
else:
pi_new = pies
# Calculate updated sigma
if 'sigma' in self.to_learn:
tracing.tracepoint("M_step:update sigma")
# Loop for sigma update:
for n in xrange(my_N):
y = my_y[n,:]-mu # length D
cand = candidates[n,:] # length Hprime
logpj = logpj_all[n,:] # length no_states
corr = logpj.max() # scalar
pjb = np.exp(logpj - corr)
# Zero active hidden causes
this_sigma = pjb[0] * (y**2).sum()
# Hidden states with one active cause
this_sigma += (pjb[1:(H+1)] * ((W-y)**2).sum(axis=1)).sum()
# Handle hidden states with more than 1 active cause
SM = self.state_matrix # is (no_states, Hprime)
W_ = W[cand] # is (Hprime x D)
Wbar = np.dot(SM,W_)
this_sigma += (pjb[(H+1):] * ((Wbar-y)**2).sum(axis=1)).sum()
denom = pjb.sum()
my_sigma += this_sigma/ denom
sigma_new = np.sqrt(comm.allreduce(my_sigma) / D / N_use)
else:
sigma_new = sigma
# Calculate updated mu:
if 'mu' in self.to_learn:
tracing.tracepoint("M_step:update mu")
mus = np.empty_like(my_mus)
all_data_sum = np.empty_like(data_sum)
comm.Allreduce( [my_mus, MPI.DOUBLE], [mus, MPI.DOUBLE] )
comm.Allreduce( [data_sum, MPI.DOUBLE], [all_data_sum, MPI.DOUBLE] )
mu_new = all_data_sum/my_N - np.inner(W_new.T/my_N,mus)
else:
mu_new = mu
for param in anneal.crit_params:
exec('this_param = ' + param)
anneal.dyn_param(param, this_param)
dlog.append('N_use', N_use)
return { 'W': W_new, 'pi': pi_new, 'sigma': sigma_new, 'mu': mu_new }
def E_step(self, anneal, model_params, my_data):
""" MCA E_step
my_data variables used:
my_data['y'] Datapoints
my_data['can'] Candidate H's according to selection func.
Annealing variables used:
anneal['T'] Temperature for det. annealing AND softmax
anneal['N_cut_factor'] 0.: no truncation; 1. trunc. according to model
"""
comm = self.comm
my_y = my_data["y"]
my_cand = my_data["candidates"]
my_N, D = my_data["y"].shape
H = self.H
state_mtx = self.state_matrix # shape: (no_states, Hprime)
state_abs = self.state_abs # shape: (no_states,)
no_states = len(state_abs)
W = model_params["W"]
pies = model_params["pi"]
sigma = model_params["sigma"]
# Precompute
T = anneal["T"]
T_rho = np.maximum(T, self.rho_temp_bound)
rho = 1.0 / (1.0 - 1.0 / T_rho)
beta = 1.0 / T
pre1 = -1.0 / 2.0 / sigma / sigma
pil_bar = np.log(pies / (1.0 - pies))
Wl = np.log(W)
Wrho = np.exp(rho * Wl)
# Allocate return structures
F = np.empty([my_N, 1 + H + no_states])
# Iterate over all datapoints
for n in xrange(my_N):
tracing.tracepoint("E_step:iterating")
y = my_y[n, :]
cand = my_cand[n, :]
# Zero active hidden causes
log_prod_joint = pre1 * (y ** 2).sum()
F[n, 0] = log_prod_joint
# Hidden states with one active cause
log_prod_joint = pil_bar + pre1 * ((W - y) ** 2).sum(axis=1)
F[n, 1 : H + 1] = log_prod_joint
# Handle hidden states with more than 1 active cause
log_prior = pil_bar * state_abs # is (no_states,)
Wrho_ = Wrho[cand] # is (Hprime x D)
Wbar = np.exp(np.log(np.dot(state_mtx, Wrho_)) / rho)
log_prod_joint = log_prior + pre1 * ((Wbar - y) ** 2).sum(axis=1)
F[n, 1 + H :] = log_prod_joint
assert np.isfinite(F).all()
return {"logpj": F}
anneal['Ncut_factor'] = [(cut_start, 0.), (cut_end, 1.)]
anneal['anneal_prior'] = anneal_prior
anneal['W_noise'] = [(noise_decrease, W_noise), (noise_end, 0.)]
anneal['pi_noise'] = [(noise_decrease, pi_noise), (noise_end, 0.)]
anneal['sigma_noise'] = [(noise_decrease, sigma_noise), (noise_end, 0.)]
anneal['partial'] = [(cut_start, partial_a), (cut_end, partial_b),
(noise_end, partial_c)]
#========================= Instantiate model ==============================
model = model_class(D, H, Hprime, gamma, to_learn)
model.rev_corr = rev_corr
if len(sys.argv) == 3:
#=============== Pick up and continue previous computation ============
dlog.progress("Picking up computation from %s" % sys.argv[2])
tracing.tracepoint("Copy old reults")
old_fname = sys.argv[2] + "/result.h5"
old_h5 = openFile(old_fname, 'r')
if comm.rank == 0:
# Copy old results
for node in old_h5.listNodes("/"):
name = node.name
rows = node.shape[0]
if name in [
'RF', 'gabor_params', 'gabor_errors', 'dog_params',
'dog_errors', 'dog_sigmas'
]:
continue
for r in xrange(rows):
anneal['Ncut_factor'] = [(cut_start, 0.),(cut_end, 1.)]
anneal['anneal_prior'] = anneal_prior
anneal['W_noise'] = [(noise_decrease, W_noise), (noise_end, 0.)]
anneal['pi_noise'] = [(noise_decrease, pi_noise), (noise_end, 0.)]
anneal['sigma_noise'] = [(noise_decrease, sigma_noise), (noise_end, 0.)]
anneal['partial'] = [(cut_start, partial_a), (cut_end, partial_b),
(noise_end, partial_c)]
#========================= Instantiate model ==============================
model = model_class(D, H, Hprime, gamma, to_learn)
model.rev_corr = rev_corr
if len(sys.argv) == 3:
#=============== Pick up and continue previous computation ============
dlog.progress("Picking up computation from %s" % sys.argv[2])
tracing.tracepoint("Copy old reults")
old_fname = sys.argv[2] + "/result.h5"
old_h5 = openFile(old_fname, 'r')
if comm.rank == 0:
# Copy old results
for node in old_h5.listNodes("/"):
name = node.name
rows = node.shape[0]
if name in ['RF', 'gabor_params', 'gabor_errors', 'dog_params', 'dog_errors', 'dog_sigmas']:
continue
for r in xrange(rows):
dlog.append(name, node[r])
# Extract current parameters
def M_step(self, anneal, model_params, my_suff_stat, my_data):
""" MCA M_step
my_data variables used:
my_data['y'] Datapoints
my_data['candidates'] Candidate H's according to selection func.
Annealing variables used:
anneal['T'] Temperature for det. annealing AND softmax
anneal['N_cut_factor'] 0.: no truncation; 1. trunc. according to model
"""
comm = self.comm
H, Hprime = self.H, self.Hprime
gamma = self.gamma
W = model_params['W']
pies = model_params['pi']
sigma = model_params['sigma']
# Read in data:
my_y = my_data['y']
my_cand = my_data['candidates']
my_logpj = my_suff_stat['logpj']
my_N, D = my_y.shape
N = comm.allreduce(my_N)
state_mtx = self.state_matrix # shape: (no_states, Hprime)
state_abs = self.state_abs # shape: (no_states,)
no_states = len(state_abs)
# Disable some warnings
old_seterr = np.seterr(divide='ignore', under='ignore')
# To compute et_loglike:
my_ldenom_sum = 0.0
ldenom_sum = 0.0
# Precompute
T = anneal['T']
T_rho = np.maximum(T, self.rho_T_bound)
rho = 1./(1.-1./T_rho)
rho = np.maximum(np.minimum(rho, self.rho_ubound), self.rho_lbound)
beta = 1./T
pre1 = -1./2./sigma/sigma
pil_bar = np.log( pies/(1.-pies) )
Wl = accel.log(np.abs(W))
Wrho = accel.exp(rho * Wl)
Wrhos = np.sign(W) * Wrho
Wsquared = W*W
# Some asserts
assert np.isfinite(pil_bar).all()
assert np.isfinite(Wl).all()
assert np.isfinite(Wrho).all()
assert (Wrho > 1e-86).all()
my_corr = beta*((my_logpj).max(axis=1)) # shape: (my_N,)
my_logpjb = beta*my_logpj - my_corr[:, None] # shape: (my_N, no_states)
my_pj = accel.exp(my_logpj) # shape: (my_N, no_states)
my_pjb = accel.exp(my_logpjb) # shape: (my_N, no_states)
# Precompute factor for pi update and ET cutting
A_pi_gamma = 0.; B_pi_gamma = 0.
for gp in xrange(0, self.gamma+1):
a = comb(H, gp) * pies**gp * (1.-pies)**(H-gp)
A_pi_gamma += a
B_pi_gamma += gp * a
# Truncate data
if anneal['Ncut_factor'] > 0.0:
tracing.tracepoint("M_step:truncating")
my_logdenoms = accel.log(my_pjb.sum(axis=1)) + my_corr
N_use = int(N * (1 - (1 - A_pi_gamma) * anneal['Ncut_factor']))
cut_denom = parallel.allsort(my_logdenoms)[-N_use]
my_sel, = np.where(my_logdenoms >= cut_denom)
my_N, = my_sel.shape
N_use = comm.allreduce(my_N)
else:
my_N,_ = my_y.shape
my_sel = np.arange(my_N)
N_use = N
# Allocate suff-stat arrays
my_Wp = np.zeros_like(W) # shape (H, D)
my_Wq = np.zeros_like(W) # shape (H, D)
my_pi = 0.0 #
my_sigma = 0.0 #
# Do reverse correlation if requested
if self.rev_corr:
my_y_rc = my_data['y_rc']
D_rev_corr = my_y_rc.shape[1]
my_rev_corr = np.zeros( (H,D_rev_corr) )
my_rev_corr_count = np.zeros(H)
# Iterate over all datapoints
tracing.tracepoint("M_step:iterating...")
dlog.append('N_use', N_use)
for n in my_sel:
y = my_y[n,:] # shape (D,)
cand = my_cand[n,:] # shape (Hprime,)
logpj = my_logpj[n,:] # shape (no_states,)
logpjb = my_logpjb[n,:] # shape (no_states,)
pj = my_pj[n,:] # shape (no_states,)
pjb = my_pjb[n,:] # shape (no_states,)
this_Wp = np.zeros_like(W) # numerator for W (current datapoint) (H, D)
this_Wq = np.zeros_like(W) # denominator for W (current datapoint) (H, D)
this_pi = 0.0 # numerator for pi update (current datapoint)
this_sigma = 0.0 # numerator for gamma update (current datapoint)
# Zero active hidden causes
# this_Wp += 0. # nothing to do
# this_Wq += 0. # nothing to do
# this_pi += 0. # nothing to do
this_sigma += pjb[0] * (y**2).sum()
# One active hidden cause
this_Wp += (pjb[1:(H+1),None]) * y[None, :]
this_Wq += (pjb[1:(H+1),None])
this_pi += pjb[1:(H+1)].sum()
this_sigma += (pjb[1:(H+1)] * ((W-y)**2).sum(axis=1)).sum()
# Handle hidden states with more than 1 active cause
W_ = W[cand] # is (Hprime, D)
Wl_ = Wl[cand] # is ( " ")
Wrho_ = Wrho[cand] # is ( " ")
Wrhos_ = Wrhos[cand] # is ( " ")
#Wbar = calc_Wbar(state_mtx, W_)
#Wlbar = np.log(np.abs(Wbar))
t0 = np.dot(state_mtx, Wrhos_)
Wlbar = accel.log(np.abs(t0)) / rho # is (no_states, D)
#Wlbar = np.maximum(Wlbar, -9.21)
Wbar = np.sign(t0)*accel.exp(Wlbar) # is (no_states, D)
t = Wlbar[:, None, :]-Wl_[None, :, :]
t = np.maximum(t, 0.)
Aid = state_mtx[:,:, None] * accel.exp(logpjb[H+1:,None,None] - (rho-1)*t)
Aid = Aid.sum(axis=0)
#Aid = calc_Aid(logpjb[H+1:], W_, Wl_, state_mtx, Wbar, Wlbar, rho)
#assert np.isfinite(Wlbar).all()
#assert np.isfinite(Wbar).all()
#assert np.isfinite(pjb).all()
#assert np.isfinite(Aid).all()
this_Wp[cand] += Aid * y[None, :]
this_Wq[cand] += Aid
this_pi += (pjb[1+H:] * state_abs).sum()
this_sigma += (pjb[1+H:] * ((Wbar-y)**2).sum(axis=1)).sum()
denom = pjb.sum()
my_Wp += this_Wp / denom
my_Wq += this_Wq / denom
my_pi += this_pi / denom
my_sigma += this_sigma / denom
#self.tbl.append("logpj", logpj)
#self.tbl.append("corr", my_corr[n])
#self.tbl.append("denom", denom)
#self.tbl.append("cand", cand)
#self.tbl.append("Aid", Aid)
my_ldenom_sum += accel.log(np.sum(accel.exp(logpj))) #For loglike computation
# Estimate reverse correlation
if self.rev_corr:
pys = pjb / denom
if np.isfinite(pys).all():
my_rev_corr += pys[1:H+1, None]*my_y_rc[n,None,:]
my_rev_corr_count += pys[1:H+1]
my_rev_corr[cand] += np.sum(state_mtx[:,:,None]*pys[H+1:,None,None]*my_y_rc[n,None,:], axis=0)
my_rev_corr_count[cand] += np.sum(state_mtx[:,:]*pys[H+1,None], axis=0)
else:
print "Not all finite rev_corr %d" % n
# Calculate updated W
if 'W' in self.to_learn:
tracing.tracepoint("M_step:update W")
Wp = np.empty_like(my_Wp)
Wq = np.empty_like(my_Wq)
assert np.isfinite(my_Wp).all()
assert np.isfinite(my_Wq).all()
comm.Allreduce( [my_Wp, MPI.DOUBLE], [Wp, MPI.DOUBLE] )
comm.Allreduce( [my_Wq, MPI.DOUBLE], [Wq, MPI.DOUBLE] )
# Make sure wo do not devide by zero
tiny = self.tol
Wq[Wq < tiny] = tiny
# Calculate updated W
W_new = Wp / Wq
# Add inertia depending on Wq
alpha = 2.5
inertia = np.maximum(1. - accel.exp(-Wq / alpha), 0.2)
W_new = inertia*W_new + (1-inertia)*W
else:
W_new = W
# Calculate updated pi
if 'pi' in self.to_learn:
tracing.tracepoint("M_step:update pi")
assert np.isfinite(my_pi).all()
pi_new = A_pi_gamma / B_pi_gamma * pies * comm.allreduce(my_pi) / N_use
else:
pi_new = pies
# Calculate updated sigma
if 'sigma' in self.to_learn: # TODO: XXX see LinCA XXX (merge!)
tracing.tracepoint("M_step:update sigma")
assert np.isfinite(my_sigma).all()
sigma_new = np.sqrt(comm.allreduce(my_sigma) / D / N_use)
else:
sigma_new = sigma
# Put all together and compute (always) et_approx_likelihood
ldenom_sum = comm.allreduce(my_ldenom_sum)
lAi = (H * np.log(1. - pi_new)) - ((D/2) * np.log(2*pi)) -( D * np.log(sigma_new))
# For practical and et approx reasons we use: sum of restected respons=1
loglike_et = (lAi * N_use) + ldenom_sum
if self.rev_corr:
rev_corr = np.empty_like(my_rev_corr)
rev_corr_count = np.empty_like(my_rev_corr_count)
comm.Allreduce( [my_rev_corr, MPI.DOUBLE], [rev_corr, MPI.DOUBLE])
comm.Allreduce( [my_rev_corr_count, MPI.DOUBLE], [rev_corr_count, MPI.DOUBLE])
rev_corr /= (1e-16+rev_corr_count[:,None])
else:
rev_corr = np.zeros( (H, D) )
# Restore np.seterr
np.seterr(**old_seterr)
return { 'W': W_new, 'pi': pi_new, 'sigma': sigma_new , 'rev_corr': rev_corr, 'Q':loglike_et}
def E_step(self, anneal, model_params, my_data):
""" MCA E_step
my_data variables used:
my_data['y'] Datapoints
my_data['can'] Candidate H's according to selection func.
Annealing variables used:
anneal['T'] Temperature for det. annealing AND softmax
anneal['N_cut_factor'] 0.: no truncation; 1. trunc. according to model
"""
comm = self.comm
my_y = my_data['y']
my_cand = my_data['candidates']
my_N, D = my_data['y'].shape
H = self.H
state_mtx = self.state_matrix # shape: (no_states, Hprime)
state_abs = self.state_abs # shape: (no_states,)
no_states = len(state_abs)
W = model_params['W']
pies = model_params['pi']
sigma = model_params['sigma']
# Disable some warnings
old_seterr = np.seterr(divide='ignore', under='ignore')
# Precompute
T = anneal['T']
T_rho = np.maximum(T, self.rho_T_bound)
rho = 1./(1.-1./T_rho)
rho = np.maximum(np.minimum(rho, self.rho_ubound), self.rho_lbound)
beta = 1./T
pre1 = -1./2./sigma/sigma
pil_bar = np.log( pies/(1.-pies) )
Wl = accel.log(np.abs(W))
Wrho = accel.exp(rho * Wl)
Wrhos = np.sign(W) * Wrho
# Allocate return structures
F = np.empty( [my_N, 1+H+no_states] )
# Iterate over all datapoints
tracing.tracepoint("E_step:iterating...")
for n in xrange(my_N):
y = my_y[n,:]
cand = my_cand[n,:]
# Zero active hidden causes
log_prod_joint = pre1 * (y**2).sum()
F[n,0] = log_prod_joint
# Hidden states with one active cause
log_prod_joint = pil_bar + pre1 * ((W-y)**2).sum(axis=1)
F[n,1:H+1] = log_prod_joint
# Handle hidden states with more than 1 active cause
log_prior = pil_bar * state_abs # is (no_states,)
Wrhos_ = Wrhos[cand] # is (Hprime, D)
t0 = np.dot(state_mtx, Wrhos_)
Wbar = np.sign(t0) * accel.exp(accel.log(np.abs(t0))/rho)
log_prod_joint = log_prior + pre1 * ((Wbar-y)**2).sum(axis=1)
F[n,1+H:] = log_prod_joint
assert np.isfinite(F).all()
# Restore np.seterr
np.seterr(**old_seterr)
return { 'logpj': F }