"""
Copyright 2018 Johns Hopkins University (Author: Jesus Villalba)
Apache 2.0 (http://www.apache.org/licenses/LICENSE-2.0)
"""
import numpy as np
import h5py
from scipy.special import erf
from ...hyp_defs import float_cpu
from ...utils.math import softmax, logsumexp
from ...utils.plotting import (
plot_gaussian_1D,
plot_gaussian_ellipsoid_2D,
plot_gaussian_ellipsoid_3D,
plot_gaussian_3D,
)
from ...clustering import KMeans
from .exp_family_mixture import ExpFamilyMixture
[docs]class GMMDiagCov(ExpFamilyMixture):
[docs] def __init__(
self,
mu=None,
Lambda=None,
var_floor=1e-3,
update_mu=True,
update_Lambda=True,
**kwargs
):
super().__init__(**kwargs)
self.mu = mu
self.Lambda = Lambda
self.var_floor = var_floor
self.update_mu = update_mu
self.update_Lambda = update_Lambda
self._compute_gmm_nat_std()
self._logLambda = None
self._cholLambda = None
self._Sigma = None
def _compute_gmm_nat_std(self):
if self.mu is not None and self.Lambda is not None:
self._validate_mu()
self._validate_Lambda()
self._compute_nat_params()
elif self.eta is not None:
self._validate_eta()
self.A = self.compute_A_nat(self.eta)
self._compute_std_params()
@property
def logLambda(self):
if self._logLambda is None:
self._logLambda = np.sum(np.log(self.Lambda), axis=-1)
return self._logLambda
@property
def cholLambda(self):
if self._cholLambda is None:
self._cholLambda = np.sqrt(self.Lambda)
return self._cholLambda
@property
def Sigma(self):
if self._Sigma is None:
self._Sigma = 1.0 / self.Lambda
return self._Sigma
[docs] def initialize(self, x=None):
if x is None and self.mu is None and self.eta is None:
assert self.num_comp == 1
self._initialize_stdnormal()
if x is not None:
self._initialize_kmeans(self.num_comp, x)
self.validate()
self._compute_gmm_nat_std()
def _initialize_stdnormal(self):
self.pi = np.array([1], dtype=float_cpu())
self.mu = np.zeros((1, self.x_dim), dtype=float_cpu())
self.Lambda = np.ones((1, self.x_dim), dtype=float_cpu())
def _initialize_kmeans(self, num_comp, x):
if num_comp == 1:
self.pi = np.array([1], dtype=float_cpu())
self.mu = np.mean(x, axis=0, keepdims=True)
self.Lambda = 1 / np.std(x, axis=0, keepdims=True) ** 2
return
kmeans = KMeans(num_clusters=num_comp)
loss, cluster_index = kmeans.fit(x, epochs=100)
self.mu = kmeans.mu
self.pi = np.zeros((self.num_comp,), dtype=float_cpu())
self.Lambda = np.zeros((self.num_comp, x.shape[-1]), dtype=float_cpu())
for k in range(num_comp):
r = cluster_index == k
self.pi[k] = np.sum(r) / x.shape[0]
self.Lambda[k] = 1 / np.std(x[r], axis=0) ** 2
[docs] def stack_suff_stats(self, F, S=None):
if S is None:
return F
return np.hstack((F, S))
[docs] def unstack_suff_stats(self, stats):
F = stats[:, : self.x_dim]
S = stats[:, self.x_dim :]
return F, S
[docs] def norm_suff_stats(self, N, u_x, return_order2=False):
F, S = self.unstack_suff_stats(acc_u_x)
F_norm = self.cholLambda * (F - N[:, None] * self.mu)
if return_order2:
S = S - 2 * self.mu * F + N * self.mu ** 2
S *= self.Lambda
return N, self.stack_suff_stats(F_norm, S)
return N, F_norm
[docs] def Mstep(self, N, u_x):
F, S = self.unstack_suff_stats(u_x)
if self.update_mu:
self.mu = F / N[:, None]
if self.update_Lambda:
S = S / N[:, None] - self.mu ** 2
S_floor = self.var_floor * np.mean(S[N > self.min_N], axis=0)
S = np.maximum(S, S_floor)
self.Lambda = 1 / S
self._Sigma = S
self._cholLambda = None
self._logLambda = None
if self.update_pi:
N0 = N < self.min_N
if np.any(N0):
N[N0] = 0
mu[N0] = 0
S[N0] = 1
self.pi = N / np.sum(N)
self._log_pi = None
self._compute_nat_params()
[docs] def split_comp(self, K=2):
std_dev = 1 / self.cholLambda
num_comp = self.num_comp * K
pi = np.repeat(self.pi, K) / K
Lambda = np.repeat(self.Lambda, K, axis=0) * (K ** 2)
mu = np.repeat(self.mu, K, axis=0)
if K == 2:
mu[::2] += std_dev
mu[1::2] -= std_dev
else:
for k in range(K):
factor = 2 * (np.random.uniform(size=std_dev.shape) > 0.5) - 1
mu[k::K] += factor * std_dev
config = self.get_config()
return GMMDiagCov(pi=pi, mu=mu, Lambda=Lambda, **config)
[docs] def log_prob_std(self, x):
r0 = self.log_pi + 0.5 * self.logLambda - 0.5 * self.x_dim * np.log(2 * np.pi)
llk_k = np.zeros((x.shape[0], self.num_comp), dtype=float_cpu())
for k in range(self.num_comp):
mah_dist2 = np.sum(((x - self.mu[k]) * self.cholLambda[k]) ** 2, axis=-1)
llk_k[:, k] = r0[k] - 0.5 * mah_dist2
return logsumexp(llk_k, axis=-1)
[docs] def log_cdf(self, x):
llk_k = np.zeros((x.shape[0], self.num_comp), dtype=float_cpu())
for k in range(self.num_comp):
delta = (x - self.mu[k]) * self.cholLambda[k]
lk = 0.5 * (1 + erf(delta / np.sqrt(2)))
llk_k[:, k] = self.log_pi[k] + np.sum(np.log(lk + 1e-20), axis=-1)
return logsumexp(llk_k)
[docs] def sample(self, num_samples, rng=None, seed=1024):
if rng is None:
rng = np.random.RandomState(seed)
r = rng.multinomial(1, self.pi, size=(num_samples,))
x = rng.normal(size=(num_samples, self.x_dim)).astype(float_cpu())
for k in range(self.num_comp):
index = r[:, k] == 1
x[index] = 1.0 / self.cholLambda[k] * x[index] + self.mu[k]
return x
[docs] def get_config(self):
config = {
"var_floor": self.var_floor,
"update_mu": self.update_mu,
"update_lambda": self.update_Lambda,
}
base_config = super(GMMDiagCov, self).get_config()
return dict(list(base_config.items()) + list(config.items()))
[docs] def save_params(self, f):
params = {"pi": self.pi, "mu": self.mu, "Lambda": self.Lambda}
self._save_params_from_dict(f, params)
[docs] @classmethod
def load_params(cls, f, config):
param_list = ["pi", "mu", "Lambda"]
params = self._load_params_to_dict(f, config["name"], param_list)
return cls(
x_dim=config["x_dim"],
pi=params["pi"],
mu=params["mu"],
Lambda=params["Lambda"],
var_floor=config["var_floor"],
min_N=config["min_n"],
update_pi=config["update_pi"],
update_mu=config["update_mu"],
update_Lambda=config["update_lambda"],
name=config["name"],
)
[docs] @classmethod
def load_from_kaldi(cls, file_path):
pi = None
eta1 = None
eta2 = None
num_comp = 0
x_dim = 0
success = False
with open(file_path, "r") as f:
while True:
line = f.readline()
if not line:
break
fields = line.rstrip().split()
if fields[0] == "<WEIGHTS>":
pi = np.array([float(v) for v in fields[2:-1]], dtype=float_cpu())
num_comp = len(pi)
elif fields[0] == "<MEANS_INVVARS>":
for k in range(num_comp):
line = f.readline()
fields = line.split()
if x_dim == 0:
x_dim = len(fields)
eta1 = np.zeros((num_comp, x_dim), dtype=float_cpu())
eta2 = np.zeros((num_comp, x_dim), dtype=float_cpu())
assert len(fields) == x_dim or len(fields) == x_dim + 1
eta1[k] = [float(v) for v in fields[:x_dim]]
elif fields[0] == "<INV_VARS>":
for k in range(num_comp):
line = f.readline()
fields = line.split()
assert len(fields) == x_dim or len(fields) == x_dim + 1
eta2[k] = [-0.5 * float(v) for v in fields[:x_dim]]
if k == num_comp - 1:
success = True
assert success
eta = np.hstack((eta1, eta2))
return cls(x_dim=x_dim, pi=pi, eta=eta)
def _validate_mu(self):
assert self.mu.shape[0] == self.num_comp
assert self.mu.shape[1] == self.x_dim
def _validate_Lambda(self):
assert self.Lambda.shape[0] == self.num_comp
assert self.Lambda.shape[1] == self.x_dim
assert np.all(self.Lambda > 0)
def _validate_eta(self):
assert self.eta.shape[0] == self.num_comp
assert self.eta.shape[1] == self.x_dim * 2
[docs] def validate(self):
if self.pi is not None:
self._validate_pi()
if self.mu is not None and self.Lambda is not None:
self._validate_mu()
self._validate_Lambda()
if self.eta is not None:
self._validate_eta()
[docs] @staticmethod
def compute_eta(mu, Lambda):
Lmu = Lambda * mu
eta = np.hstack((Lmu, -0.5 * Lambda))
return eta
[docs] @staticmethod
def compute_std(eta):
x_dim = int(eta.shape[-1] / 2)
eta1 = eta[:, :x_dim]
eta2 = eta[:, x_dim:]
mu = -0.5 * eta1 / eta2
Lambda = -2 * eta2
return mu, Lambda
[docs] @staticmethod
def compute_A_nat(eta):
x_dim = int(eta.shape[-1] / 2)
eta1 = eta[:, :x_dim]
eta2 = eta[:, x_dim:]
r1 = 0.5 * x_dim * np.log(2 * np.pi)
r2 = -1 / 4 * np.sum(eta1 * eta1 / eta2, axis=-1)
r3 = -1 / 2 * np.sum(np.log(-2 * eta2), axis=-1)
return r1 + r2 + r3
[docs] @staticmethod
def compute_A_std(mu, Lambda):
x_dim = mu.shape[1]
r1 = 0.5 * x_dim * np.log(2 * np.pi)
r2 = -0.5 * np.sum(np.log(Lambda), axis=-1)
r3 = 0.5 * np.sum(mu * mu * Lambda, axis=-1)
return r1 + r2 + r3
def _compute_nat_params(self):
self.eta = self.compute_eta(self.mu, self.Lambda)
self.A = self.compute_A_nat(self.eta)
def _compute_std_params(self):
self.mu, self.Lambda = self.compute_std(self.eta)
self._cholLambda = None
self._logLambda = None
self._Sigma = None
[docs] @staticmethod
def compute_suff_stats(x):
d = x.shape[-1]
u = np.zeros((x.shape[0], 2 * d), dtype=float_cpu())
u[:, :d] = x
u[:, d:] = x * x
return u
[docs] def plot1D(self, feat_idx=0, num_sigmas=2, num_pts=100, **kwargs):
mu = self.mu[:, feat_idx]
C = 1 / self.Lambda[:, feat_idx]
for k in range(mu.shape[0]):
plot_gaussian_1D(mu[k], C[k], num_sigmas, num_pts, **kwargs)
[docs] def plot2D(self, feat_idx=[0, 1], num_sigmas=2, num_pts=100, **kwargs):
mu = self.mu[:, feat_idx]
C = 1 / self.Lambda[:, feat_idx]
for k in range(mu.shape[0]):
C_k = np.diag(C[k])
plot_gaussian_ellipsoid_2D(mu[k], C_k, num_sigmas, num_pts, **kwargs)
[docs] def plot3D(self, feat_idx=[0, 1], num_sigmas=2, num_pts=100, **kwargs):
mu = self.mu[:, feat_idx]
C = 1 / self.Lambda[:, feat_idx]
for k in range(mu.shape[0]):
C_k = np.diag(C[k])
plot_gaussian_3D(mu[k], C_k, num_sigmas, num_pts, **kwargs)
[docs] def plot3D_ellipsoid(self, feat_idx=[0, 1, 2], num_sigmas=2, num_pts=100, **kwargs):
mu = self.mu[:, feat_idx]
C = 1 / self.Lambda[:, feat_idx]
for k in range(mu.shape[0]):
C_k = np.diag(C[k])
plot_gaussian_ellipsoid_3D(mu[k], C_k, num_sigmas, num_pts, **kwargs)
DiagGMM = GMMDiagCov