def init_with_logreg(self, scores, same_spk, valid, ptar, std_for_mats=0):
scores = scores[valid]
labels = same_spk[valid]
tar = scores[labels==1]
non = scores[labels==0]
a, b = calibration.logregCal(tar, non, ptar, return_params=True)
if self.is_durdep:
# Dur-dep calibration (might also have an si-dependent stage)
self.durdep_alpha.init_with_constant(a, std_for_mats)
self.durdep_beta.init_with_constant(b, std_for_mats)
if self.is_sidep:
self.sidep_alpha.init_with_constant(1.0, std_for_mats)
self.sidep_beta.init_with_constant(0.0, std_for_mats)
elif not self.is_sidep:
# Global calibration
utils.replace_state_dict(self, {'alpha': a, 'beta': b})
else:
# Only si-dependent cal
self.sidep_alpha.init_with_constant(a, std_for_mats)
self.sidep_beta.init_with_constant(b, std_for_mats)
def init_with_lda(self, x, class_ids, init_params, complement=True, sec_ids=None, gaussian_backend=False):
if self.has_bias is False:
raise Exception("Cannot initialize this component with init_with_lda because it was created with bias=False")
weights = compute_class_weights(class_ids, sec_ids, init_params.get('balance_by_domain'))
BCov, WCov, GCov, mu, mu_per_class, _ = compute_lda_model(x, class_ids, weights)
if gaussian_backend:
W = linalg.solve(WCov, mu_per_class.T, sym_pos=True)
b = - 0.5 * (W * mu_per_class.T).sum(0)
else:
evals, evecs = linalg.eigh(BCov, WCov)
evecs = evecs[:, np.argsort(evals)[::-1]]
lda_dim = self.W.shape[1]
if complement:
W = evecs[:,:lda_dim]
else:
W = evecs[:,-lda_dim:]
# Normalize each dimension so that output features will have variance 1.0
if init_params.get('variance_norm_lda', True):
W = W @ (np.diag(1. / np.sqrt(np.diag(W.T @ GCov @ W))))
# Finally, estimate the shift so that output features have mean 0.0
mu = mu @ W
b = -mu
utils.replace_state_dict(self, {'W': W, 'b': b})
def init_with_constant(self, k, std_for_mats=0):
# Initialize k with a given value and, optionally, the
# L G and C matrices with a normal
utils.replace_state_dict(self, {'k': k})
if std_for_mats>0:
nn.init.normal_(self.L, 0.0, std_for_mats)
nn.init.normal_(self.G, 0.0, std_for_mats)
nn.init.normal_(self.C, 0.0, std_for_mats)
def init_with_plda(self, x, speaker_ids, init_params, domain_ids=None):
# Compute a PLDA model with the input data, approximating the
# model with just the usual initialization without the EM iterations
weights = compute_class_weights(speaker_ids, domain_ids,
init_params.get('balance_by_domain'))
# Debugging of weight usage in PLDA:
# Repeat the data from the first 5000 speakers twice either explicitely or through the weights
# These two models should be identical (and they are!)
#sela = speaker_ids<5000
#selb = speaker_ids>=5000
#x2 = np.concatenate([x[sela],x[sela],x[selb]])
#speaker_ids2 = np.concatenate((speaker_ids[sela], speaker_ids[sela]+np.max(speaker_ids)+1, speaker_ids[selb]))
#weights2 = np.ones(len(np.unique(speaker_ids2)))
#BCov2, WCov2, mu2 = compute_2cov_plda_model(x2, speaker_ids2, weights2, 10)
#weights3 = weights.copy()
#weights3[0:5000] *= 2
#BCov3, WCov3, mu3 = compute_2cov_plda_model(x, speaker_ids, weights3, 10)
#assert np.allclose(BCov2,BCov3)
#assert np.allclose(WCov2,WCov3)
#assert np.allclose(mu2, mu3)
# Bi and Wi are the between and within covariance matrices and mu is the global (weighted) mean
Bi, Wi, mu = compute_2cov_plda_model(x, speaker_ids, weights,
init_params.get('plda_em_its', 0))
# Equations (14) and (16) in Cumani's paper
# Note that the paper has an error in the formula for k (a 1/2 missing before k_tilde)
# that is fixed in the equations below
# To compute L_tild and G_tilde we use the following equality:
# inv( inv(C) + n*inv(D) ) == C @ inv(D + n*C) @ D == C @ solve(D + n*C, D)
B = utils.CholInv(Bi)
W = utils.CholInv(Wi)
Bmu = B @ mu.T
L_tilde = Bi @ np.linalg.solve(Wi + 2 * Bi, Wi)
G_tilde = Bi @ np.linalg.solve(Wi + Bi, Wi)
WtGL = W @ (L_tilde - G_tilde)
logdet_L_tilde = np.linalg.slogdet(L_tilde)[1]
logdet_G_tilde = np.linalg.slogdet(G_tilde)[1]
logdet_B = B.logdet()
k_tilde = -2.0 * logdet_G_tilde + logdet_L_tilde - logdet_B + mu @ Bmu
k = 0.5 * k_tilde + 0.5 * Bmu.T @ (L_tilde - 2 * G_tilde) @ Bmu
L = 0.5 * (W @ (W @ L_tilde)).T
G = 0.5 * (W @ WtGL).T
C = (WtGL @ Bmu)
state_dict = {'L': L, 'G': G, 'C': C, 'k': k.squeeze()}
utils.replace_state_dict(self, state_dict)
def init_with_plda(self, x, speaker_ids, init_params, domain_ids=None):
# Compute a PLDA model with the input data, approximating the
# model with just the usual initialization without the EM iterations
# Get the within and between-class covariance matrices
# WCov is the covariance of the noise term in SPLDA and BCov = inverse(V V^t)
weights = compute_sample_weights(speaker_ids, domain_ids, init_params)
BCov, WCov, _, mu, _ = compute_lda_model(x, speaker_ids, weights)
Binv = np.linalg.inv(BCov)
Winv = np.linalg.inv(WCov)
# Equations (14) and (16) in Cumani's paper
# Note that the paper has a couple of errors in the derivations, in the k_tilde formula and in k
# that are fixed in the equations below
Bmu = np.dot(Binv,mu)
L_tilde = np.linalg.inv(Binv+2*Winv)
G_tilde = np.linalg.inv(Binv+Winv)
WtGL = np.dot(Winv.T,L_tilde-G_tilde)
_, logdet_L_tilde = np.linalg.slogdet(L_tilde)
_, logdet_G_tilde = np.linalg.slogdet(G_tilde)
_, logdet_Binv = np.linalg.slogdet(Binv)
k_tilde = -2.0*logdet_G_tilde - logdet_Binv + logdet_L_tilde + np.dot(mu.T, Bmu)
k = 0.5 * k_tilde + 0.5 * np.dot(Bmu.T, np.dot(G_tilde - 2*L_tilde, Bmu))
L = 0.5 * np.dot(Winv.T,np.dot(L_tilde,Winv))
G = 0.5 * np.dot(WtGL,Winv)
C = np.dot(WtGL,Bmu)[:,np.newaxis]
if init_params.get('norm_plda_params'):
# Divide all params by k so that we get rid of that scale at init
# It will be compensated by the calibration params anyway. This is to make
# the params more comparable across different initializations so that
# regularization works similarly.
L /= k
G /= k
C /= k
k = 1.0
state_dict = {'L': L, 'G': G, 'C': C, 'k': k}
utils.replace_state_dict(self, state_dict)
def init_with_weighted_means(self, data, weights):
Wl = list()
for i in np.arange(self.W.shape[0]):
Wl.append(np.dot(data.T, weights[:,i])/np.sum(weights[:,i]))
utils.replace_state_dict(self, {'W': np.c_[Wl]})
def init_with_constant(self, k, std_for_mats=0):
# Initialize k with a given value and, optionally, the
# L G and C matrices with a normal
if std_for_mats>0:
self.init_random(std_for_mats)
utils.replace_state_dict(self, {'k': k})
def init_with_weighted_means(self, data, weights):
Wl = list()
for w in weights.T:
Wl.append(np.dot(data.T, w) / np.sum(w))
utils.replace_state_dict(self, {'W': np.c_[Wl].T})
