""" Sampling history for MCMC. MCMC keeps track of a number of things during sampling. The results may be queried as follows:: draws, generation, thinning sample(condition) returns draws, points, logp logp() returns draws, logp acceptance_rate() returns draws, AR chains() returns draws, chains, logp CR_weight() returns draws, CR_weight best() returns best_x, best_logp outliers() returns outliers show()/save(file)/load(file) Data is stored in circular arrays, which keeps the last N generations and throws the rest away. draws is the total number of draws from the sampler. generation is the total number of generations. thinning is the number of generations per stored sample. draws[i] is the number of draws including those required to produce the information in the corresponding return vector. Note that draw numbers need not be linearly spaced, since techniques like delayed rejection will result in a varying number of samples per generation. logp[i] is the set of log likelihoods, one for each member of the population. The logp() method returns the complete set, and the sample() method returns a thinned set, with on element of logp[i] for each vector point[i, :]. AR[i] is the acceptance rate at generation i, showing the proportion of proposed points which are accepted into the population. chains[i, :, :] is the set of points in the differential evolution population at thinned generation i. Ideally, the thinning rate of the MCMC process is chosen so that thinned generations i and i+1 are independent samples from the posterior distribution, though there is a chance that this may not be the case, and indeed, some points in generation i+1 may be identical to those in generation i. Actual generation number is i*thinning. points[i, :] is the ith point in a returned sample. The i is just a place holder; there is no inherent ordering to the sample once they have been extracted from the chains. Note that the sample may be from a marginal distribution. R[i] is the Gelman R statistic measuring convergence of the Markov chain. CR_weight[i] is the set of weights used for selecting between the crossover ratios available to the candidate generation process of differential evolution. These will be fixed early in the sampling, even when adaptive differential evolution is selected. outliers[i] is a vector containing the thinned generation number at which an outlier chain was removed, the id of the chain that was removed and the id of the chain that replaced it. We leave it to the reader to decide if the cloned samples, point[:generation, :, removed_id], should be included in further analysis. best_logp is the highest log likelihood observed during the analysis and best_x is the corresponding point at which it was observed. generation is the last generation number """ #TODO: state should be collected in files as we go from __future__ import division, print_function __all__ = ['MCMCDraw', 'load_state', 'save_state'] import os.path import re import gzip import numpy as np from numpy import empty, sum, asarray, inf, argmax, hstack, dstack from numpy import savetxt, reshape from .convergence import burn_point from .outliers import identify_outliers from .util import draw, rng from .gelman import gelman EXT = ".mc.gz" CREATE = gzip.open #EXT = ".mc" #CREATE = open # CRUFT: python 2 uses bytes rather than unicode for strings try: # python 2.x unicode def write(fid, s): fid.write(s) except NameError: # python 3.x def write(fid, s): fid.write(s.encode('utf-8') if isinstance(s, str) else s) class NoTrace: def write(self, data): pass def flush(self): pass def close(self): pass def save_state(state, filename): trace = NoTrace() #trace = open(filename+"-trace.mc", "w") write(trace, "starting trace\n") # Build 2-D data structures write(trace, "extracting draws, logp\n") draws, logp = state.logp(full=True) write(trace, "extracting acceptance rate\n") _, AR = state.acceptance_rate() write(trace, "building chain from draws, AR and logp\n") chain = hstack((draws[:, None], AR[:, None], logp)) write(trace, "extracting point, logp\n") _, point, logp = state.chains() Nthin, Npop, Nvar = point.shape write(trace, "shape is %d,%d,%d\n" % (Nthin, Npop, Nvar)) write(trace, "adding logp to point\n") point = dstack((logp[:, :, None], point)) write(trace, "collapsing to draws x point\n") point = reshape(point, (point.shape[0]*point.shape[1], point.shape[2])) write(trace, "extracting CR_weight\n") draws, CR_weight = state.CR_weight() Nupdate, Ncr = CR_weight.shape write(trace, "building stats\n") stats = hstack((draws[:, None], CR_weight)) #TODO: missing _outliers from save_state # Write convergence info write(trace, "writing chain\n") fid = CREATE(filename+'-chain'+EXT, 'wb') write(fid, '# draws acceptance_rate %d*logp\n' % Npop) savetxt(fid, chain) fid.close() # Write point info write(trace, "writing point\n") fid = CREATE(filename+'-point'+EXT, 'wb') write(fid, '# logp point (Nthin x Npop x Nvar = [%d,%d,%d])\n' % (Nthin, Npop, Nvar)) savetxt(fid, point) fid.close() # Write stats write(trace, "writing stats\n") fid = CREATE(filename+'-stats'+EXT, 'wb') write(fid, '# draws %d*CR_weight\n' % Ncr) savetxt(fid, stats) fid.close() write(trace, "done state save\n") trace.close() IND_PAT = re.compile('-1#IND') INF_PAT = re.compile('1#INF') def loadtxt(file, report=0): """ Like numpy loadtxt, but adapted for windows non-finite numbers. """ if not hasattr(file, 'readline'): if file.endswith('.gz'): #print("opening with gzip") fh = gzip.open(file, 'rt') else: fh = open(file, 'rt') else: fh = file res = [] section = 0 lineno = 0 for line in fh: lineno += 1 if report and lineno%report == 0: print("read", section*report) section += 1 IND_PAT.sub('nan', line) INF_PAT.sub('inf', line) line = line.split('#')[0].strip() values = line.split() if len(values) > 0: try: res.append([float(v) for v in values]) except ValueError: print("Parse error:", values) if fh != file: fh.close() return asarray(res) def path_contains_saved_state(filename): chain_file = filename + '-chain' + EXT return os.path.exists(chain_file) def openmc(filename): if filename.endswith('.gz'): if os.path.exists(filename): #print("opening with gzip") fh = gzip.open(filename, 'rt') elif os.path.exists(filename[:-3]): fh = open(filename[:-3], 'rt') else: raise RuntimeError("file %s does not exist"%filename) else: if os.path.exists(filename): fh = open(filename, 'rt') elif os.path.exists(filename+".gz"): #print("opening with gzip") fh = gzip.open(filename+".gz", 'rt') else: raise RuntimeError("file %s does not exist"%filename) return fh def load_state(filename, skip=0, report=0, derived_vars=0): # Read chain file with openmc(filename+'-chain'+EXT) as fid: chain = loadtxt(fid) # Read point file with openmc(filename+'-point'+EXT) as fid: line = fid.readline() point_dims = line[line.find('[')+1:line.find(']')] Nthin, Npop, Nvar = eval(point_dims) for _ in range(skip*Npop): fid.readline() point = loadtxt(fid, report=report*Npop) # Read stats file with openmc(filename+'-stats'+EXT) as fd: stats_header = fd.readline() stats = loadtxt(fd) # Determine number of R-stat stored in the stats file if 'R-stat' in stats_header: # Old header looks like: # # draws {Nvar}*R-stat {Ncr}*CR_weight # however, number of R-stat stored in stats file is the number of # variables stored each generation, not including the derived variables # calculated after the MCMC has completed. num_r = int(stats_header.split('*')[0].split()[-1]) - derived_vars else: num_r = 0 # Guess dimensions Ngen = chain.shape[0] thinning = 1 Nthin -= skip Nupdate = stats.shape[0] # Create empty draw and fill it with loaded data state = MCMCDraw(0, 0, 0, 0, 0, 0, thinning) #print("gen, var, pop", Ngen, Nvar, Npop) state.draws = Ngen * Npop state.generation = Ngen state._gen_index = 0 state._gen_draws = chain[:, 0] state._gen_acceptance_rate = chain[:, 1] state._gen_logp = chain[:, 2:] state.thinning = thinning state._thin_count = Ngen//thinning state._thin_index = 0 state._thin_draws = state._gen_draws[(skip+1)*thinning-1::thinning] state._thin_logp = point[:, 0].reshape((Nthin, Npop)) state._thin_point = reshape(point[:, 1:Nvar+1-derived_vars], (Nthin, Npop, -1)) state._gen_current = state._thin_point[-1].copy() state._update_count = Nupdate state._update_index = 0 state._update_draws = stats[:, 0] state._update_CR_weight = stats[:, 1+num_r:] state._outliers = [] bestidx = np.argmax(point[:, 0]) state._best_logp = point[bestidx, 0] state._best_x = point[bestidx, 1:Nvar+1-derived_vars] state._best_gen = 0 return state class MCMCDraw(object): """ """ _labels = None _integer_vars = None # boolean array of integer variables, or None title = None def __init__(self, Ngen, Nthin, Nupdate, Nvar, Npop, Ncr, thinning): # Total number of draws so far self.draws = 0 # Maximum observed likelihood self._best_x = None self._best_logp = -inf self._best_gen = 0 # Per generation iteration self.generation = 0 self._gen_index = 0 self._gen_draws = empty(Ngen, 'i') self._gen_logp = empty((Ngen, Npop)) self._gen_acceptance_rate = empty(Ngen) # If we are thinning, we need to keep the current generation # separately. [Note: don't remember why we need both the _gen_* # and _thin_*] [Note: the caller x vector is assigned to # _gen_current; this may lead to unexpected behaviour if x is # changed by the caller. self._gen_current = None # Per thinned generation iteration self.thinning = thinning self._thin_index = 0 self._thin_count = 0 self._thin_timer = 0 self._thin_draws = empty(Nthin, 'i') self._thin_point = empty((Nthin, Npop, Nvar)) self._thin_logp = empty((Nthin, Npop)) # Per update iteration self._update_index = 0 self._update_count = 0 self._update_draws = empty(Nupdate, 'i') self._update_CR_weight = empty((Nupdate, Ncr)) self._outliers = [] # Query functions will not return outlier chains; initially, all # chains are marked as good. Call mark_outliers to remove # outlier chains from the set. self._good_chains = slice(None, None) @property def Ngen(self): return self._gen_draws.shape[0] @property def Nsamples(self): return self._gen_logp.size @property def Nthin(self): return self._thin_draws.shape[0] @property def Nupdate(self): return self._update_draws.shape[0] @property def Nvar(self): """Number of parameters in the fit""" return self._thin_point.shape[2] @property def Npop(self): return self._gen_logp.shape[1] @property def Ncr(self): return self._update_CR_weight.shape[1] def resize(self, Ngen, Nthin, Nupdate, Nvar, Npop, Ncr, thinning): if self.Nvar != Nvar or self.Npop != Npop or self.Ncr != Ncr: raise ValueError("Cannot change Nvar, Npop or Ncr on resize") # For now, only handle the case where the we have one complete # frame of data, such as on reloading the state vector assert (self._gen_index == 0 and self._update_index == 0 and self._thin_index == 0) assert (self.generation == self.Ngen and self._update_count == self.Nupdate and self._thin_count == self.Nthin) self.thinning = thinning if Ngen > self.Ngen: self._gen_index = self.Ngen # must happen before resize!! self._gen_draws = np.resize(self._gen_draws, Ngen) self._gen_logp = np.resize(self._gen_logp, (Ngen, Npop)) self._gen_acceptance_rate \ = np.resize(self._gen_acceptance_rate, Ngen) elif Ngen < self.Ngen: self._gen_draws = self._gen_draws[-Ngen:].copy() self._gen_logp = self._gen_logp[-Ngen:, :].copy() self._gen_acceptance_rate \ = self._gen_acceptance_rate[-Ngen:].copy() if Nthin > self.Nthin: self._thin_index = self.Nthin # must happen before resize!! self._thin_draws = np.resize(self._thin_draws, Nthin) self._thin_point = np.resize(self._thin_point, (Nthin, Npop, Nvar)) self._thin_logp = np.resize(self._thin_logp, (Nthin, Npop)) elif Nthin < self.Nthin: self._thin_draws = self._thin_draws[-Nthin:].copy() self._thin_point = self._thin_point[-Nthin:, :, :].copy() self._thin_logp = self._thin_logp[-Nthin:, :].copy() if Nupdate > self.Nupdate: self._update_count = self.Nupdate # must happen before resize!! self._update_draws = np.resize(self._update_draws, Nupdate) self._update_CR_weight \ = np.resize(self._update_CR_weight, (Nupdate, Ncr)) elif Nupdate < self.Nupdate: self._update_draws = self._update_draws[-Nupdate:].copy() self._update_CR_weight = self._update_CR_weight[-Nupdate:, :].copy() def save(self, filename): save_state(self, filename) def trim_portion(self): index = burn_point(self) portion = 1 - (index/self.Ngen) if index >= 0 else 0.5 return portion def show(self, portion=1.0, figfile=None): from .views import plot_all plot_all(self, portion=portion, figfile=figfile) def _last_gen(self): """ Returns x, logp for most recent generation to dream.py. """ # Note: if generation number has wrapped and _gen_index is 0 # (the usual case when this function is called to resume an # existing chain), then this returns the last row in the array. return (self._thin_point[self._thin_index-1], self._thin_logp[self._thin_index-1]) def _generation(self, new_draws, x, logp, accept, force_keep=False): """ Called from dream.py after each generation is completed with a set of accepted points and their values. """ # Keep track of the total number of draws # Note: this is first so that we tag the record with the number of # draws taken so far, including the current draw. self.draws += new_draws self.generation += 1 # Record if this is the best so far maxid = argmax(logp) if logp[maxid] > self._best_logp: self._best_logp = logp[maxid] self._best_x = x[maxid, :]+0 # Force a copy self._best_gen = self.generation #print("new best", logp[maxid], self.generation) # Record acceptance rate and cost i = self._gen_index #print("generation", i, self.draws, "\n x", x, "\n logp", logp, "\n accept", accept) self._gen_draws[i] = self.draws self._gen_acceptance_rate[i] = 100*sum(accept)/new_draws self._gen_logp[i] = logp i = i+1 if i == len(self._gen_draws): i = 0 self._gen_index = i # Keep every nth iteration self._thin_timer += 1 if self._thin_timer == self.thinning or force_keep: self._thin_timer = 0 self._thin_count += 1 i = self._thin_index self._thin_draws[i] = self.draws self._thin_point[i] = x self._thin_logp[i] = logp i = i+1 if i == len(self._thin_draws): i = 0 self._thin_index = i self._gen_current = x+0 # force a copy else: self._gen_current = x+0 # force a copy def _update(self, CR_weight): """ Called from dream.py when a series of DE steps is completed and summary statistics/adaptations are ready to be stored. """ self._update_count += 1 i = self._update_index #print("update", i, self.draws, "\n CR weight", CR_weight) self._update_draws[i] = self.draws self._update_CR_weight[i] = CR_weight i = i+1 if i == len(self._update_draws): i = 0 self._update_index = i @property def labels(self): if self._labels is None: return ["P%d"%i for i in range(self._thin_point.shape[2])] else: return self._labels @labels.setter def labels(self, v): self._labels = v def _draw_pop(self): """ Return the current population. """ return self._gen_current def _draw_large_pop(self, Npop): _, chains, _ = self.chains() Ngen, Nchain, Nvar = chains.shape points = reshape(chains, (Ngen*Nchain, Nvar)) # There are two complications with the history buffer: # (1) due to thinning, not every generation is stored # (2) because it is circular, the cursor may be in the middle # If the current generation isn't in the buffer (but is instead # stored separately as _gen_current), then the entire buffer # becomes the history pool. # otherwise we need to exclude the current generation from # the pool. If (2) happens, we need to increment everything # above the cursor by the number of chains. if self._gen_current is not None: pool_size = Ngen*Nchain cursor = pool_size # infinite else: pool_size = (Ngen-1)*Nchain k = len(self._thin_draws) cursor = Nchain*((k+self._thin_index-1)%k) # Make a return population and fill it with the current generation pop = empty((Npop, Nvar), 'd') if self._gen_current is not None: pop[:Nchain] = self._gen_current else: #print(pop.shape, points.shape, chains.shape) pop[:Nchain] = points[cursor:cursor+Nchain] if Npop > Nchain: # Find the remainder with unique ancestors. # Again, because this is a circular buffer, their may be random # numbers generated at or above the cursor. All of these must # be shifted by Nchains to avoid the cursor. perm = draw(Npop-Nchain, pool_size) perm[perm >= cursor] += Nchain #print("perm", perm; raw_input('wait')) pop[Nchain:] = points[perm] return pop def _unroll(self): """ Unroll the circular queue so that data access can be done inplace. Call this when done stepping, and before plotting. Calls to logp, sample, etc. assume the data is already unrolled. """ if self.generation > self._gen_index > 0: self._gen_draws[:] = np.roll(self._gen_draws, -self._gen_index, axis=0) self._gen_logp[:] = np.roll(self._gen_logp, -self._gen_index, axis=0) self._gen_acceptance_rate[:] = np.roll(self._gen_acceptance_rate, -self._gen_index, axis=0) self._gen_index = 0 if self._thin_count > self._thin_index > 0: self._thin_draws[:] = np.roll(self._thin_draws, -self._thin_index, axis=0) self._thin_point[:] = np.roll(self._thin_point, -self._thin_index, axis=0) self._thin_logp[:] = np.roll(self._thin_logp, -self._thin_index, axis=0) self._thin_index = 0 if self._update_count > self._update_index > 0: self._update_draws[:] = np.roll(self._update_draws, -self._update_index, axis=0) self._update_CR_weight[:] = np.roll(self._update_CR_weight, -self._update_index, axis=0) self._update_index = 0 def remove_outliers(self, x, logp, test='IQR'): """ Replace outlier chains with clones of good ones. This should happen early in the sampling processes so the clones have an opportunity to evolve their own identity. Only the head of the chain is modified. *state* contains the chains, with log likelihood for each point. *x*, *logp* are the current population and the corresponding log likelihoods; these are updated with cloned chain values. *test* is the name of the test to use (one of IQR, Grubbs, Mahal or none). See :func:`.outliers.identify_outliers` for details. Updates *state*, *x* and *logp* to reflect the changes. Returns a list of the outliers that were removed. """ # Grab the last part of the chain histories _, chains = self.logp() chain_len, Nchains = chains.shape outliers = identify_outliers(test, chains, x) #if len(outliers): print("old llf", logp[outliers]) # Loop over each outlier chain, replacing each with another for old in outliers: # Draw another chain at random, with replacement # TODO: consider using relative likelihood as a weight factor while True: new = rng.randint(Nchains) if new not in outliers: break # Update the saved state and current population self._replace_outlier(old=old, new=new) x[old, :] = x[new, :] logp[old] = logp[new] #if len(outliers): print("new llf", logp[outliers]) return outliers def _replace_outlier(self, old, new): """ Called from outliers.py when a chain is replaced by the clone of another. """ self._outliers.append((self._thin_index, old, new)) # 2017-10-06 [PAK] only replace the head, not the full chain index = self._gen_index self._gen_current[old] = self._gen_current[new] self._gen_logp[index, old] = self._gen_logp[index, new] self._thin_logp[index, old] = self._thin_logp[index, new] self._thin_point[index, old, :] = self._thin_point[index, new, :] def mark_outliers(self, test='IQR', portion=1.0): """ Mark some chains as outliers but don't remove them. This can happen after drawing is complete, so that chains that did not converge are not included in the statistics. *test* is 'IQR', 'Mahol' or 'none'. *portion* indicates what portion of the samples should be included in the outlier test. The default is to include all of them. """ _, chains, logp = self.chains() if test == 'none': self._good_chains = slice(None, None) else: Ngen = chains.shape[0] start = int(Ngen*(1-portion)) if portion else 0 outliers = identify_outliers(test, logp[start:], chains[-1]) #print("outliers", outliers) #print(logp.shape, chains.shape) if len(outliers) > 0: self._good_chains = np.array([i for i in range(logp.shape[1]) if i not in outliers]) else: self._good_chains = slice(None, None) #print(self._good_chains) def logp(self, full=False): """ Return the iteration number and the log likelihood for each point in the individual sequences in that iteration. For example, to plot the convergence of each sequence:: draw, logp = state.logp() plot(draw, logp) Note that draw[i] represents the total number of samples taken, including those for the samples in logp[i]. If full is True, then return all chains, not just good chains. """ #self._unroll() #draws, logp = self._gen_draws, self._gen_logp #if self.generation == self._gen_index: # draws, logp = [v[:self.generation] for v in (draws, logp)] # Don't do a full unroll here if self.generation == self._gen_index: draws = self._gen_draws[:self.generation] logp = self._gen_logp[:self.generation] elif self._gen_index > 0: draws = np.roll(self._gen_draws, -self._gen_index, axis=0) logp = np.roll(self._gen_logp, -self._gen_index, axis=0) else: draws = self._gen_draws logp = self._gen_logp # TODO: just return logp, not logp and draws return draws, (logp if full else logp[:, self._good_chains]) def logp_slice(self, n): """ Return a slice of the logp chains, either the first n if n > 0 or the last n if n < 0. Avoids unrolling the circular buffer if possible. """ if n < 0: # tail if self._gen_index >= -n: return self._gen_logp[self._gen_index+n:self._gen_index] elif self._gen_index == 0: return self._gen_logp[n:] else: # unroll across boundary return np.vstack((self._gen_logp[n+self._gen_index:], self._gen_logp[:self._gen_index])) else: # head if self.generation < self.Ngen: return self._gen_logp[:n] elif self._gen_index+n <= self.Ngen: return self._gen_logp[self._gen_index:self._gen_index+n] else: return np.vstack((self._gen_logp[self._gen_index:], self._gen_logp[-n+self._gen_index:])) def min_slice(self, n): """ Return the minimum logp for n slices, from the head if positive or the tail if negative. This is a specialized function so it can be fast. Convergence can be quickly rejected if the min in a short head is smaller than the min in a long tail. Unfortunately, if the data is wrapped, then the max function will cost extra. """ # Copy the logic of slice if n < 0: # tail if self._gen_index >= -n: return np.min(self._gen_logp[self._gen_index+n:self._gen_index]) elif self._gen_index == 0: return np.min(self._gen_logp[n:]) else: # max across boundary return min(np.min(self._gen_logp[n+self._gen_index:]), np.min(self._gen_logp[:self._gen_index])) else: # head if self.generation < self.Ngen: return np.min(self._gen_logp[:n]) elif self._gen_index+n <= self.Ngen: return np.min(self._gen_logp[self._gen_index:self._gen_index+n]) else: return min(np.min(self._gen_logp[self._gen_index:]), np.min(self._gen_logp[-n+self._gen_index:])) def acceptance_rate(self): """ Return the iteration number and the acceptance rate for that iteration. For example, to plot the acceptance rate over time:: draw, AR = state.acceptance_rate() plot(draw, AR) """ retval = self._gen_draws, self._gen_acceptance_rate if self.generation == self._gen_index: retval = [v[:self.generation] for v in retval] elif self._gen_index > 0: retval = [np.roll(v, -self._gen_index, axis=0) for v in retval] return retval def chains(self): """ Returns the observed Markov chains and the corresponding likelihoods. The return value is a tuple (*draws*, *chains*, *logp*). *draws* is the number of samples taken up to and including the samples for the current generation. *chains* is a three dimensional array of generations X chains X vars giving the set of points observed for each chain in every generation. Only the thinned samples are returned. *logp* is a two dimensional array of generation X population giving the log likelihood of observing the set of variable values given in chains. """ self._unroll() retval = self._thin_draws, self._thin_point, self._thin_logp if self._thin_count == self._thin_index: retval = [v[:self._thin_count] for v in retval] return retval def gelman(self): """ Compute the R-statistic for the current frame """ # Calculate Gelman and Rubin convergence diagnostic if self.generation < self.Ngen: return gelman(self._thin_point[:self.generation], portion=1.0) else: return gelman(self._thin_point, portion=1.0) def CR_weight(self): """ Return the crossover ratio weights to be used in the next generation. For example, to see if the adaptive CR is stable use:: draw, weight = state.CR_weight() plot(draw, weight) See :mod:`.crossover` for details. """ self._unroll() retval = self._update_draws, self._update_CR_weight if self._update_count == self._update_index: retval = [v[:self._update_count] for v in retval] return retval def outliers(self): """ Return a list of outlier removal operations. Each outlier operation is a tuple giving the thinned generation in which it occurred, the old chain id and the new chain id. The chains themselves have already been updated to reflect the removal. Curiously, it is possible for the maximum likelihood seen so far to be removed by this operation. """ return asarray(self._outliers, 'i') def best(self): """ Return the best point seen and its log likelihood. """ return self._best_x, self._best_logp def stable_best(self): """ Return the best point seen and its log likelihood. """ return (self._best_gen + self.Ngen <= self.generation) def keep_best(self): """ Place the best point at the end of the last good chain. Good chains are defined by mark_outliers. Because the Markov chain is designed to wander the parameter space, the best individual seen during the random walk may have been observed during the burn-in period, and may no longer be present in the chain. If this is the case, replace the final point with the best, otherwise swap the positions of the final and the best. """ # Get state as a 1D array _, chains, logp = self.chains() Ngen, Npop, Nvar = chains.shape points = reshape(chains, (Ngen*Npop, Nvar)) logp = reshape(logp, Ngen*Npop) # Set the final position to the end of the last good chain. If # mark_outliers has not been called, then _good_chains will # just be slice(None, None) if isinstance(self._good_chains, slice): final = -1 else: final = self._good_chains[-1] - Npop # Find the location of the best point if it exists and swap with # the final position idx = np.where(logp == self._best_logp)[0] if len(idx) == 0: logp[final] = self._best_logp points[final, :] = self._best_x else: idx = idx[0] logp[final], logp[idx] = logp[idx], logp[final] points[final, :], points[idx, :] = points[idx, :], points[final, :] # For multiple minima, arbitrarily choose one of them # TODO: this will lead to possible confusion when the best value # spontaneously changes when the fit is complete. self._best_p = points[final] self._best_logp = logp[final] def sample(self, **kw): """ Return a sample from the posterior distribution. **Deprecated** use :meth:`draw` instead. """ drawn = self.draw(**kw) return drawn.points, drawn.logp def entropy(self, vars=None, portion=1.0, selection=None, n_est=10000, thin=None, method=None): r""" Return entropy estimate and uncertainty from an MCMC draw. *portion* is the portion of each chain to use *vars* is the set of variables to marginalize over. It is None for the visible variables, or a list of variables. *vars* is the list of variables to use for marginalization. *selection* sets the range each parameter in the returned distribution, using {variable: (low, high)}. Missing variables use the full range. *n_est* is the number of points to use from the draw when estimating the entropy (default=10000). *thin* is the amount of thinning to use when selecting points from the draw. *method* determines which entropy calculation to use: * gmm: fit sample to a gaussian mixture model (GMM) with $5 \sqrt{d}$ components where $d$ is the number fitted parameters and estimate entropy by sampling from the GMM. * llf: estimates likelihood scale factor from ratio of density estimate to model likelihood, then computes Monte Carlo entropy from sample; this does not work for marginal likelihood estimates. DOI:10.1109/CCA.2010.5611198 * mvn: fit sample to a multi-variate Gaussian and return the entropy of the best fit gaussian; uses bootstrap to estimate uncertainty. * wnn: estimate entropy from nearest-neighbor distances in sample. DOI:10.1214/18-AOS1688 """ from . import entropy # Get the sample from the state. # set default thinning to max((steps * samples/step) // n_est, 1) if thin is None: Nsteps = min(self.Nthin, self._thin_count) thin = max(Nsteps*self.Npop//n_est, 1) #print("thin", thin, Nsteps, self.Npop, self.Nthin, self._thin_count) drawn = self.draw(portion=portion, vars=vars, selection=selection, thin=thin) # TODO: don't print within a library function! M = entropy.MVNEntropy(drawn.points) print("Entropy from MVN: %s"%str(M)) if method is None: # TODO: change default to gmm method = "llf" if method == "llf": S, Serr = entropy.entropy(drawn.points, drawn.logp, N_entropy=n_est) #print("Entropy from llf (Kramer): %s"%str(S)) elif method == "gmm": # Try pure gmm ... pretty good S, Serr = entropy.gmm_entropy(drawn.points, n_est=n_est) #print("Entropy from gmm: %g +/- %g"% (S, Serr)) elif method == "wnn": # Try pure wnn ... no good S, Serr = entropy.wnn_entropy(drawn.points, n_est=n_est) #print("Entropy from wnn: %s"%str(S)) elif method == "mvn": S, Serr = entropy.mvn_entropy_bootstrap(drawn.points) #print("Entropy from mvn: %s"%str(S)) else: raise ValueError("unknown method %r" % method) # Always return entropy estimate from draw, even if it is normal return S, Serr def draw(self, portion=1.0, vars=None, selection=None, thin=1): """ Return a sample from the posterior distribution. *portion* is the portion of each chain to use *vars* is a list of variables to return for each point *selection* sets the range each parameter in the returned distribution, using {variable: (low, high)}. Missing variables use the full range. *thin* takes every nth item. To plot the distribution for parameter p1:: draw = state.draw() hist(draw.points[:, 0]) To plot the interdependence of p1 and p2:: draw = state.sample() plot(draw.points[:, 0], draw.points[:, 1], '.') """ vars = vars if vars is not None else getattr(self, '_shown', None) return Draw(self, portion=portion, vars=vars, selection=selection, thin=thin) def set_visible_vars(self, labels): self._shown = [self.labels.index(v) for v in labels] #print("\n".join(str(pair) for pair in enumerate(self.labels))) #print(labels) #print(self._shown) def set_integer_vars(self, labels): """ Indicate tha variables should be considered integer variables when computing statistics. """ self._integer_vars = np.array([var in labels for var in self.labels]) def derive_vars(self, fn, labels=None): """ Generate derived variables from the current sample, adding columns for the derived variables to each sample of every chain. The new columns are treated as part of the sample. *fn* is a function taking points p[:, k] for k in 0 ... samples and returning a set of derived variables pj[k] for each sample k. The variables can be returned as any kind of sequence including an array or a tuple with one entry per variable. The caller uses asarray to convert the returned variables into a vars X samples array. For convenience, a single variable can be returned by itself. *labels* are the labels to use for the derived variables. The following example adds the new variable x+y = P[0] + P[1]:: state.derive_vars(lambda p: p[0]+p[1], labels=["x+y"]) """ # Grab all samples as a set of points _, chains, _ = self.chains() Ngen, Npop, Nvar = chains.shape points = reshape(chains, (Ngen*Npop, Nvar)) # Compute new variables from the points newvars = asarray(fn(points.T)).T Nnew = newvars.shape[1] if len(newvars.shape) == 2 else 1 newvars.reshape((Ngen, Npop, Nnew)) # Extend new variables to be the same length as the stored selection Nthin = self._thin_point.shape[0] newvars = np.resize(newvars, (Nthin, Npop, Nnew)) # Add new variables to the points self._thin_point = dstack((self._thin_point, newvars)) # Add labels for the new variables, if available. if labels is not None: self.labels = self.labels + labels elif self._labels is not None: labels = ["P%d" % i for i in range(Nvar, Nvar+Nnew)] self.labels = self.labels + labels else: # no labels specified, old or new pass class Draw(object): def __init__(self, state, vars=None, portion=None, selection=None, thin=1): self.state = state self.vars = vars self.portion = portion self.selection = selection self.points, self.logp = _sample( state, portion=portion, vars=vars, selection=selection, thin=thin) self.labels \ = state.labels if vars is None else [state.labels[v] for v in vars] self._stats = None self.weights = None self.num_vars = len(self.labels) if state._integer_vars is not None: self.integers = state._integer_vars[vars] if vars else None else: self.integers = None def _sample(state, portion, vars, selection, thin): """ Return a sample from a set of chains. """ draw, chains, logp = state.chains() start = int((1-portion)*len(draw)) if portion else 0 # Collect the subset we are interested in chains = chains[start::thin, state._good_chains, :] logp = logp[start::thin, state._good_chains] Ngen, Npop, Nvar = chains.shape points = reshape(chains, (-1, Nvar)) logp = reshape(logp, (-1)) if selection not in [None, {}]: idx = True for v, r in selection.items(): if v == 'logp': idx = idx & (logp >= r[0]) & (logp <= r[1]) else: idx = idx & (points[:, v] >= r[0]) & (points[:, v] <= r[1]) points = points[idx, :] logp = logp[idx] if vars is not None: points = points[:, vars] return points, logp def test(): from numpy.linalg import norm from numpy.random import rand from numpy import arange # Make some fake data Nupdate, Nstep = 3, 5 Ngen = Nupdate*Nstep Nvar, Npop, Ncr = 3, 6, 2 xin = rand(Ngen, Npop, Nvar) pin = rand(Ngen, Npop) accept = rand(Ngen, Npop) < 0.8 CRin = rand(Nupdate, Ncr) #thinning = 2 #Nthin = int(Ngen/thinning) # Put it into a state thinning = 2 Nthin = int(Ngen/thinning) state = MCMCDraw(Ngen=Ngen, Nthin=Nthin, Nupdate=Nupdate, Nvar=Nvar, Npop=Npop, Ncr=Ncr, thinning=thinning) for i in range(Nupdate): state._update(CR_weight=CRin[i]) for j in range(Nstep): gen = i*Nstep+j state._generation(new_draws=Npop, x=xin[gen], logp=pin[gen], accept=accept[gen]) # Check that it got there draws, logp = state.logp() assert norm(draws - Npop*arange(1, Ngen+1)) == 0 assert norm(logp - pin) == 0 draws, AR = state.acceptance_rate() assert norm(draws - Npop*arange(1, Ngen+1)) == 0 assert norm(AR - 100*sum(accept, axis=1)/Npop) == 0 draws, logp = state.sample() #assert norm(draws - thinning*Npop*arange(1, Nthin+1)) == 0 #assert norm(sample - xin[thinning-1::thinning]) == 0 #assert norm(logp - pin[thinning-1::thinning]) == 0 draws, CR = state.CR_weight() assert norm(draws - Npop*Nstep*arange(Nupdate)) == 0 assert norm(CR - CRin) == 0 x, p = state.best() bestid = argmax(pin) i, j = bestid//Npop, bestid%Npop assert pin[i, j] == p assert norm(xin[i, j, :]-x) == 0 # Check that outlier updates properly state._replace_outlier(1, 2) outliers = state.outliers() draws, logp = state.sample() assert norm(outliers - asarray([[state._thin_index, 1, 2]])) == 0 #assert norm(sample[:, 1, :] - xin[thinning-1::thinning, 2, :]) == 0 #assert norm(sample[:, 2, :] - xin[thinning-1::thinning, 2, :]) == 0 #assert norm(logp[:, 1] - pin[thinning-1::thinning, 2]) == 0 #assert norm(logp[:, 2] - pin[thinning-1::thinning, 2]) == 0 from .stats import var_stats, format_vars vstats = var_stats(state.draw()) print (format_vars(vstats)) if __name__ == "__main__": test()