def log_add_by_margs(probability_distr):
tot = 0
for row in probability_distr:
tot += logsumexp(row)
return tot
def __init__(self, hist_array, labels, phasing=None, ignore_nan=False):
conv = 1e-40
# We need to noramlize the array to 1. This is hard.
# This step does the following:
# convert to log space after adding a small convolution paramter so we don't get INF and NAN
# for each mutation
# normalize the row to 1 in logspace.
hist = np.asarray(hist_array, dtype=np.float32) + conv
if (~(hist > 0)).any():
logging.error("Negative histogram bin or NAN mutation!")
if ignore_nan:
logging.warning(
"Caught ignore nan flag, not exiting, setting nan values to zero"
)
hist[np.logical_not(hist > 0)] = conv
else:
sys.exit(1)
n_samples = np.shape(hist)[1]
for sample in range(n_samples):
hist[:, :, 0] = conv ##set zero bins
self._hist_array = np.apply_over_axes(
lambda x, y: np.apply_along_axis(lambda z: z - logsumexp(z), y, x),
np.log(hist), 2)
####
self._labels = labels
self._label_ids = dict([[y, x] for x, y in enumerate(labels)])
self._phasing = {} if phasing is None else phasing
self.n_samples = np.shape(hist_array)[1]
self.n_bins = np.shape(hist_array)[-1]
def sselogsum(v):
"""
Fastest log sum exp on v array:
https://github.com/rmcgibbo/logsumexp
:param v: must be np.type32
"""
return sselogsumexp.logsumexp(v)
def sselogsum(v):
"""
Fastest log sum exp on v array:
https://github.com/rmcgibbo/logsumexp
:param v: must be np.type32
"""
return sselogsumexp.logsumexp(v)
def get_norm_marg_hist(log_sum, log_prior):
# Normalize in each dimension
log_f_LL = log_sum + log_prior
log_f_post = []
for row in log_f_LL:
log_f_post.append(row - logsumexp(row))
return np.array(log_f_post, dtype=np.float32)
def change_of_variables(x_in, y_in, x_out):
##################################################################
# Function to do a change of variables for prob density function #
##################################################################
# x_in -- list, original domain
# y_in -- list, original pdf
# x_out -- list, transformed domain (has to be same dim as x_in)
# bin x_in
delta_x_in = bin_x_and_calculate_delta(x_in)
# calculate the integral of the function over all bins and renormalize
y_in = np.array(y_in, dtype=np.float32)
# y_in = y_in - logsumexp(y_in + np.log( delta_x_in,dtype=np.float32))
# for each bin, keep integral of each bin consistent, but transform widths according to transformation
delta_x_out = bin_x_and_calculate_delta(x_out)
y_out = np.array(y_in + np.log(delta_x_in) - np.log(delta_x_out), dtype=np.float32)
return y_out - logsumexp(y_out)
def offline_changepoint_detection(data,
prior_func,
observation_log_likelihood_function,
truncate=-np.inf):
"""Compute the likelihood of changepoints on data.
Keyword arguments:
data -- the time series data
prior_func -- a function given the likelihood of a changepoint given the distance to the last one
observation_log_likelihood_function -- a function giving the log likelihood
of a data part
truncate -- the cutoff probability 10^truncate to stop computation for that changepoint log likelihood
P -- the likelihoods if pre-computed
"""
n = len(data)
Q = np.zeros((n, ))
g = np.zeros((n, ))
G = np.zeros((n, ))
P = np.ones((n, n)) * -np.inf
# save everything in log representation
for t in range(n):
g[t] = np.log(prior_func(t))
if t == 0:
G[t] = g[t]
else:
G[t] = np.logaddexp(G[t - 1], g[t])
P[n - 1, n - 1] = observation_log_likelihood_function(data, n - 1, n)
Q[n - 1] = P[n - 1, n - 1]
for t in reversed(range(n - 1)):
P_next_cp = -np.inf # == log(0)
for s in range(t, n - 1):
P[t, s] = observation_log_likelihood_function(data, t, s + 1)
# compute recursion
summand = P[t, s] + Q[s + 1] + g[s + 1 - t]
P_next_cp = np.logaddexp(P_next_cp, summand)
# truncate sum to become approx. linear in time (see
# Fearnhead, 2006, eq. (3))
if summand - P_next_cp < truncate:
break
P[t, n - 1] = observation_log_likelihood_function(data, t, n)
# (1 - G) is numerical stable until G becomes numerically 1
if G[n - 1 - t] < -1e-15: # exp(-1e-15) = .99999...
antiG = np.log(1 - np.exp(G[n - 1 - t]))
else:
# (1 - G) is approx. -log(G) for G close to 1
antiG = np.log(-G[n - 1 - t])
Q[t] = np.logaddexp(P_next_cp, P[t, n - 1] + antiG)
Pcp = np.ones((n - 1, n - 1)) * -np.inf
for t in range(n - 1):
Pcp[0, t] = P[0, t] + Q[t + 1] + g[t] - Q[0]
if np.isnan(Pcp[0, t]):
Pcp[0, t] = -np.inf
for j in range(1, n - 1):
for t in range(j, n - 1):
tmp_cond = Pcp[j - 1, j -
1:t] + P[j:t + 1,
t] + Q[t + 1] + g[0:t - j + 1] - Q[j:t + 1]
Pcp[j, t] = logsumexp(tmp_cond.astype(np.float32))
if np.isnan(Pcp[j, t]):
Pcp[j, t] = -np.inf
return Q, P, Pcp
def offline_changepoint_detection(data, prior_func,
observation_log_likelihood_function,
truncate=-np.inf):
"""Compute the likelihood of changepoints on data.
Keyword arguments:
data -- the time series data
prior_func -- a function given the likelihood of a changepoint given the distance to the last one
observation_log_likelihood_function -- a function giving the log likelihood
of a data part
truncate -- the cutoff probability 10^truncate to stop computation for that changepoint log likelihood
P -- the likelihoods if pre-computed
"""
n = len(data)
Q = np.zeros((n,))
g = np.zeros((n,))
G = np.zeros((n,))
P = np.ones((n, n)) * -np.inf
# save everything in log representation
for t in range(n):
g[t] = np.log(prior_func(t))
if t == 0:
G[t] = g[t]
else:
G[t] = np.logaddexp(G[t-1], g[t])
P[n-1, n-1] = observation_log_likelihood_function(data, n-1, n)
Q[n-1] = P[n-1, n-1]
for t in reversed(range(n-1)):
P_next_cp = -np.inf # == log(0)
for s in range(t, n-1):
P[t, s] = observation_log_likelihood_function(data, t, s+1)
# compute recursion
summand = P[t, s] + Q[s + 1] + g[s + 1 - t]
P_next_cp = np.logaddexp(P_next_cp, summand)
# truncate sum to become approx. linear in time (see
# Fearnhead, 2006, eq. (3))
if summand - P_next_cp < truncate:
break
P[t, n-1] = observation_log_likelihood_function(data, t, n)
# (1 - G) is numerical stable until G becomes numerically 1
if G[n-1-t] < -1e-15: # exp(-1e-15) = .99999...
antiG = np.log(1 - np.exp(G[n-1-t]))
else:
# (1 - G) is approx. -log(G) for G close to 1
antiG = np.log(-G[n-1-t])
Q[t] = np.logaddexp(P_next_cp, P[t, n-1] + antiG)
Pcp = np.ones((n-1, n-1)) * -np.inf
for t in range(n-1):
Pcp[0, t] = P[0, t] + Q[t + 1] + g[t] - Q[0]
if np.isnan(Pcp[0, t]):
Pcp[0, t] = -np.inf
for j in range(1, n-1):
for t in range(j, n-1):
tmp_cond = Pcp[j-1, j-1:t] + P[j:t+1, t] + Q[t + 1] + g[0:t-j+1] - Q[j:t+1]
Pcp[j, t] = logsumexp(tmp_cond.astype(np.float32))
if np.isnan(Pcp[j, t]):
Pcp[j, t] = -np.inf
return Q, P, Pcp
def normalize_loghist_with_prior(self, loghist):
# Normalize in each dimension
return np.apply_along_axis(lambda x: x - logsumexp(x), 1, loghist + self.logprior)
def logsum_of_marginals_per_sample(loghist):
return np.apply_along_axis(lambda x: logsumexp(x), 1, np.array(loghist, dtype=np.float32))
def logsum_of_marginals(loghist):
return np.sum(np.apply_along_axis(lambda x: logsumexp(x), 1, loghist))
def _normalize_loghist_with_prior(self, loghist):
""" Normalize in each dimension in log space """
loghist = np.asarray(loghist, dtype=np.float32)
return np.apply_along_axis(lambda x: x - logsumexp(x), 1,
loghist + self._logprior)
def offline_changepoint_detection(data,
prior_function,
log_likelihood_class,
truncate: int = -40):
"""
Compute the likelihood of changepoints on data.
Parameters:
data -- the time series data
truncate -- the cutoff probability 10^truncate to stop computation for that changepoint log likelihood
Outputs:
P -- the log-likelihood of a datasequence [t, s], given there is no changepoint between t and s
Q -- the log-likelihood of data
Pcp -- the log-likelihood that the i-th changepoint is at time step t. To actually get the probility of a changepoint at time step t sum the probabilities.
"""
# Set up the placeholders for each parameter
n = len(data)
Q = np.zeros((n, ))
g = np.zeros((n, ))
G = np.zeros((n, ))
P = np.ones((n, n)) * -np.inf
# save everything in log representation
for t in range(n):
g[t] = prior_function(t)
if t == 0:
G[t] = g[t]
else:
G[t] = np.logaddexp(G[t - 1], g[t])
P[n - 1, n - 1] = log_likelihood_class.pdf(data, t=n - 1, s=n)
Q[n - 1] = P[n - 1, n - 1]
for t in reversed(range(n - 1)):
P_next_cp = -np.inf # == log(0)
for s in range(t, n - 1):
P[t, s] = log_likelihood_class.pdf(data, t=t, s=s + 1)
# compute recursion
summand = P[t, s] + Q[s + 1] + g[s + 1 - t]
P_next_cp = np.logaddexp(P_next_cp, summand)
# truncate sum to become approx. linear in time (see
# Fearnhead, 2006, eq. (3))
if summand - P_next_cp < truncate:
break
P[t, n - 1] = log_likelihood_class.pdf(data, t=t, s=n)
# (1 - G) is numerical stable until G becomes numerically 1
if G[n - 1 - t] < -1e-15: # exp(-1e-15) = .99999...
antiG = np.log(1 - np.exp(G[n - 1 - t]))
else:
# (1 - G) is approx. -log(G) for G close to 1
antiG = np.log(-G[n - 1 - t])
Q[t] = np.logaddexp(P_next_cp, P[t, n - 1] + antiG)
Pcp = np.ones((n - 1, n - 1)) * -np.inf
for t in range(n - 1):
Pcp[0, t] = P[0, t] + Q[t + 1] + g[t] - Q[0]
if np.isnan(Pcp[0, t]):
Pcp[0, t] = -np.inf
for j in range(1, n - 1):
for t in range(j, n - 1):
tmp_cond = (Pcp[j - 1, j - 1:t] + P[j:t + 1, t] + Q[t + 1] +
g[0:t - j + 1] - Q[j:t + 1])
Pcp[j, t] = logsumexp(tmp_cond.astype(np.float32))
if np.isnan(Pcp[j, t]):
Pcp[j, t] = -np.inf
return Q, P, Pcp