def expand(self, base_kernels='SE'):
"""
Expand this kernel using grammar defined in grammar.py.
:returns: list of GPCKernel resulting from the expansion
"""
ndim = self.data.getDim()
g = grammar.MultiDGrammar(ndim, base_kernels=base_kernels, rules=None)
kernels = grammar.expand(self.kernel, g)
kernels = [k.canonical() for k in kernels]
kernels = ff.remove_duplicates(kernels)
for k in kernels:
k.initialise_params(data_shape=self.data.getDataShape())
kernels = [k.simplified() for k in kernels]
kernels = ff.remove_duplicates(kernels)
kernels = [k for k in kernels if not isinstance(k, ff.NoneKernel)]
kernels = [GPCKernel(k, self.data, depth=self.depth+1, parent=self) for k in kernels]
return kernels
def expand_kernels(D, seed_kernels, base_kernels='SE', rules=None):
'''Makes a list of all expansions of a set of kernels in D dimensions.'''
g = MultiDGrammar(D, base_kernels=base_kernels, rules=rules)
kernels = []
for k in seed_kernels:
kernels = kernels + expand(k, g)
kernels = [k.canonical() for k in kernels]
kernels = ff.remove_duplicates(kernels)
kernels = [k for k in kernels if not isinstance(k, ff.NoneKernel)]
return kernels
def expand_kernels(D, seed_kernels, base_kernels='SE', rules=None):
'''Makes a list of all expansions of a set of kernels in D dimensions.'''
g = MultiDGrammar(D, base_kernels=base_kernels, rules=rules)
kernels = []
for k in seed_kernels:
kernels = kernels + expand(k, g)
kernels = [k.canonical() for k in kernels]
kernels = ff.remove_duplicates(kernels)
kernels = [k for k in kernels if not isinstance(k, ff.NoneKernel)]
return kernels
def expand(self, base_kernels='SE'):
"""
Expand this kernel using grammar defined in grammar.py.
:returns: list of GPCKernel resulting from the expansion
"""
ndim = self.data.getDim()
g = grammar.MultiDGrammar(ndim, base_kernels=base_kernels, rules=None)
kernels = grammar.expand(self.kernel, g)
kernels = [k.canonical() for k in kernels]
kernels = ff.remove_duplicates(kernels)
for k in kernels:
k.initialise_params(data_shape=self.data.getDataShape())
kernels = [k.simplified() for k in kernels]
kernels = ff.remove_duplicates(kernels)
kernels = [k for k in kernels if not isinstance(k, ff.NoneKernel)]
kernels = [
GPCKernel(k, self.data, depth=self.depth + 1, parent=self)
for k in kernels
]
return kernels
def perform_kernel_search(X, y, D, experiment_data_file_name, results_filename, exp):
'''Search for the best kernel, in parallel on fear or local machine.'''
# Initialise random seeds - randomness may be used in e.g. data subsetting
utils.misc.set_all_random_seeds(exp.random_seed)
# Create location, scale and minimum period parameters to pass around for initialisations
data_shape = {}
data_shape['x_mean'] = [np.mean(X[:,dim]) for dim in range(X.shape[1])]
data_shape['y_mean'] = np.mean(y) #### TODO - should this be modified for non real valued data
data_shape['x_sd'] = np.log([np.std(X[:,dim]) for dim in range(X.shape[1])])
data_shape['y_sd'] = np.log(np.std(y)) #### TODO - should this be modified for non real valued data
data_shape['y_min'] = np.min(y)
data_shape['y_max'] = np.max(y)
data_shape['x_min'] = [np.min(X[:,dim]) for dim in range(X.shape[1])]
data_shape['x_max'] = [np.max(X[:,dim]) for dim in range(X.shape[1])]
# Initialise period at a multiple of the shortest / average distance between points, to prevent Nyquist problems.
if exp.period_heuristic_type == 'none':
data_shape['min_period'] = None
if exp.period_heuristic_type == 'min':
data_shape['min_period'] = np.log([exp.period_heuristic * utils.misc.min_abs_diff(X[:,i]) for i in range(X.shape[1])])
elif exp.period_heuristic_type == 'average':
data_shape['min_period'] = np.log([exp.period_heuristic * np.ptp(X[:,i]) / X.shape[0] for i in range(X.shape[1])])
elif exp.period_heuristic_type == 'both':
data_shape['min_period'] = np.log([max(exp.period_heuristic * utils.misc.min_abs_diff(X[:,i]), exp.period_heuristic * np.ptp(X[:,i]) / X.shape[0]) for i in range(X.shape[1])])
else:
warnings.warn('Unrecognised period heuristic type : using most conservative heuristic')
data_shape['min_period'] = np.log([max(exp.period_heuristic * utils.misc.min_abs_diff(X[:,i]), exp.period_heuristic * np.ptp(X[:,i]) / X.shape[0]) for i in range(X.shape[1])])
data_shape['max_period'] = [np.log((1.0/exp.max_period_heuristic)*(data_shape['x_max'][i] - data_shape['x_min'][i])) for i in range(X.shape[1])]
# Initialise mean, kernel and likelihood
m = eval(exp.mean)
k = eval(exp.kernel)
l = eval(exp.lik)
current_models = [ff.GPModel(mean=m, kernel=k, likelihood=l, ndata=y.size)]
print '\n\nStarting search with this model:\n'
print current_models[0].pretty_print()
print ''
# Perform the initial expansion
current_models = grammar.expand_models(D=D, models=current_models, base_kernels=exp.base_kernels, rules=exp.search_operators)
# Convert to additive form if desired
if exp.additive_form:
current_models = [model.additive_form() for model in current_models]
current_models = ff.remove_duplicates(current_models)
# Set up lists to record search
all_results = [] # List of scored kernels
results_sequence = [] # List of lists of results, indexed by level of expansion.
nan_sequence = [] # List of list of nan scored results
oob_sequence = [] # List of list of out of bounds results
best_models = None
# Other setup
best_score = np.Inf
# Perform search
for depth in range(exp.max_depth):
if exp.debug==True:
current_models = current_models[0:4]
# Add random restarts to kernels
current_models = ff.add_random_restarts(current_models, exp.n_rand, exp.sd, data_shape=data_shape)
# Print result of expansion
if exp.debug:
print '\nRandomly restarted kernels\n'
for model in current_models:
print model.pretty_print()
# Remove any redundancy introduced into kernel expressions
current_models = [model.simplified() for model in current_models]
# Print result of simplification
if exp.debug:
print '\nSimplified kernels\n'
for model in current_models:
print model.pretty_print()
current_models = ff.remove_duplicates(current_models)
# Print result of duplicate removal
if exp.debug:
print '\nDuplicate removed kernels\n'
for model in current_models:
print model.pretty_print()
# Add jitter to parameter values (empirically discovered to help optimiser)
current_models = ff.add_jitter(current_models, exp.jitter_sd)
# Print result of jitter
if exp.debug:
print '\nJittered kernels\n'
for model in current_models:
print model.pretty_print()
# Add the previous best models - in case we just need to optimise more rather than changing structure
if not best_models is None:
for a_model in best_models:
current_models = current_models + [a_model.copy()] + ff.add_jitter_to_models([a_model.copy() for dummy in range(exp.n_rand)], exp.jitter_sd)
# Randomise the order of the model to distribute computational load evenly
np.random.shuffle(current_models)
# Print current models
if exp.debug:
print '\nKernels to be evaluated\n'
for model in current_models:
print model.pretty_print()
# Optimise parameters of and score the kernels
new_results = jc.evaluate_models(current_models, X, y, verbose=exp.verbose, local_computation=exp.local_computation,
zip_files=True, max_jobs=exp.max_jobs, iters=exp.iters, random_seed=exp.random_seed,
subset=exp.subset, subset_size=exp.subset_size, full_iters=exp.full_iters, bundle_size=exp.bundle_size)
# Remove models that were optimised to be out of bounds (this is similar to a 0-1 prior)
new_results = [a_model for a_model in new_results if not a_model.out_of_bounds(data_shape)]
oob_results = [a_model for a_model in new_results if a_model.out_of_bounds(data_shape)]
oob_results = sorted(oob_results, key=lambda a_model : GPModel.score(a_model, exp.score), reverse=True)
oob_sequence.append(oob_results)
# Some of the scores may have failed - remove nans to prevent sorting algorithms messing up
(new_results, nan_results) = remove_nan_scored_models(new_results, exp.score)
nan_sequence.append(nan_results)
assert(len(new_results) > 0) # FIXME - Need correct control flow if this happens
# Sort the new results
new_results = sorted(new_results, key=lambda a_model : GPModel.score(a_model, exp.score), reverse=True)
print '\nAll new results\n'
for result in new_results:
print 'NLL=%0.1f' % result.nll, 'BIC=%0.1f' % result.bic, 'AIC=%0.1f' % result.aic, 'PL2=%0.3f' % result.pl2, result.pretty_print()
all_results = all_results + new_results
all_results = sorted(all_results, key=lambda a_model : GPModel.score(a_model, exp.score), reverse=True)
results_sequence.append(all_results)
# Extract the best k kernels from the new all_results
best_results = sorted(new_results, key=lambda a_model : GPModel.score(a_model, exp.score))[0:exp.k]
# Print best kernels
if exp.debug:
print '\nBest models\n'
for model in best_results:
print model.pretty_print()
# Expand the best models
current_models = grammar.expand_models(D=D, models=best_results, base_kernels=exp.base_kernels, rules=exp.search_operators)
# Print expansion
if exp.debug:
print '\nExpanded models\n'
for model in current_models:
print model.pretty_print()
# Convert to additive form if desired
if exp.additive_form:
current_models = [model.additive_form() for model in current_models]
current_models = ff.remove_duplicates(current_models)
# Print expansion
if exp.debug:
print '\Converted into additive\n'
for model in current_models:
print model.pretty_print()
# Reduce number of kernels when in debug mode
if exp.debug==True:
current_models = current_models[0:4]
# Write all_results to a temporary file at each level.
all_results = sorted(all_results, key=lambda a_model : GPModel.score(a_model, exp.score), reverse=True)
with open(results_filename + '.unfinished', 'w') as outfile:
outfile.write('Experiment all_results for\n datafile = %s\n\n %s \n\n' \
% (experiment_data_file_name, experiment_fields_to_str(exp)))
for (i, all_results) in enumerate(results_sequence):
outfile.write('\n%%%%%%%%%% Level %d %%%%%%%%%%\n\n' % i)
if exp.verbose_results:
for result in all_results:
print >> outfile, result
else:
# Only print top k kernels - i.e. those used to seed the next level of the search
for result in sorted(all_results, key=lambda a_model : GPModel.score(a_model, exp.score))[0:exp.k]:
print >> outfile, result
# Write nan scored kernels to a log file
with open(results_filename + '.nans', 'w') as outfile:
outfile.write('Experiment nan results for\n datafile = %s\n\n %s \n\n' \
% (experiment_data_file_name, experiment_fields_to_str(exp)))
for (i, nan_results) in enumerate(nan_sequence):
outfile.write('\n%%%%%%%%%% Level %d %%%%%%%%%%\n\n' % i)
for result in nan_results:
print >> outfile, result
# Write oob kernels to a log file
with open(results_filename + '.oob', 'w') as outfile:
outfile.write('Experiment oob results for\n datafile = %s\n\n %s \n\n' \
% (experiment_data_file_name, experiment_fields_to_str(exp)))
for (i, nan_results) in enumerate(oob_sequence):
outfile.write('\n%%%%%%%%%% Level %d %%%%%%%%%%\n\n' % i)
for result in nan_results:
print >> outfile, result
# Have we hit a stopping criterion?
if 'no_improvement' in exp.stopping_criteria:
new_best_score = min(GPModel.score(a_model, exp.score) for a_model in new_results)
if new_best_score < best_score - exp.improvement_tolerance:
best_score = new_best_score
else:
# Insufficient improvement
print 'Insufficient improvement to score - stopping search'
break
# Rename temporary results file to actual results file
os.rename(results_filename + '.unfinished', results_filename)
def perform_kernel_search(X, y, D, experiment_data_file_name, results_filename,
exp):
'''Search for the best kernel, in parallel on fear or local machine.'''
# Initialise random seeds - randomness may be used in e.g. data subsetting
utils.misc.set_all_random_seeds(exp.random_seed)
# Create location, scale and minimum period parameters to pass around for initialisations
data_shape = {}
data_shape['x_mean'] = [np.mean(X[:, dim]) for dim in range(X.shape[1])]
data_shape['y_mean'] = np.mean(
y) #### TODO - should this be modified for non real valued data
data_shape['x_sd'] = np.log(
[np.std(X[:, dim]) for dim in range(X.shape[1])])
data_shape['y_sd'] = np.log(np.std(
y)) #### TODO - should this be modified for non real valued data
data_shape['y_min'] = np.min(y)
data_shape['y_max'] = np.max(y)
data_shape['x_min'] = [np.min(X[:, dim]) for dim in range(X.shape[1])]
data_shape['x_max'] = [np.max(X[:, dim]) for dim in range(X.shape[1])]
data_shape['x_min_abs_diff'] = np.log(
[utils.misc.min_abs_diff(X[:, i]) for i in range(X.shape[1])])
# Initialise period at a multiple of the shortest / average distance between points, to prevent Nyquist problems.
if exp.period_heuristic_type == 'none':
data_shape['min_period'] = None
if exp.period_heuristic_type == 'min':
data_shape['min_period'] = np.log([
exp.period_heuristic * utils.misc.min_abs_diff(X[:, i])
for i in range(X.shape[1])
])
elif exp.period_heuristic_type == 'average':
data_shape['min_period'] = np.log([
exp.period_heuristic * np.ptp(X[:, i]) / X.shape[0]
for i in range(X.shape[1])
])
elif exp.period_heuristic_type == 'both':
data_shape['min_period'] = np.log([
max(exp.period_heuristic * utils.misc.min_abs_diff(X[:, i]),
exp.period_heuristic * np.ptp(X[:, i]) / X.shape[0])
for i in range(X.shape[1])
])
else:
warnings.warn(
'Unrecognised period heuristic type : using most conservative heuristic'
)
data_shape['min_period'] = np.log([
max(exp.period_heuristic * utils.misc.min_abs_diff(X[:, i]),
exp.period_heuristic * np.ptp(X[:, i]) / X.shape[0])
for i in range(X.shape[1])
])
data_shape['max_period'] = [
np.log((1.0 / exp.max_period_heuristic) *
(data_shape['x_max'][i] - data_shape['x_min'][i]))
for i in range(X.shape[1])
]
# Initialise mean, kernel and likelihood
m = eval(exp.mean)
k = eval(exp.kernel)
l = eval(exp.lik)
current_models = [ff.GPModel(mean=m, kernel=k, likelihood=l, ndata=y.size)]
print '\n\nStarting search with this model:\n'
print current_models[0].pretty_print()
print ''
# Perform the initial expansion
current_models = grammar.expand_models(D=D,
models=current_models,
base_kernels=exp.base_kernels,
rules=exp.search_operators)
# Convert to additive form if desired
if exp.additive_form:
current_models = [model.additive_form() for model in current_models]
current_models = ff.remove_duplicates(current_models)
# Set up lists to record search
all_results = [] # List of scored kernels
results_sequence = [
] # List of lists of results, indexed by level of expansion.
nan_sequence = [] # List of list of nan scored results
oob_sequence = [] # List of list of out of bounds results
best_models = None
# Other setup
best_score = np.Inf
# Perform search
for depth in range(exp.max_depth):
if exp.debug == True:
current_models = current_models[0:4]
# Add random restarts to kernels
current_models = ff.add_random_restarts(current_models,
exp.n_rand,
exp.sd,
data_shape=data_shape)
# Print result of expansion
if exp.debug:
print '\nRandomly restarted kernels\n'
for model in current_models:
print model.pretty_print()
# Remove any redundancy introduced into kernel expressions
current_models = [model.simplified() for model in current_models]
# Print result of simplification
if exp.debug:
print '\nSimplified kernels\n'
for model in current_models:
print model.pretty_print()
current_models = ff.remove_duplicates(current_models)
# Print result of duplicate removal
if exp.debug:
print '\nDuplicate removed kernels\n'
for model in current_models:
print model.pretty_print()
# Add jitter to parameter values (empirically discovered to help optimiser)
current_models = ff.add_jitter(current_models, exp.jitter_sd)
# Print result of jitter
if exp.debug:
print '\nJittered kernels\n'
for model in current_models:
print model.pretty_print()
# Add the previous best models - in case we just need to optimise more rather than changing structure
if not best_models is None:
for a_model in best_models:
current_models = current_models + [
a_model.copy()
] + ff.add_jitter_to_models(
[a_model.copy()
for dummy in range(exp.n_rand)], exp.jitter_sd)
# Randomise the order of the model to distribute computational load evenly
np.random.shuffle(current_models)
# Print current models
if exp.debug:
print '\nKernels to be evaluated\n'
for model in current_models:
print model.pretty_print()
# Optimise parameters of and score the kernels
new_results = jc.my_evaluate_models(
current_models,
X,
y,
verbose=exp.verbose,
local_computation=exp.local_computation,
zip_files=True,
max_jobs=exp.max_jobs,
iters=exp.iters,
random_seed=exp.random_seed,
subset=exp.subset,
subset_size=exp.subset_size,
full_iters=exp.full_iters,
bundle_size=exp.bundle_size)
# Remove models that were optimised to be out of bounds (this is similar to a 0-1 prior)
new_results = [
a_model for a_model in new_results
if not a_model.out_of_bounds(data_shape)
]
oob_results = [
a_model for a_model in new_results
if a_model.out_of_bounds(data_shape)
]
#new_results = [a_model for a_model in new_results]
#oob_results = [a_model for a_model in new_results]
oob_results = sorted(
oob_results,
key=lambda a_model: GPModel.score(a_model, exp.score),
reverse=True)
oob_sequence.append(oob_results)
# Some of the scores may have failed - remove nans to prevent sorting algorithms messing up
(new_results,
nan_results) = remove_nan_scored_models(new_results, exp.score)
nan_sequence.append(nan_results)
assert (len(new_results) > 0
) # FIXME - Need correct control flow if this happens
# Sort the new results
new_results = sorted(
new_results,
key=lambda a_model: GPModel.score(a_model, exp.score),
reverse=True)
print '\nAll new results\n'
for result in new_results:
print 'NLL=%0.1f' % result.nll, 'BIC=%0.1f' % result.bic, 'AIC=%0.1f' % result.aic, 'PL2=%0.3f' % result.pl2, result.pretty_print(
)
all_results = all_results + new_results
all_results = sorted(
all_results,
key=lambda a_model: GPModel.score(a_model, exp.score),
reverse=True)
results_sequence.append(all_results)
# Extract the best k kernels from the new all_results
best_results = sorted(
new_results,
key=lambda a_model: GPModel.score(a_model, exp.score))[0:exp.k]
# Print best kernels
if exp.debug:
print '\nBest models\n'
for model in best_results:
print model.pretty_print()
# Expand the best models
current_models = grammar.expand_models(D=D,
models=best_results,
base_kernels=exp.base_kernels,
rules=exp.search_operators)
# Print expansion
if exp.debug:
print '\nExpanded models\n'
for model in current_models:
print model.pretty_print()
# Convert to additive form if desired
if exp.additive_form:
current_models = [
model.additive_form() for model in current_models
]
current_models = ff.remove_duplicates(current_models)
# Print expansion
if exp.debug:
print '\Converted into additive\n'
for model in current_models:
print model.pretty_print()
# Reduce number of kernels when in debug mode
if exp.debug == True:
current_models = current_models[0:4]
# Write all_results to a temporary file at each level.
all_results = sorted(
all_results,
key=lambda a_model: GPModel.score(a_model, exp.score),
reverse=True)
with open(results_filename + '.unfinished', 'w') as outfile:
outfile.write('Experiment all_results for\n datafile = %s\n\n %s \n\n' \
% (experiment_data_file_name, experiment_fields_to_str(exp)))
for (i, all_results) in enumerate(results_sequence):
outfile.write('\n%%%%%%%%%% Level %d %%%%%%%%%%\n\n' % i)
if exp.verbose_results:
for result in all_results:
print >> outfile, result
else:
# Only print top k kernels - i.e. those used to seed the next level of the search
i = 0
for result in sorted(all_results,
key=lambda a_model: GPModel.score(
a_model, exp.score))[0:exp.k]:
print >> outfile, result
scipy.io.savemat(
results_filename + 'lvl_' + str(depth) + '_' +
str(i) + '.mat1', result.gpml_result)
i += 1
# Write nan scored kernels to a log file
with open(results_filename + '.nans', 'w') as outfile:
outfile.write('Experiment nan results for\n datafile = %s\n\n %s \n\n' \
% (experiment_data_file_name, experiment_fields_to_str(exp)))
for (i, nan_results) in enumerate(nan_sequence):
outfile.write('\n%%%%%%%%%% Level %d %%%%%%%%%%\n\n' % i)
for result in nan_results:
print >> outfile, result
# Write oob kernels to a log file
with open(results_filename + '.oob', 'w') as outfile:
outfile.write('Experiment oob results for\n datafile = %s\n\n %s \n\n' \
% (experiment_data_file_name, experiment_fields_to_str(exp)))
for (i, nan_results) in enumerate(oob_sequence):
outfile.write('\n%%%%%%%%%% Level %d %%%%%%%%%%\n\n' % i)
for result in nan_results:
print >> outfile, result
# Have we hit a stopping criterion?
if 'no_improvement' in exp.stopping_criteria:
new_best_score = min(
GPModel.score(a_model, exp.score) for a_model in new_results)
if new_best_score < best_score - exp.improvement_tolerance:
best_score = new_best_score
else:
# Insufficient improvement
print 'Insufficient improvement to score - stopping search'
break
# Rename temporary results file to actual results file
os.rename(results_filename + '.unfinished', results_filename)