def get_trueFIs(ds_stats,
res_filename,
min_freq,
delta,
gap=0.0,
use_additional_knowledge=False):
""" Compute the True Frequent Itemsets using the VC method we present in the
paper.
The parameter 'use_additional_knowledge' can be used to incorporate
additional knowledge about the data generation process.
'gap' controls how close to the optimal solution we ask the CPLEX solver to
go. The right way to implement this would be to use a
user-defined function in CPLEX.
Returns a pair (trueFIs, stats).
'trueFIs' is a dict whose keys are itemsets (frozensets) and values are
frequencies. This collection of itemsets contains only TFIs with
probability at least 1 - delta.
'stats' is a dict containing various statistics used in computing the
collection of itemsets."""
stats = dict()
# One may want to play with giving different values for the different error
# probabilities, but there isn't really much point in it.
lower_delta = 1.0 - math.sqrt(1 - delta)
# Compute the maximum frequency of an itemset in the dataset
with open(res_filename, 'rt') as FILE:
size_line = FILE.readline()
try:
size_str = size_line.split("(")[1].split(")")[0]
except IndexError:
error_exit(
"Cannot compute size of the dataset: '{}' is not in the recognized format\n"
.format(size_line))
try:
size = int(size_str)
except ValueError:
error_exit(
"Cannot compute size of the dataset: '{}' is not a number\n".
format(size_line.split("(")[1].split(")")[0]))
max_freq_line = FILE.readline()
if max_freq_line.find("(") > -1:
tokens = max_freq_line.split("(")
itemset = frozenset(map(int, tokens[0].split()))
try:
support = int(tokens[1][:-2])
except ValueError:
error_exit(
"Cannot compute the maximum frequency: '{}' is not a number\n"
.format(tokens[1][:-2]))
max_freq = support / size
else:
error_exit(
"Cannot compute the maximum frequency: '{}' is not in the recognized format\n"
.format(max_freq_line))
# Compute the first epsilon using results from the paper (Riondato and
# Upfal 2014)
# Incorporate or not 'previous knowledge' about generative process in
# computation of the VC-dimension, depending on the option passed on the
# command line
(eps_vc_dim, eps_shatter,
returned) = epsilon.epsilon_dataset(lower_delta, ds_stats,
use_additional_knowledge, max_freq)
stats['epsilon_1'] = min(eps_vc_dim, eps_shatter)
items = ds_stats['items']
items_num = len(items)
lengths_dict = ds_stats['lengths']
lengths = sorted(lengths_dict.keys(), reverse=True)
# Extract the first (and largest) set of itemsets with frequency at least
# min_freq - stats['epsilon_1']
lower_bound_freq = min_freq - stats['epsilon_1'] - (1 / ds_stats['size'])
freq_itemsets_1_dict = utils.create_results(res_filename, lower_bound_freq)
freq_itemsets_1_set = frozenset(freq_itemsets_1_dict.keys())
freq_itemsets_1_sorted = sorted(freq_itemsets_1_set,
key=lambda x: freq_itemsets_1_dict[x])
freq_items_1 = set()
for itemset in freq_itemsets_1_set:
if len(itemset) == 1:
freq_items_1 |= itemset
freq_items_1_num = len(freq_items_1)
sys.stderr.write("First set of FI's: {} itemsets\n".format(
len(freq_itemsets_1_set)))
sys.stderr.flush()
constr_start_str = "cplex.SparsePair(ind = ["
constr_end_str = "], val = vals)"
# Compute the "base set" (terrible name), that is the set of
# itemsets with frequency < min_freq + epsilon_1 (but greater than min_freq
# - stats['epsilon_1']. In the paper we call it \mathcal{G}.
sys.stderr.write("Creating base set...")
sys.stderr.flush()
base_set = dict()
# We use the maximum frequency in the base set to compute the epislon
max_freq_base_set = 0
for itemset in freq_itemsets_1_sorted:
if freq_itemsets_1_dict[itemset] < min_freq + stats['epsilon_1']:
base_set[itemset] = freq_itemsets_1_dict[itemset]
if freq_itemsets_1_dict[itemset] > max_freq_base_set:
max_freq_base_set = freq_itemsets_1_dict[itemset]
else:
break
stats['base_set'] = len(base_set)
sys.stderr.write("done: {} itemsets\n".format(stats['base_set']))
sys.stderr.flush()
# Compute Closed Itemsets. We need them to compute the maximal.
sys.stderr.write("Computing closed itemsets...")
sys.stderr.flush()
closed_itemsets = utils.get_closed_itemsets(base_set)
closed_itemsets_len = len(closed_itemsets)
sys.stderr.write(
"done. Found {} closed itemsets\n".format(closed_itemsets_len))
sys.stderr.flush()
# Compute maximal itemsets. We will use them to compute the negative
# border. An itemset is maximal frequent if none of its immediate supersets
# is frequent.
sys.stderr.write("Computing maximal itemsets...")
sys.stderr.flush()
maximal_itemsets_dict = utils.get_maximal_itemsets(closed_itemsets)
maximal_itemsets = list(maximal_itemsets_dict.keys())
stats['maximal_itemsets'] = len(maximal_itemsets)
sys.stderr.write("done. Found {} maximal itemsets\n".format(
stats['maximal_itemsets']))
sys.stderr.flush()
# Compute the negative border
sys.stderr.write("Computing negative border...")
sys.stderr.flush()
negative_border = set()
negative_border_items = set()
# The idea is to look for "children" of maximal itemsets, and for
# "siblings" of maximal itemsets
for maximal in maximal_itemsets:
for item_to_remove_from_maximal in maximal:
reduced_maximal = maximal - frozenset([
item_to_remove_from_maximal,
])
for item in freq_items_1:
if item in maximal:
continue
# Create sibling
candidate = reduced_maximal | frozenset([item])
if candidate in freq_itemsets_1_set:
continue
if candidate in negative_border:
continue
to_add = True
for item_to_remove in candidate:
subset = candidate - frozenset([item_to_remove])
if subset not in freq_itemsets_1_set:
to_add = False
break
if to_add:
negative_border.add(candidate)
negative_border_items |= candidate
if not to_add:
# if we added the sibling, there's no way we can add the
# child
candidate2 = maximal | frozenset([item]) # create child
if candidate2 in negative_border:
continue
to_add = True
for item_to_remove in candidate2:
subset = candidate2 - frozenset([item_to_remove])
if subset not in freq_itemsets_1_set:
to_add = False
break
if to_add:
negative_border.add(candidate2)
negative_border_items |= candidate
# We don't need to add the non-frequent-items because none of them (or
# their supersets) will ever be included in the output, so at most we lose
# some statistical power, but it's not a problem of avoiding false
# positives.
# for item in non_freq_items_1:
# negative_border.add(frozenset([item]))
# negative_border_items.add(item)
original_negative_border_len = len(negative_border)
sys.stderr.write(
"done. Length now: {}\n".format(original_negative_border_len))
sys.stderr.flush()
# Add the "base set" to negative_border, so that it becomes a superset of
# the "true" negative border (with some caveats about non-frequent single
# items and their supersets, see comment above)
sys.stderr.write("Adding base set...")
sys.stderr.flush()
for itemset in base_set:
negative_border.add(itemset)
negative_border_items |= itemset
sys.stderr.write("done. Length now: {}\n".format(len(negative_border)))
sys.stderr.flush()
negative_border = sorted(negative_border, key=len, reverse=True)
stats['negative_border'] = len(negative_border)
negative_border_items_sorted = sorted(negative_border_items)
# Create the graph that we will use to compute the chain constraints.
# The nodes are the itemsets in negative_border. There is an edge between
# two nodes if one is contained in the other or vice-versa.
# Cliques on this graph are chains.
sys.stderr.write("Creating graph...")
sys.stderr.flush()
graph = nx.Graph()
graph.add_nodes_from(negative_border)
sys.stderr.write("added nodes...adding edges...")
sys.stderr.flush()
negative_border_items_in_sets_dict = dict()
negative_border_itemset_index = 0
itemset_indexes_dict = dict()
for first_itemset_index in range(stats['negative_border']):
first_itemset = negative_border[first_itemset_index]
for second_itemset_index in range(first_itemset_index + 1,
stats['negative_border']):
second_itemset = negative_border[second_itemset_index]
if first_itemset < second_itemset or \
second_itemset < first_itemset:
graph.add_edge(first_itemset, second_itemset)
for item in first_itemset:
if item in negative_border_items_in_sets_dict:
negative_border_items_in_sets_dict[item].append(
negative_border_itemset_index)
else:
negative_border_items_in_sets_dict[item] = \
[negative_border_itemset_index, ]
itemset_indexes_dict[first_itemset] = negative_border_itemset_index
negative_border_itemset_index += 1
sys.stderr.write("done\n")
sys.stderr.flush()
capacity = freq_items_1_num - 1
if use_additional_knowledge and 2 * ds_stats['maxlen'] < capacity:
sys.stderr.write("Lowering capacity={} to {}\n".format(
capacity, 2 * ds_stats['maxlen']))
sys.stderr.flush()
capacity = 2 * ds_stats['maxlen']
vars_num = stats['negative_border'] + len(negative_border_items)
constr_names = []
(tmpfile_handle, tmpfile_name) = tempfile.mkstemp(prefix="cplx",
dir=os.environ['PWD'],
text=True)
os.close(tmpfile_handle)
with open(tmpfile_name, 'wt') as cplex_script:
cplex_script.write("capacity = {}\n".format(capacity))
cplex_script.write("import cplex, os, sys\n")
cplex_script.write("from cplex.exceptions import CplexError\n")
cplex_script.write("\n")
cplex_script.write("\n")
cplex_script.write(" ".join(
("os.environ[\"ILOG_LICENSE_FILE\"] =",
"\"/local/projects/cplex/ilm/site.access.ilm\"\n")))
cplex_script.write("vals = [-1.0, 1.0]\n")
cplex_script.write("sets_num = {}\n".format(stats['negative_border']))
cplex_script.write("items_num = {}\n".format(
len(negative_border_items)))
cplex_script.write("vars_num = {}\n".format(vars_num))
cplex_script.write("my_ub = [1.0] * vars_num\n")
cplex_script.write(
"my_types = \"\".join(\"I\" for i in range(vars_num))\n")
cplex_script.write(
"my_obj = ([1.0] * sets_num) + ([0.0] * items_num)\n")
cplex_script.write(" ".join(
("my_colnames =",
"[\"set{0}\".format(i) for i in range(sets_num)] +",
"[\"item{0}\".format(j) for j in range(items_num)]\n")))
cplex_script.write("rows = [ ")
sys.stderr.write("Writing knapsack constraints...")
sys.stderr.flush()
constr_num = 0
for item_index in range(len(negative_border_items)):
try:
for itemset_index in negative_border_items_in_sets_dict[
negative_border_items_sorted[item_index]]:
constr_str = "".join(
(constr_start_str, "\"set{}\",\"item{}\"".format(
itemset_index, item_index), constr_end_str))
cplex_script.write("{},".format(constr_str))
constr_num += 1
name = "s{}i{}".format(item_index, itemset_index)
constr_names.append(name)
except KeyError:
sys.stderr.write(" ".join(
("item_index={}".format(item_index),
"neg_border_items_sorted[item_index]={}\n".format(
negative_border_items_sorted[item_index]))))
sys.stderr.write("{} in items: {}\n".format(
negative_border_items_sorted[item_index],
negative_border_items_sorted[item_index] in items))
sys.stderr.write("{} in freq_items_1: {}\n".format(
negative_border_items_sorted[item_index],
negative_border_items_sorted[item_index] in freq_items_1))
non_freq_items_1 = items - freq_items_1
sys.stderr.write("{} in non_freq_items_1: {}\n".format(
negative_border_items_sorted[item_index],
negative_border_items_sorted[item_index]
in non_freq_items_1))
in_pos_border = False
pos_border_itemset = frozenset()
for itemset in maximal_itemsets:
if negative_border_items_sorted[item_index] in itemset:
in_pos_border = True
pos_border_itemset = itemset
break
sys.stderr.write(
"{} in maximal_itemsets: {}. Itemset: {}\n".format(
negative_border_items_sorted[item_index],
in_pos_border, pos_border_itemset))
in_neg_border = False
neg_border_itemset = frozenset()
for itemset in negative_border:
if negative_border_items_sorted[item_index] in itemset:
in_neg_border = True
neg_border_itemset = itemset
break
sys.stderr.write(
"{} in negative_border: {}. Itemset: {}\n".format(
negative_border_items_sorted[item_index],
in_neg_border, neg_border_itemset))
sys.exit(1)
# Create capacity constraints and write it to script
constr_str = "".join(
(constr_start_str,
",".join("\"item{}\"".format(j)
for j in range(len(negative_border_items))), "], val=[",
",".join("1.0" for j in range(len(negative_border_items))), "])"))
cplex_script.write(constr_str)
last_tell = cplex_script.tell()
cplex_script.write(",")
cap_constr_name = "capacity"
constr_names.append(cap_constr_name)
sys.stderr.write("done\n")
sys.stderr.flush()
# Create chain constraints and write them to script
sys.stderr.write("Writing chain constraints...")
sys.stderr.flush()
chains_index = 0
for clique in nx.find_cliques(graph):
if len(clique) == 1:
continue
constr_str = "".join(
(constr_start_str, ",".join(
"\"set{}\"".format(j)
for j in map(lambda x: itemset_indexes_dict[x], clique)),
"], val=[1.0] * {}".format(len(clique)), ")"))
cplex_script.write(constr_str)
last_tell = cplex_script.tell()
cplex_script.write(",")
name = "chain{}".format(chains_index)
constr_names.append(name)
chains_index += 1
sys.stderr.write("done\n")
sys.stderr.flush()
sys.stderr.write(" ".join(
("Optimization problem: capacity={}".format(capacity),
"vars_num={}".format(vars_num),
"negative_border_size={}".format(stats['negative_border']),
"negative_border_items_num={}".format(len(negative_border_items)),
"constr_num={}".format(constr_num),
"chains_index={}\n".format(chains_index))))
sys.stderr.flush()
# Go back one character to remove last comma ","
cplex_script.seek(last_tell)
cplex_script.write("]\n")
cplex_script.write("my_rownames = {}\n".format(constr_names))
cplex_script.write("constr_num = {}\n".format(constr_num))
cplex_script.write("chain_constr_num = {}\n".format(chains_index))
cplex_script.write(" ".join(
("my_senses = [\"G\"] * constr_num +",
"[\"L\"] + [\"L\"] * chain_constr_num\n")))
cplex_script.write(" ".join(
("my_rhs = [0.0] * constr_num + [capacity] +",
"[1.0] * chain_constr_num\n")))
cplex_script.write("\n")
cplex_script.write("try:\n")
cplex_script.write(" prob = cplex.Cplex()\n")
cplex_script.write(" prob.set_error_stream(sys.stderr)\n")
cplex_script.write(" prob.set_log_stream(sys.stderr)\n")
cplex_script.write(" prob.set_results_stream(sys.stderr)\n")
cplex_script.write(" prob.set_warning_stream(sys.stderr)\n")
# cplex_script.write(" prob.parameters.mip.strategy.file.set(2)\n")
cplex_script.write(
" prob.parameters.mip.tolerances.mipgap.set({})\n".format(gap))
cplex_script.write(
" prob.parameters.timelimit.set({})\n".format(600))
# cplex_script.write("
# prob.parameters.mip.strategy.variableselect.set(3) # strong
# branching\n")
cplex_script.write(
" prob.objective.set_sense(prob.objective.sense.maximize)\n")
cplex_script.write(" ".join(
(" prob.variables.add(obj = my_obj, ub = my_ub,",
"types = my_types, names = my_colnames)\n")))
cplex_script.write(" ".join(
(" prob.linear_constraints.add(lin_expr = rows,",
"senses = my_senses, rhs = my_rhs, names = my_rownames)\n")))
cplex_script.write(" ".join(
(" prob.MIP_starts.add(cplex.SparsePair(",
"ind = [i for i in range(vars_num)],", "val = [1.0] * vars_num),",
"prob.MIP_starts.effort_level.auto)\n")))
cplex_script.write(" prob.solve()\n")
cplex_script.write("".join(
(" print (prob.solution.get_status(),",
"prob.solution.status[prob.solution.get_status()],",
"prob.solution.MIP.get_best_objective(),",
"prob.solution.MIP.get_mip_relative_gap())\n")))
cplex_script.write("except CplexError, exc:\n")
cplex_script.write(" print exc\n")
# Run script, solve optimization problem, extract solution
my_environ = os.environ
if "ILOG_LICENSE_FILE" not in my_environ:
my_environ["ILOG_LICENSE_FILE"] = \
"/local/projects/cplex/ilm/site.access.ilm"
try:
cplex_output_binary_str = subprocess.check_output(
["python2.6", tmpfile_name], env=my_environ, cwd=os.environ["PWD"])
except subprocess.CalledProcessError as err:
os.remove(tmpfile_name)
utils.error_exit("CPLEX exited with error code {}: {}\n".format(
err.returncode, err.output))
# finally:
# os.remove(tmpfile_name)
cplex_output = cplex_output_binary_str.decode(
locale.getpreferredencoding())
cplex_output_lines = cplex_output.split("\n")
cplex_solution_line = cplex_output_lines[-1 if len(cplex_output_lines[-1]
) > 0 else -2]
try:
cplex_solution = eval(cplex_solution_line)
except Exception:
utils.error_exit(
"Error evaluating the CPLEX solution line: {}\n".format(
cplex_solution_line))
sys.stderr.write("cplex_solution={}\n".format(cplex_solution))
sys.stderr.flush()
# if cplex_solution[0] not in (1, 101, 102):
# utils.error_exit("CPLEX didn't find the optimal solution: {} {}
# {}\n".format(cplex_solution[0], cplex_solution[1], cplex_solution[2]))
# This is also an upper bound to the size of the true negative border
optimal_sol_upp_bound = int(
math.floor(cplex_solution[2] * (1 + cplex_solution[3])))
# Compute non-empirical VC-dimension and first candidate to epsilon_2
stats['not_emp_vc_dim'] = int(math.floor(
math.log2(optimal_sol_upp_bound))) + 1
if stats['not_emp_vc_dim'] > math.log2(len(negative_border)):
sys.stderr.write(
"Lowering non_empirical VC-dimension to maximum value\n")
stats['not_emp_vc_dim'] = int(
math.floor(math.log2(len(negative_border))))
not_emp_epsilon_2 = epsilon.get_eps_vc_dim(lower_delta, ds_stats['size'],
stats['not_emp_vc_dim'])
sys.stderr.write(" ".join(
("items_num-1={}".format(items_num - 1),
"optimal_sol_upp_bound={}".format(optimal_sol_upp_bound),
"not_emp_vc_dim={}".format(stats['not_emp_vc_dim']),
"not_emp_e2={}\n".format(not_emp_epsilon_2))))
sys.stderr.flush()
# Loop to compute empirical VC-dimension using lengths distribution
items_num_str_len = len(str(len(negative_border_items) - 1))
longer_equal = 0
for i in range(len(lengths)):
cand_len = lengths[i]
if cand_len == items_num:
continue
longer_equal += lengths_dict[cand_len]
# No need to include tests to check whether cand_len is lower than
# 2*ds_stats['maxlen'] if use_additional_knowledge is True: it is
# always true given that cand_len <= ds_stats['maxlen']
if cand_len >= len(negative_border_items):
cand_len = len(negative_border_items) - 1
# Modify the script to use the new capacity.
with open(tmpfile_name, 'r+t') as cplex_script:
cplex_script.seek(0)
cplex_script.write("capacity = {}\n".format(
str(cand_len).ljust(items_num_str_len)))
# Run the script, solve optimization problem, extract solution
my_environ = os.environ
if "ILOG_LICENSE_FILE" not in my_environ:
my_environ["ILOG_LICENSE_FILE"] = \
"/local/projects/cplex/ilm/site.access.ilm"
try:
cplex_output_binary_str = subprocess.check_output(
["python2.6", tmpfile_name],
env=my_environ,
cwd=os.environ["PWD"])
except subprocess.CalledProcessError as err:
os.remove(tmpfile_name)
utils.error_exit("CPLEX exited with error code {}: {}\n".format(
err.returncode, err.output))
# finally:
# os.remove(tmpfile_name)
cplex_output = cplex_output_binary_str.decode(
locale.getpreferredencoding())
cplex_output_lines = cplex_output.split("\n")
cplex_solution_line = cplex_output_lines[
-1 if len(cplex_output_lines[-1]) > 0 else -2]
try:
cplex_solution = eval(cplex_solution_line)
except Exception:
utils.error_exit(
"Error evaluating the CPLEX solution line: {}\n".format(
cplex_solution_line))
sys.stderr.write("{}\n".format(cplex_solution))
# if cplex_solution[0] not in (1, 101, 102):
# utils.error_exit("CPLEX didn't find the optimal solution: {} {}
# {}\n".format(cplex_solution[0], cplex_solution[1],
# cplex_solution[2]))
# if cplex_solution[0] == 102:
optimal_sol_upp_bound_emp = int(
math.floor(cplex_solution[2] * (1 + cplex_solution[3])))
# else:
# optimal_sol_upp_bound_emp = cplex_solution[0]
stats['emp_vc_dim'] = int(
math.floor(math.log2(optimal_sol_upp_bound_emp))) + 1
if stats['emp_vc_dim'] > math.log2(len(negative_border)):
sys.stderr.write("Lowering VC-dimension to maximum value\n")
stats['emp_vc_dim'] = int(
math.floor(math.log2(len(negative_border))))
sys.stderr.write(" ".join(
("cand_len={}".format(cand_len),
"longer_equal={}".format(longer_equal),
"emp_vc_dim={}".format(stats['emp_vc_dim']),
"optimal_sol_upp_bound_emp={}\n".format(optimal_sol_upp_bound_emp)
)))
sys.stderr.flush()
# If stopping condition is satisfied, exit.
if stats['emp_vc_dim'] <= longer_equal:
break
# sys.stderr.write("{} {} {}\n".format(vc_dim_cand, vc_dim_cand2,
# vc_dim_cand3))
os.remove(tmpfile_name)
# Compute the bound to the shatter coefficient, which we use to compute
# epsilon
bound = min((math.log(optimal_sol_upp_bound), stats['emp_vc_dim'] *
math.log(math.e * ds_stats['size'] / stats['emp_vc_dim'])))
sys.stderr.write(
"bound to shatter coeff: log_of_range_size={}, log_using_vc_dim={}\n".
format(
math.log(optimal_sol_upp_bound), stats['emp_vc_dim'] *
math.log(math.e * ds_stats['size'] / stats['emp_vc_dim'])))
sys.stderr.flush()
# The following assert is to check that we are better than another bound to
# the shatter coefficient which used the number of closed itemsets in the
# base set and the size of the negative border of the base set.
# Intuitively, the assert should not fail. =)
assert (optimal_sol_upp_bound <=
original_negative_border_len + closed_itemsets_len)
# Compute second candidate to epsilon_2
emp_epsilon_2 = epsilon.get_eps_shattercoeff_bound(lower_delta,
ds_stats['size'], bound,
max_freq_base_set)
sys.stderr.write(
"cand_len={} opt_sol_upp_bound_emp={} emp_vc_dim={} bound={} max_freq_base_set={} emp_e2={}\n"
.format(cand_len, optimal_sol_upp_bound_emp, stats['emp_vc_dim'],
bound, max_freq_base_set, emp_epsilon_2))
sys.stderr.flush()
sys.stderr.write("not_emp_e2={}, emp_e2={}\n".format(
not_emp_epsilon_2, emp_epsilon_2))
sys.stderr.flush()
stats['epsilon_2'] = min(emp_epsilon_2, not_emp_epsilon_2)
# Extract TFIs using epsilon_2
sys.stderr.write("Extracting TFIs using epsilon_2...")
sys.stderr.flush()
trueFIs = dict()
for itemset in reversed(freq_itemsets_1_sorted):
if freq_itemsets_1_dict[itemset] >= min_freq + stats['epsilon_2']:
trueFIs[itemset] = freq_itemsets_1_dict[itemset]
else:
break
sys.stderr.write("done ({} TFIS)\n".format(len(trueFIs)))
sys.stderr.flush()
return (trueFIs, stats)
def get_trueFIs(ds_stats, res_filename, min_freq, delta, gap=0.0,
use_additional_knowledge=False):
""" Compute the True Frequent Itemsets using the VC method we present in the
paper.
The parameter 'use_additional_knowledge' can be used to incorporate
additional knowledge about the data generation process.
'gap' controls how close to the optimal solution we ask the CPLEX solver to
go. The right way to implement this would be to use a
user-defined function in CPLEX.
Returns a pair (trueFIs, stats).
'trueFIs' is a dict whose keys are itemsets (frozensets) and values are
frequencies. This collection of itemsets contains only TFIs with
probability at least 1 - delta.
'stats' is a dict containing various statistics used in computing the
collection of itemsets."""
stats = dict()
# One may want to play with giving different values for the different error
# probabilities, but there isn't really much point in it.
lower_delta = 1.0 - math.sqrt(1 - delta)
# Compute the maximum frequency of an itemset in the dataset
with open(res_filename, 'rt') as FILE:
size_line = FILE.readline()
try:
size_str = size_line.split("(")[1].split(")")[0]
except IndexError:
error_exit("Cannot compute size of the dataset: '{}' is not in the recognized format\n".format(size_line))
try:
size = int(size_str)
except ValueError:
error_exit("Cannot compute size of the dataset: '{}' is not a number\n".format(size_line.split("(")[1].split(")")[0]))
max_freq_line = FILE.readline()
if max_freq_line.find("(") > -1:
tokens = max_freq_line.split("(")
itemset = frozenset(map(int, tokens[0].split()))
try:
support = int(tokens[1][:-2])
except ValueError:
error_exit("Cannot compute the maximum frequency: '{}' is not a number\n".format(tokens[1][:-2]))
max_freq = support / size
else:
error_exit("Cannot compute the maximum frequency: '{}' is not in the recognized format\n".format(max_freq_line))
# Compute the first epsilon using results from the paper (Riondato and
# Upfal 2014)
# Incorporate or not 'previous knowledge' about generative process in
# computation of the VC-dimension, depending on the option passed on the
# command line
(eps_vc_dim, eps_shatter, returned) = epsilon.epsilon_dataset(
lower_delta, ds_stats, use_additional_knowledge, max_freq)
stats['epsilon_1'] = min(eps_vc_dim, eps_shatter)
items = ds_stats['items']
items_num = len(items)
lengths_dict = ds_stats['lengths']
lengths = sorted(lengths_dict.keys(), reverse=True)
# Extract the first (and largest) set of itemsets with frequency at least
# min_freq - stats['epsilon_1']
lower_bound_freq = min_freq - stats['epsilon_1'] - (1 / ds_stats['size'])
freq_itemsets_1_dict = utils.create_results(res_filename, lower_bound_freq)
freq_itemsets_1_set = frozenset(freq_itemsets_1_dict.keys())
freq_itemsets_1_sorted = sorted(freq_itemsets_1_set,
key=lambda x: freq_itemsets_1_dict[x])
freq_items_1 = set()
for itemset in freq_itemsets_1_set:
if len(itemset) == 1:
freq_items_1 |= itemset
freq_items_1_num = len(freq_items_1)
sys.stderr.write("First set of FI's: {} itemsets\n".format(
len(freq_itemsets_1_set)))
sys.stderr.flush()
constr_start_str = "cplex.SparsePair(ind = ["
constr_end_str = "], val = vals)"
# Compute the "base set" (terrible name), that is the set of
# itemsets with frequency < min_freq + epsilon_1 (but greater than min_freq
# - stats['epsilon_1']. In the paper we call it \mathcal{G}.
sys.stderr.write("Creating base set...")
sys.stderr.flush()
base_set = dict()
# We use the maximum frequency in the base set to compute the epislon
max_freq_base_set = 0
for itemset in freq_itemsets_1_sorted:
if freq_itemsets_1_dict[itemset] < min_freq + stats['epsilon_1']:
base_set[itemset] = freq_itemsets_1_dict[itemset]
if freq_itemsets_1_dict[itemset] > max_freq_base_set:
max_freq_base_set = freq_itemsets_1_dict[itemset]
else:
break
stats['base_set'] = len(base_set)
sys.stderr.write("done: {} itemsets\n".format(stats['base_set']))
sys.stderr.flush()
# Compute Closed Itemsets. We need them to compute the maximal.
sys.stderr.write("Computing closed itemsets...")
sys.stderr.flush()
closed_itemsets = utils.get_closed_itemsets(base_set)
closed_itemsets_len = len(closed_itemsets)
sys.stderr.write("done. Found {} closed itemsets\n".format(
closed_itemsets_len))
sys.stderr.flush()
# Compute maximal itemsets. We will use them to compute the negative
# border. An itemset is maximal frequent if none of its immediate supersets
# is frequent.
sys.stderr.write("Computing maximal itemsets...")
sys.stderr.flush()
maximal_itemsets_dict = utils.get_maximal_itemsets(closed_itemsets)
maximal_itemsets = list(maximal_itemsets_dict.keys())
stats['maximal_itemsets'] = len(maximal_itemsets)
sys.stderr.write("done. Found {} maximal itemsets\n".format(
stats['maximal_itemsets']))
sys.stderr.flush()
# Compute the negative border
sys.stderr.write("Computing negative border...")
sys.stderr.flush()
negative_border = set()
negative_border_items = set()
# The idea is to look for "children" of maximal itemsets, and for
# "siblings" of maximal itemsets
for maximal in maximal_itemsets:
for item_to_remove_from_maximal in maximal:
reduced_maximal = maximal - frozenset(
[item_to_remove_from_maximal, ])
for item in freq_items_1:
if item in maximal:
continue
# Create sibling
candidate = reduced_maximal | frozenset([item])
if candidate in freq_itemsets_1_set:
continue
if candidate in negative_border:
continue
to_add = True
for item_to_remove in candidate:
subset = candidate - frozenset([item_to_remove])
if subset not in freq_itemsets_1_set:
to_add = False
break
if to_add:
negative_border.add(candidate)
negative_border_items |= candidate
if not to_add:
# if we added the sibling, there's no way we can add the
# child
candidate2 = maximal | frozenset([item]) # create child
if candidate2 in negative_border:
continue
to_add = True
for item_to_remove in candidate2:
subset = candidate2 - frozenset([item_to_remove])
if subset not in freq_itemsets_1_set:
to_add = False
break
if to_add:
negative_border.add(candidate2)
negative_border_items |= candidate
# We don't need to add the non-frequent-items because none of them (or
# their supersets) will ever be included in the output, so at most we lose
# some statistical power, but it's not a problem of avoiding false
# positives.
# for item in non_freq_items_1:
# negative_border.add(frozenset([item]))
# negative_border_items.add(item)
original_negative_border_len = len(negative_border)
sys.stderr.write("done. Length now: {}\n".format(
original_negative_border_len))
sys.stderr.flush()
# Add the "base set" to negative_border, so that it becomes a superset of
# the "true" negative border (with some caveats about non-frequent single
# items and their supersets, see comment above)
sys.stderr.write("Adding base set...")
sys.stderr.flush()
for itemset in base_set:
negative_border.add(itemset)
negative_border_items |= itemset
sys.stderr.write("done. Length now: {}\n".format(len(negative_border)))
sys.stderr.flush()
negative_border = sorted(negative_border, key=len, reverse=True)
stats['negative_border'] = len(negative_border)
negative_border_items_sorted = sorted(negative_border_items)
# Create the graph that we will use to compute the chain constraints.
# The nodes are the itemsets in negative_border. There is an edge between
# two nodes if one is contained in the other or vice-versa.
# Cliques on this graph are chains.
sys.stderr.write("Creating graph...")
sys.stderr.flush()
graph = nx.Graph()
graph.add_nodes_from(negative_border)
sys.stderr.write("added nodes...adding edges...")
sys.stderr.flush()
negative_border_items_in_sets_dict = dict()
negative_border_itemset_index = 0
itemset_indexes_dict = dict()
for first_itemset_index in range(stats['negative_border']):
first_itemset = negative_border[first_itemset_index]
for second_itemset_index in range(first_itemset_index + 1,
stats['negative_border']):
second_itemset = negative_border[second_itemset_index]
if first_itemset < second_itemset or \
second_itemset < first_itemset:
graph.add_edge(first_itemset, second_itemset)
for item in first_itemset:
if item in negative_border_items_in_sets_dict:
negative_border_items_in_sets_dict[item].append(
negative_border_itemset_index)
else:
negative_border_items_in_sets_dict[item] = \
[negative_border_itemset_index, ]
itemset_indexes_dict[first_itemset] = negative_border_itemset_index
negative_border_itemset_index += 1
sys.stderr.write("done\n")
sys.stderr.flush()
capacity = freq_items_1_num - 1
if use_additional_knowledge and 2 * ds_stats['maxlen'] < capacity:
sys.stderr.write("Lowering capacity={} to {}\n".format(
capacity, 2 * ds_stats['maxlen']))
sys.stderr.flush()
capacity = 2 * ds_stats['maxlen']
vars_num = stats['negative_border'] + len(negative_border_items)
constr_names = []
(tmpfile_handle, tmpfile_name) = tempfile.mkstemp(
prefix="cplx", dir=os.environ['PWD'], text=True)
os.close(tmpfile_handle)
with open(tmpfile_name, 'wt') as cplex_script:
cplex_script.write("capacity = {}\n".format(capacity))
cplex_script.write("import cplex, os, sys\n")
cplex_script.write("from cplex.exceptions import CplexError\n")
cplex_script.write("\n")
cplex_script.write("\n")
cplex_script.write(
" ".join(
("os.environ[\"ILOG_LICENSE_FILE\"] =",
"\"/local/projects/cplex/ilm/site.access.ilm\"\n")))
cplex_script.write("vals = [-1.0, 1.0]\n")
cplex_script.write("sets_num = {}\n".format(stats['negative_border']))
cplex_script.write("items_num = {}\n".format(
len(negative_border_items)))
cplex_script.write("vars_num = {}\n".format(vars_num))
cplex_script.write("my_ub = [1.0] * vars_num\n")
cplex_script.write(
"my_types = \"\".join(\"I\" for i in range(vars_num))\n")
cplex_script.write(
"my_obj = ([1.0] * sets_num) + ([0.0] * items_num)\n")
cplex_script.write(
" ".join(
("my_colnames =",
"[\"set{0}\".format(i) for i in range(sets_num)] +",
"[\"item{0}\".format(j) for j in range(items_num)]\n")))
cplex_script.write("rows = [ ")
sys.stderr.write("Writing knapsack constraints...")
sys.stderr.flush()
constr_num = 0
for item_index in range(len(negative_border_items)):
try:
for itemset_index in negative_border_items_in_sets_dict[
negative_border_items_sorted[item_index]]:
constr_str = "".join(
(constr_start_str,
"\"set{}\",\"item{}\"".format(
itemset_index, item_index), constr_end_str))
cplex_script.write("{},".format(constr_str))
constr_num += 1
name = "s{}i{}".format(item_index, itemset_index)
constr_names.append(name)
except KeyError:
sys.stderr.write(
" ".join(
("item_index={}".format(item_index),
"neg_border_items_sorted[item_index]={}\n".format(
negative_border_items_sorted[item_index]))))
sys.stderr.write("{} in items: {}\n".format(
negative_border_items_sorted[item_index],
negative_border_items_sorted[item_index] in items))
sys.stderr.write("{} in freq_items_1: {}\n".format(
negative_border_items_sorted[item_index],
negative_border_items_sorted[item_index] in freq_items_1))
non_freq_items_1 = items - freq_items_1
sys.stderr.write("{} in non_freq_items_1: {}\n".format(
negative_border_items_sorted[item_index],
negative_border_items_sorted[item_index] in
non_freq_items_1))
in_pos_border = False
pos_border_itemset = frozenset()
for itemset in maximal_itemsets:
if negative_border_items_sorted[item_index] in itemset:
in_pos_border = True
pos_border_itemset = itemset
break
sys.stderr.write(
"{} in maximal_itemsets: {}. Itemset: {}\n".format(
negative_border_items_sorted[item_index],
in_pos_border, pos_border_itemset))
in_neg_border = False
neg_border_itemset = frozenset()
for itemset in negative_border:
if negative_border_items_sorted[item_index] in itemset:
in_neg_border = True
neg_border_itemset = itemset
break
sys.stderr.write(
"{} in negative_border: {}. Itemset: {}\n".format(
negative_border_items_sorted[item_index],
in_neg_border, neg_border_itemset))
sys.exit(1)
# Create capacity constraints and write it to script
constr_str = "".join(
(constr_start_str,
",".join(
"\"item{}\"".format(j) for j in range(
len(negative_border_items))),
"], val=[", ",".join(
"1.0" for j in range(len(negative_border_items))), "])"))
cplex_script.write(constr_str)
last_tell = cplex_script.tell()
cplex_script.write(",")
cap_constr_name = "capacity"
constr_names.append(cap_constr_name)
sys.stderr.write("done\n")
sys.stderr.flush()
# Create chain constraints and write them to script
sys.stderr.write("Writing chain constraints...")
sys.stderr.flush()
chains_index = 0
for clique in nx.find_cliques(graph):
if len(clique) == 1:
continue
constr_str = "".join(
(constr_start_str,
",".join("\"set{}\"".format(j) for j in map(
lambda x: itemset_indexes_dict[x], clique)),
"], val=[1.0] * {}".format(len(clique)), ")"))
cplex_script.write(constr_str)
last_tell = cplex_script.tell()
cplex_script.write(",")
name = "chain{}".format(chains_index)
constr_names.append(name)
chains_index += 1
sys.stderr.write("done\n")
sys.stderr.flush()
sys.stderr.write(
" ".join(
("Optimization problem: capacity={}".format(capacity),
"vars_num={}".format(vars_num),
"negative_border_size={}".format(stats['negative_border']),
"negative_border_items_num={}".format(
len(negative_border_items)),
"constr_num={}".format(constr_num),
"chains_index={}\n".format(chains_index))))
sys.stderr.flush()
# Go back one character to remove last comma ","
cplex_script.seek(last_tell)
cplex_script.write("]\n")
cplex_script.write("my_rownames = {}\n".format(constr_names))
cplex_script.write("constr_num = {}\n".format(constr_num))
cplex_script.write("chain_constr_num = {}\n".format(chains_index))
cplex_script.write(
" ".join(
("my_senses = [\"G\"] * constr_num +",
"[\"L\"] + [\"L\"] * chain_constr_num\n")))
cplex_script.write(
" ".join(
("my_rhs = [0.0] * constr_num + [capacity] +",
"[1.0] * chain_constr_num\n")))
cplex_script.write("\n")
cplex_script.write("try:\n")
cplex_script.write(" prob = cplex.Cplex()\n")
cplex_script.write(" prob.set_error_stream(sys.stderr)\n")
cplex_script.write(" prob.set_log_stream(sys.stderr)\n")
cplex_script.write(" prob.set_results_stream(sys.stderr)\n")
cplex_script.write(" prob.set_warning_stream(sys.stderr)\n")
# cplex_script.write(" prob.parameters.mip.strategy.file.set(2)\n")
cplex_script.write(
" prob.parameters.mip.tolerances.mipgap.set({})\n".format(gap))
cplex_script.write(
" prob.parameters.timelimit.set({})\n".format(600))
# cplex_script.write("
# prob.parameters.mip.strategy.variableselect.set(3) # strong
# branching\n")
cplex_script.write(
" prob.objective.set_sense(prob.objective.sense.maximize)\n")
cplex_script.write(
" ".join(
(" prob.variables.add(obj = my_obj, ub = my_ub,",
"types = my_types, names = my_colnames)\n")))
cplex_script.write(
" ".join(
(" prob.linear_constraints.add(lin_expr = rows,",
"senses = my_senses, rhs = my_rhs, names = my_rownames)\n")))
cplex_script.write(
" ".join(
(" prob.MIP_starts.add(cplex.SparsePair(",
"ind = [i for i in range(vars_num)],",
"val = [1.0] * vars_num),",
"prob.MIP_starts.effort_level.auto)\n")))
cplex_script.write(" prob.solve()\n")
cplex_script.write(
"".join(
(" print (prob.solution.get_status(),",
"prob.solution.status[prob.solution.get_status()],",
"prob.solution.MIP.get_best_objective(),",
"prob.solution.MIP.get_mip_relative_gap())\n")))
cplex_script.write("except CplexError, exc:\n")
cplex_script.write(" print exc\n")
# Run script, solve optimization problem, extract solution
my_environ = os.environ
if "ILOG_LICENSE_FILE" not in my_environ:
my_environ["ILOG_LICENSE_FILE"] = \
"/local/projects/cplex/ilm/site.access.ilm"
try:
cplex_output_binary_str = subprocess.check_output(
["python2.6", tmpfile_name], env=my_environ,
cwd=os.environ["PWD"])
except subprocess.CalledProcessError as err:
os.remove(tmpfile_name)
utils.error_exit("CPLEX exited with error code {}: {}\n".format(
err.returncode, err.output))
# finally:
# os.remove(tmpfile_name)
cplex_output = cplex_output_binary_str.decode(
locale.getpreferredencoding())
cplex_output_lines = cplex_output.split("\n")
cplex_solution_line = cplex_output_lines[
-1 if len(cplex_output_lines[-1]) > 0 else -2]
try:
cplex_solution = eval(cplex_solution_line)
except Exception:
utils.error_exit(
"Error evaluating the CPLEX solution line: {}\n".format(
cplex_solution_line))
sys.stderr.write("cplex_solution={}\n".format(cplex_solution))
sys.stderr.flush()
# if cplex_solution[0] not in (1, 101, 102):
# utils.error_exit("CPLEX didn't find the optimal solution: {} {}
# {}\n".format(cplex_solution[0], cplex_solution[1], cplex_solution[2]))
# This is also an upper bound to the size of the true negative border
optimal_sol_upp_bound = int(
math.floor(cplex_solution[2] * (1 + cplex_solution[3])))
# Compute non-empirical VC-dimension and first candidate to epsilon_2
stats['not_emp_vc_dim'] = int(
math.floor(math.log2(optimal_sol_upp_bound))) + 1
if stats['not_emp_vc_dim'] > math.log2(len(negative_border)):
sys.stderr.write(
"Lowering non_empirical VC-dimension to maximum value\n")
stats['not_emp_vc_dim'] = int(
math.floor(math.log2(len(negative_border))))
not_emp_epsilon_2 = epsilon.get_eps_vc_dim(
lower_delta, ds_stats['size'], stats['not_emp_vc_dim'])
sys.stderr.write(
" ".join(
("items_num-1={}".format(items_num - 1),
"optimal_sol_upp_bound={}".format(optimal_sol_upp_bound),
"not_emp_vc_dim={}".format(stats['not_emp_vc_dim']),
"not_emp_e2={}\n".format(not_emp_epsilon_2))))
sys.stderr.flush()
# Loop to compute empirical VC-dimension using lengths distribution
items_num_str_len = len(str(len(negative_border_items) - 1))
longer_equal = 0
for i in range(len(lengths)):
cand_len = lengths[i]
if cand_len == items_num:
continue
longer_equal += lengths_dict[cand_len]
# No need to include tests to check whether cand_len is lower than
# 2*ds_stats['maxlen'] if use_additional_knowledge is True: it is
# always true given that cand_len <= ds_stats['maxlen']
if cand_len >= len(negative_border_items):
cand_len = len(negative_border_items) - 1
# Modify the script to use the new capacity.
with open(tmpfile_name, 'r+t') as cplex_script:
cplex_script.seek(0)
cplex_script.write("capacity = {}\n".format(
str(cand_len).ljust(items_num_str_len)))
# Run the script, solve optimization problem, extract solution
my_environ = os.environ
if "ILOG_LICENSE_FILE" not in my_environ:
my_environ["ILOG_LICENSE_FILE"] = \
"/local/projects/cplex/ilm/site.access.ilm"
try:
cplex_output_binary_str = subprocess.check_output(
["python2.6", tmpfile_name], env=my_environ,
cwd=os.environ["PWD"])
except subprocess.CalledProcessError as err:
os.remove(tmpfile_name)
utils.error_exit("CPLEX exited with error code {}: {}\n".format(
err.returncode, err.output))
# finally:
# os.remove(tmpfile_name)
cplex_output = cplex_output_binary_str.decode(
locale.getpreferredencoding())
cplex_output_lines = cplex_output.split("\n")
cplex_solution_line = cplex_output_lines[
-1 if len(cplex_output_lines[-1]) > 0 else -2]
try:
cplex_solution = eval(cplex_solution_line)
except Exception:
utils.error_exit(
"Error evaluating the CPLEX solution line: {}\n".format(
cplex_solution_line))
sys.stderr.write("{}\n".format(cplex_solution))
# if cplex_solution[0] not in (1, 101, 102):
# utils.error_exit("CPLEX didn't find the optimal solution: {} {}
# {}\n".format(cplex_solution[0], cplex_solution[1],
# cplex_solution[2]))
# if cplex_solution[0] == 102:
optimal_sol_upp_bound_emp = int(
math.floor(cplex_solution[2] * (1 + cplex_solution[3])))
# else:
# optimal_sol_upp_bound_emp = cplex_solution[0]
stats['emp_vc_dim'] = int(
math.floor(math.log2(optimal_sol_upp_bound_emp))) + 1
if stats['emp_vc_dim'] > math.log2(len(negative_border)):
sys.stderr.write("Lowering VC-dimension to maximum value\n")
stats['emp_vc_dim'] = int(
math.floor(math.log2(len(negative_border))))
sys.stderr.write(
" ".join(
("cand_len={}".format(cand_len),
"longer_equal={}".format(longer_equal),
"emp_vc_dim={}".format(stats['emp_vc_dim']),
"optimal_sol_upp_bound_emp={}\n".format(optimal_sol_upp_bound_emp))))
sys.stderr.flush()
# If stopping condition is satisfied, exit.
if stats['emp_vc_dim'] <= longer_equal:
break
# sys.stderr.write("{} {} {}\n".format(vc_dim_cand, vc_dim_cand2,
# vc_dim_cand3))
os.remove(tmpfile_name)
# Compute the bound to the shatter coefficient, which we use to compute
# epsilon
bound = min((math.log(optimal_sol_upp_bound), stats['emp_vc_dim'] *
math.log(math.e * ds_stats['size'] / stats['emp_vc_dim'])))
sys.stderr.write("bound to shatter coeff: log_of_range_size={}, log_using_vc_dim={}\n".format(
math.log(optimal_sol_upp_bound),
stats['emp_vc_dim'] * math.log(math.e * ds_stats['size'] / stats['emp_vc_dim'])))
sys.stderr.flush()
# The following assert is to check that we are better than another bound to
# the shatter coefficient which used the number of closed itemsets in the
# base set and the size of the negative border of the base set.
# Intuitively, the assert should not fail. =)
assert(optimal_sol_upp_bound <= original_negative_border_len +
closed_itemsets_len)
# Compute second candidate to epsilon_2
emp_epsilon_2 = epsilon.get_eps_shattercoeff_bound(lower_delta,
ds_stats['size'], bound, max_freq_base_set)
sys.stderr.write(
"cand_len={} opt_sol_upp_bound_emp={} emp_vc_dim={} bound={} max_freq_base_set={} emp_e2={}\n".format(
cand_len, optimal_sol_upp_bound_emp, stats['emp_vc_dim'], bound,
max_freq_base_set, emp_epsilon_2))
sys.stderr.flush()
sys.stderr.write("not_emp_e2={}, emp_e2={}\n".format(
not_emp_epsilon_2, emp_epsilon_2))
sys.stderr.flush()
stats['epsilon_2'] = min(emp_epsilon_2, not_emp_epsilon_2)
# Extract TFIs using epsilon_2
sys.stderr.write("Extracting TFIs using epsilon_2...")
sys.stderr.flush()
trueFIs = dict()
for itemset in reversed(freq_itemsets_1_sorted):
if freq_itemsets_1_dict[itemset] >= min_freq + stats['epsilon_2']:
trueFIs[itemset] = freq_itemsets_1_dict[itemset]
else:
break
sys.stderr.write("done ({} TFIS)\n".format(len(trueFIs)))
sys.stderr.flush()
return (trueFIs, stats)
def get_trueFIs(exp_res_filename,
eval_res_filename,
min_freq,
delta,
gap=0.0,
first_epsilon=1.0,
vcdim=-1):
""" Compute the True Frequent Itemsets using the 'holdout-VC' method.
TODO Add more details."""
stats = dict()
with open(exp_res_filename) as FILE:
size_line = FILE.readline()
try:
size_str = size_line.split("(")[1].split(")")[0]
except IndexError:
utils.error_exit(" ".join(
("Cannot compute size of the explore dataset:",
"'{}' is not in the recognized format\n".format(size_line))))
try:
stats['exp_size'] = int(size_str)
except ValueError:
utils.error_exit(" ".join(
("Cannot compute size of the explore dataset:",
"{} is not a number\n".format(size_str))))
with open(eval_res_filename) as FILE:
size_line = FILE.readline()
try:
size_str = size_line.split("(")[1].split(")")[0]
except IndexError:
utils.error_exit(" ".join(
("Cannot compute size of the eval dataset:",
"'{}' is not in the recognized format\n".format(size_line))))
try:
stats['eval_size'] = int(size_str)
except ValueError:
utils.error_exit(" ".join(
("Cannot compute size of the eval dataset:",
"'{}' is not a number\n".format(size_str))))
stats['orig_size'] = stats['exp_size'] + stats['eval_size']
exp_res = utils.create_results(exp_res_filename, min_freq)
stats['exp_res'] = len(exp_res)
exp_res_set = set(exp_res.keys())
eval_res = utils.create_results(eval_res_filename, min_freq)
stats['eval_res'] = len(eval_res)
eval_res_set = set(eval_res.keys())
intersection = exp_res_set & eval_res_set
stats['holdout_intersection'] = len(intersection)
stats['holdout_false_negatives'] = len(exp_res_set - eval_res_set)
stats['holdout_false_positives'] = len(eval_res_set - exp_res_set)
stats['holdout_jaccard'] = len(intersection) / \
len(exp_res_set | eval_res_set)
# One may want to play with giving different values for the different error
# probabilities, but there isn't really much point in it.
lower_delta = 1.0 - math.sqrt(1 - delta)
stats['epsilon_1'] = first_epsilon
sys.stderr.write("Computing candidates...")
sys.stderr.flush()
freq_bound = min_freq + stats['epsilon_1']
candidates = []
candidates_items = set()
trueFIs = dict()
for itemset in exp_res:
if exp_res[itemset] < freq_bound:
candidates.append(itemset)
candidates_items |= itemset
else:
# Add itemsets with frequency at last freq_bound to the TFIs
trueFIs[itemset] = exp_res[itemset]
sys.stderr.write("done: {} candidates ({} items)\n".format(
len(candidates), len(candidates_items)))
sys.stderr.flush()
if len(candidates
) > 0 and vcdim > -1 and len(candidates_items) - 1 > vcdim:
sys.stderr.write("Using additional knowledge\n")
candidates_items_sorted = sorted(candidates_items)
candidates_items_in_sets_dict = dict()
candidates_itemset_index = 0
itemset_indexes_dict = dict()
for first_itemset_index in range(len(candidates)):
first_itemset = candidates[first_itemset_index]
for item in first_itemset:
if item in candidates_items_in_sets_dict:
candidates_items_in_sets_dict[item].append(
candidates_itemset_index)
else:
candidates_items_in_sets_dict[item] = \
[candidates_itemset_index, ]
itemset_indexes_dict[first_itemset] = candidates_itemset_index
candidates_itemset_index += 1
# Compute an upper-bound to the VC-dimension of the set of candidates.
constr_start_str = "cplex.SparsePair(ind = ["
constr_end_str = "], val = vals)"
vars_num = len(candidates) + len(candidates_items)
constr_names = []
capacity = vcdim
(tmpfile_handle,
tmpfile_name) = tempfile.mkstemp(prefix="cplx",
dir=os.environ['PWD'],
text=True)
os.close(tmpfile_handle)
with open(tmpfile_name, 'wt') as cplex_script:
cplex_script.write("capacity = {}\n".format(capacity))
cplex_script.write("import cplex, os, sys\n")
cplex_script.write("from cplex.exceptions import CplexError\n")
cplex_script.write("\n")
cplex_script.write("\n")
cplex_script.write(" ".join(
("os.environ[\"ILOG_LICENSE_FILE\"] ="
"\"/local/projects/cplex/ilm/site.access.ilm\"\n")))
cplex_script.write("vals = [-1.0, 1.0]\n")
cplex_script.write("sets_num = {}\n".format(len(candidates)))
cplex_script.write("items_num = {}\n".format(
len(candidates_items)))
cplex_script.write("vars_num = {}\n".format(vars_num))
cplex_script.write("my_ub = [1.0] * vars_num\n")
cplex_script.write(
"my_types = \"\".join(\"I\" for i in range(vars_num))\n")
cplex_script.write(
"my_obj = ([1.0] * sets_num) + ([0.0] * items_num)\n")
cplex_script.write(" ".join(
("my_colnames ="
"[\"set{0}\".format(i) for i in range(sets_num)]",
"+ [\"item{0}\".format(j) for j in range(items_num)]\n")))
cplex_script.write("rows = [ ")
sys.stderr.write("Writing knapsack constraints...")
sys.stderr.flush()
constr_num = 0
for item_index in range(len(candidates_items)):
try:
for itemset_index in \
candidates_items_in_sets_dict[
candidates_items_sorted[item_index]]:
constr_str = "".join(
(constr_start_str, "\"set{}\",\"item{}\"".format(
itemset_index, item_index), constr_end_str))
cplex_script.write("{},".format(constr_str))
constr_num += 1
name = "s{}i{}".format(item_index, itemset_index)
constr_names.append(name)
except KeyError:
sys.stderr.write(" ".join(
("item_index={}".format(item_index),
"candidates_items_sorted[item_index]={}\n".format(
candidates_items_sorted[item_index]))))
in_candidates = False
candidates_itemset = frozenset()
for itemset in candidates:
if candidates_items_sorted[item_index] in itemset:
in_candidates = True
candidates_itemset = itemset
break
sys.stderr.write(
"{} in negative_border: {}. Itemset: {}\n".format(
candidates_items_sorted[item_index], in_candidates,
candidates_itemset))
sys.exit(1)
# Create capacity constraints and write it to script
constr_str = "".join(
(constr_start_str,
",".join("\"item{}\"".format(j)
for j in range(len(candidates_items))), "], val=[",
",".join("1.0" for j in range(len(candidates_items))), "])"))
cplex_script.write(constr_str)
cplex_script.write("]\n")
cap_constr_name = "capacity"
constr_names.append(cap_constr_name)
sys.stderr.write("done\n")
sys.stderr.flush()
sys.stderr.write(" ".join(
("Optimization problem: capacity={}".format(capacity),
"vars_num={}".format(vars_num),
"candidates={}".format(len(candidates)),
"candidates_items_num={}".format(len(candidates_items)),
"constr_num={}\n".format(constr_num))))
sys.stderr.flush()
cplex_script.write("my_rownames = {}\n".format(constr_names))
cplex_script.write("constr_num = {}\n".format(constr_num))
cplex_script.write("my_senses = [\"G\"] * constr_num + [\"L\"]\n")
cplex_script.write("my_rhs = [0.0] * constr_num + [capacity]\n")
cplex_script.write("\n")
cplex_script.write("try:\n")
cplex_script.write(" prob = cplex.Cplex()\n")
cplex_script.write(" prob.set_error_stream(sys.stderr)\n")
cplex_script.write(" prob.set_log_stream(sys.stderr)\n")
cplex_script.write(" prob.set_results_stream(sys.stderr)\n")
cplex_script.write(" prob.set_warning_stream(sys.stderr)\n")
# cplex_script.write("
# prob.parameters.mip.strategy.file.set(2)\n")
cplex_script.write(
" prob.parameters.mip.tolerances.mipgap.set({})\n".format(
gap))
cplex_script.write(
" prob.parameters.timelimit.set({})\n".format(600))
# cplex_script.write("
# prob.parameters.mip.strategy.variableselect.set(3) # strong
# branching\n")
cplex_script.write("".join((" prob.objective.set_sense(",
"prob.objective.sense.maximize)\n")))
cplex_script.write(" ".join(
(" prob.variables.add(obj = my_obj, ub = my_ub,",
"types = my_types, names = my_colnames)\n")))
cplex_script.write(" ".join(
(" prob.linear_constraints.add(lin_expr = rows,",
"senses = my_senses, rhs = my_rhs,",
"names = my_rownames)\n")))
cplex_script.write(" ".join(
(" prob.MIP_starts.add(cplex.SparsePair(ind =",
"[i for i in range(vars_num)], val = [1.0] * vars_num),",
"prob.MIP_starts.effort_level.auto)\n")))
cplex_script.write(" prob.solve()\n")
cplex_script.write(",".join(
(" print (prob.solution.get_status()",
"prob.solution.status[prob.solution.get_status()]",
"prob.solution.MIP.get_best_objective()"
"prob.solution.MIP.get_mip_relative_gap())\n")))
cplex_script.write("except CplexError, exc:\n")
cplex_script.write(" print exc\n")
# Run script, solve optimization problem, extract solution
my_environ = os.environ
if "ILOG_LICENSE_FILE" not in my_environ:
my_environ["ILOG_LICENSE_FILE"] = \
"/local/projects/cplex/ilm/site.access.ilm"
try:
cplex_output_binary_str = subprocess.check_output(
["python2.6", tmpfile_name],
env=my_environ,
cwd=os.environ["PWD"])
except subprocess.CalledProcessError as err:
os.remove(tmpfile_name)
utils.error_exit("CPLEX exited with error code {}: {}\n".format(
err.returncode, err.output))
# finally:
# os.remove(tmpfile_name)
cplex_output = cplex_output_binary_str.decode(
locale.getpreferredencoding())
cplex_output_lines = cplex_output.split("\n")
cplex_solution_line = cplex_output_lines[
-1 if len(cplex_output_lines[-1]) > 0 else -2]
try:
cplex_solution = eval(cplex_solution_line)
except Exception:
utils.error_exit(
"Error evaluating the CPLEX solution line: {}\n".format(
cplex_solution_line))
sys.stderr.write("cplex_solution={}\n".format(cplex_solution))
sys.stderr.flush()
# if cplex_solution[0] not in (1, 101, 102):
# utils.error_exit("CPLEX didn't find the optimal solution: {} {}
# {}\n".format(cplex_solution[0], cplex_solution[1],
# cplex_solution[2]))
optimal_sol_upp_bound = int(
math.floor(cplex_solution[2] * (1 + cplex_solution[3])))
stats['vcdim'] = int(math.floor(math.log2(optimal_sol_upp_bound))) + 1
if stats['vcdim'] > math.log2(len(candidates)):
sys.stderr.write("Lowering VC-dimension to maximum value\n")
sys.stderr.flush()
stats['vcdim'] = int(math.floor(math.log2(len(candidates))))
stats['epsilon_2_vc'] = epsilon.get_eps_vc_dim(lower_delta,
stats['orig_size'],
stats['vcdim'])
elif len(candidates
) > 0 and vcdim > -1 and len(candidates_items) - 1 <= vcdim:
sys.stderr.write("Additional knowledge is useless\n")
sys.stderr.flush()
stats['vcdim'] = int(math.floor(math.log2(len(candidates))))
stats['epsilon_2_vc'] = epsilon.get_eps_vc_dim(lower_delta,
stats['orig_size'],
stats['vcdim'])
elif len(candidates) > 0 and vcdim == -1:
sys.stderr.write("Not using additional knowledge\n")
sys.stderr.flush()
stats['vcdim'] = int(math.floor(math.log2(len(candidates))))
stats['epsilon_2_vc'] = epsilon.get_eps_vc_dim(lower_delta,
stats['orig_size'],
stats['vcdim'])
else:
sys.stderr.write("There are no candidates\n")
sys.stderr.flush()
stats['vcdim'] = 0
stats['epsilon_2_vc'] = 0
# Loop to compute empirical VC-dimension using lengths distribution
capacity_str_len = len(str(capacity))
longer_equal = 0
lengths_dict = ds_stats['lengths']
lengths = sorted(lengths_dict.keys(), reverse=True)
start_len_idx = 0
while start_len_idx < len(lengths):
if lengths[start_len_idx] > len(candidates_items) - 1:
longer_equal += lengths_dict[start_len_idx]
start_len_idx += 1
else:
break
for i in range(start_len_idx, len(lengths)):
cand_len = lengths[i]
longer_equal += lengths_dict[cand_len]
# Modify the script to use the new capacity.
with open(tmpfile_name, 'r+t') as cplex_script:
cplex_script.seek(0)
cplex_script.write("capacity = {}\n".format(
str(cand_len).ljust(capacity_str_len)))
# Run the script, solve optimization problem, extract solution
my_environ = os.environ
if "ILOG_LICENSE_FILE" not in my_environ:
my_environ["ILOG_LICENSE_FILE"] = \
"/local/projects/cplex/ilm/site.access.ilm"
try:
cplex_output_binary_str = subprocess.check_output(
["python2.6", tmpfile_name],
env=my_environ,
cwd=os.environ["PWD"])
except subprocess.CalledProcessError as err:
os.remove(tmpfile_name)
utils.error_exit("CPLEX exited with error code {}: {}\n".format(
err.returncode, err.output))
# finally:
# os.remove(tmpfile_name)
cplex_output = cplex_output_binary_str.decode(
locale.getpreferredencoding())
cplex_output_lines = cplex_output.split("\n")
cplex_solution_line = cplex_output_lines[
-1 if len(cplex_output_lines[-1]) > 0 else -2]
try:
cplex_solution = eval(cplex_solution_line)
except Exception:
utils.error_exit(
"Error evaluating the CPLEX solution line: {}\n".format(
cplex_solution_line))
sys.stderr.write("{}\n".format(cplex_solution))
# if cplex_solution[0] not in (1, 101, 102):
# utils.error_exit("CPLEX didn't find the optimal solution: {} {}
# {}\n".format(cplex_solution[0], cplex_solution[1],
# cplex_solution[2]))
# if cplex_solution[0] == 102:
optimal_sol_upp_bound_emp = int(
math.floor(cplex_solution[2] * (1 + cplex_solution[3])))
# else:
# optimal_sol_upp_bound_emp = cplex_solution[0]
stats['emp_vc_dim'] = int(
math.floor(math.log2(optimal_sol_upp_bound_emp))) + 1
if stats['emp_vc_dim'] > math.log2(len(negative_border)):
sys.stderr.write("Lowering VC-dimension to maximum value\n")
stats['emp_vc_dim'] = int(
math.floor(math.log2(len(negative_border))))
sys.stderr.write(" ".join(
("cand_len={}".format(cand_len),
"longer_equal={}".format(longer_equal),
"emp_vc_dim={}".format(stats['emp_vc_dim']),
"optimal_sol_upp_bound_emp={}\n".format(optimal_sol_upp_bound_emp)
)))
sys.stderr.flush()
# If stopping condition is satisfied, exit.
if stats['emp_vc_dim'] <= longer_equal:
break
os.remove(tmpfile_name)
# Compute the bound to the shatter coefficient, which we use to compute
# epsilon
bound = min((math.log(len(candidates)), stats['emp_vc_dim'] *
math.log(math.e * stats['eval_size'] / stats['emp_vc_dim'])))
# Compute second candidate to epsilon_2
emp_epsilon_2 = epsilon.get_eps_shattercoeff_bound(lower_delta,
stats['eval_size'],
bound,
max_freq_base_set)
sys.stderr.write(
"cand_len={} opt_sol_upp_bound_emp={} emp_vc_dim={} bound={} max_freq_base_set={} emp_e2={}\n"
.format(cand_len, optimal_sol_upp_bound_emp, stats['emp_vc_dim'],
bound, max_freq_base_set, emp_epsilon_2))
sys.stderr.flush()
sys.stderr.write("not_emp_e2={}, emp_e2={}\n".format(
stats['epsilon_2_vc'], emp_epsilon_2))
sys.stderr.flush()
stats['epsilon_2'] = min(emp_epsilon_2, stats['epsilon_2_vc'])
if len(candidates) > 0:
sys.stderr.write("Computing the candidates that are TFIs...")
sys.stderr.flush()
freq_bound = min_freq + stats['epsilon_2']
eval_res_itemsets = frozenset(eval_res.keys())
for itemset in sorted(frozenset(candidates) & eval_res_itemsets,
key=lambda x: eval_res[x],
reverse=True):
if eval_res[itemset] >= freq_bound:
trueFIs[itemset] = eval_res[itemset]
sys.stderr.write("done\n")
sys.stderr.flush()
return (trueFIs, stats)
def get_trueFIs(exp_res_filename, eval_res_filename, min_freq, delta, gap=0.0, first_epsilon=1.0, vcdim=-1):
""" Compute the True Frequent Itemsets using the 'holdout-VC' method.
TODO Add more details."""
stats = dict()
with open(exp_res_filename) as FILE:
size_line = FILE.readline()
try:
size_str = size_line.split("(")[1].split(")")[0]
except IndexError:
utils.error_exit(
" ".join(
(
"Cannot compute size of the explore dataset:",
"'{}' is not in the recognized format\n".format(size_line),
)
)
)
try:
stats["exp_size"] = int(size_str)
except ValueError:
utils.error_exit(
" ".join(("Cannot compute size of the explore dataset:", "{} is not a number\n".format(size_str)))
)
with open(eval_res_filename) as FILE:
size_line = FILE.readline()
try:
size_str = size_line.split("(")[1].split(")")[0]
except IndexError:
utils.error_exit(
" ".join(
(
"Cannot compute size of the eval dataset:",
"'{}' is not in the recognized format\n".format(size_line),
)
)
)
try:
stats["eval_size"] = int(size_str)
except ValueError:
utils.error_exit(
" ".join(("Cannot compute size of the eval dataset:", "'{}' is not a number\n".format(size_str)))
)
stats["orig_size"] = stats["exp_size"] + stats["eval_size"]
exp_res = utils.create_results(exp_res_filename, min_freq)
stats["exp_res"] = len(exp_res)
exp_res_set = set(exp_res.keys())
eval_res = utils.create_results(eval_res_filename, min_freq)
stats["eval_res"] = len(eval_res)
eval_res_set = set(eval_res.keys())
intersection = exp_res_set & eval_res_set
stats["holdout_intersection"] = len(intersection)
stats["holdout_false_negatives"] = len(exp_res_set - eval_res_set)
stats["holdout_false_positives"] = len(eval_res_set - exp_res_set)
stats["holdout_jaccard"] = len(intersection) / len(exp_res_set | eval_res_set)
# One may want to play with giving different values for the different error
# probabilities, but there isn't really much point in it.
lower_delta = 1.0 - math.sqrt(1 - delta)
stats["epsilon_1"] = first_epsilon
sys.stderr.write("Computing candidates...")
sys.stderr.flush()
freq_bound = min_freq + stats["epsilon_1"]
candidates = []
candidates_items = set()
trueFIs = dict()
for itemset in exp_res:
if exp_res[itemset] < freq_bound:
candidates.append(itemset)
candidates_items |= itemset
else:
# Add itemsets with frequency at last freq_bound to the TFIs
trueFIs[itemset] = exp_res[itemset]
sys.stderr.write("done: {} candidates ({} items)\n".format(len(candidates), len(candidates_items)))
sys.stderr.flush()
if len(candidates) > 0 and vcdim > -1 and len(candidates_items) - 1 > vcdim:
sys.stderr.write("Using additional knowledge\n")
candidates_items_sorted = sorted(candidates_items)
candidates_items_in_sets_dict = dict()
candidates_itemset_index = 0
itemset_indexes_dict = dict()
for first_itemset_index in range(len(candidates)):
first_itemset = candidates[first_itemset_index]
for item in first_itemset:
if item in candidates_items_in_sets_dict:
candidates_items_in_sets_dict[item].append(candidates_itemset_index)
else:
candidates_items_in_sets_dict[item] = [candidates_itemset_index]
itemset_indexes_dict[first_itemset] = candidates_itemset_index
candidates_itemset_index += 1
# Compute an upper-bound to the VC-dimension of the set of candidates.
constr_start_str = "cplex.SparsePair(ind = ["
constr_end_str = "], val = vals)"
vars_num = len(candidates) + len(candidates_items)
constr_names = []
capacity = vcdim
(tmpfile_handle, tmpfile_name) = tempfile.mkstemp(prefix="cplx", dir=os.environ["PWD"], text=True)
os.close(tmpfile_handle)
with open(tmpfile_name, "wt") as cplex_script:
cplex_script.write("capacity = {}\n".format(capacity))
cplex_script.write("import cplex, os, sys\n")
cplex_script.write("from cplex.exceptions import CplexError\n")
cplex_script.write("\n")
cplex_script.write("\n")
cplex_script.write(
" ".join(('os.environ["ILOG_LICENSE_FILE"] =' '"/local/projects/cplex/ilm/site.access.ilm"\n'))
)
cplex_script.write("vals = [-1.0, 1.0]\n")
cplex_script.write("sets_num = {}\n".format(len(candidates)))
cplex_script.write("items_num = {}\n".format(len(candidates_items)))
cplex_script.write("vars_num = {}\n".format(vars_num))
cplex_script.write("my_ub = [1.0] * vars_num\n")
cplex_script.write('my_types = "".join("I" for i in range(vars_num))\n')
cplex_script.write("my_obj = ([1.0] * sets_num) + ([0.0] * items_num)\n")
cplex_script.write(
" ".join(
(
"my_colnames =" '["set{0}".format(i) for i in range(sets_num)]',
'+ ["item{0}".format(j) for j in range(items_num)]\n',
)
)
)
cplex_script.write("rows = [ ")
sys.stderr.write("Writing knapsack constraints...")
sys.stderr.flush()
constr_num = 0
for item_index in range(len(candidates_items)):
try:
for itemset_index in candidates_items_in_sets_dict[candidates_items_sorted[item_index]]:
constr_str = "".join(
(constr_start_str, '"set{}","item{}"'.format(itemset_index, item_index), constr_end_str)
)
cplex_script.write("{},".format(constr_str))
constr_num += 1
name = "s{}i{}".format(item_index, itemset_index)
constr_names.append(name)
except KeyError:
sys.stderr.write(
" ".join(
(
"item_index={}".format(item_index),
"candidates_items_sorted[item_index]={}\n".format(candidates_items_sorted[item_index]),
)
)
)
in_candidates = False
candidates_itemset = frozenset()
for itemset in candidates:
if candidates_items_sorted[item_index] in itemset:
in_candidates = True
candidates_itemset = itemset
break
sys.stderr.write(
"{} in negative_border: {}. Itemset: {}\n".format(
candidates_items_sorted[item_index], in_candidates, candidates_itemset
)
)
sys.exit(1)
# Create capacity constraints and write it to script
constr_str = "".join(
(
constr_start_str,
",".join('"item{}"'.format(j) for j in range(len(candidates_items))),
"], val=[",
",".join("1.0" for j in range(len(candidates_items))),
"])",
)
)
cplex_script.write(constr_str)
cplex_script.write("]\n")
cap_constr_name = "capacity"
constr_names.append(cap_constr_name)
sys.stderr.write("done\n")
sys.stderr.flush()
sys.stderr.write(
" ".join(
(
"Optimization problem: capacity={}".format(capacity),
"vars_num={}".format(vars_num),
"candidates={}".format(len(candidates)),
"candidates_items_num={}".format(len(candidates_items)),
"constr_num={}\n".format(constr_num),
)
)
)
sys.stderr.flush()
cplex_script.write("my_rownames = {}\n".format(constr_names))
cplex_script.write("constr_num = {}\n".format(constr_num))
cplex_script.write('my_senses = ["G"] * constr_num + ["L"]\n')
cplex_script.write("my_rhs = [0.0] * constr_num + [capacity]\n")
cplex_script.write("\n")
cplex_script.write("try:\n")
cplex_script.write(" prob = cplex.Cplex()\n")
cplex_script.write(" prob.set_error_stream(sys.stderr)\n")
cplex_script.write(" prob.set_log_stream(sys.stderr)\n")
cplex_script.write(" prob.set_results_stream(sys.stderr)\n")
cplex_script.write(" prob.set_warning_stream(sys.stderr)\n")
# cplex_script.write("
# prob.parameters.mip.strategy.file.set(2)\n")
cplex_script.write(" prob.parameters.mip.tolerances.mipgap.set({})\n".format(gap))
cplex_script.write(" prob.parameters.timelimit.set({})\n".format(600))
# cplex_script.write("
# prob.parameters.mip.strategy.variableselect.set(3) # strong
# branching\n")
cplex_script.write("".join((" prob.objective.set_sense(", "prob.objective.sense.maximize)\n")))
cplex_script.write(
" ".join(
(" prob.variables.add(obj = my_obj, ub = my_ub,", "types = my_types, names = my_colnames)\n")
)
)
cplex_script.write(
" ".join(
(
" prob.linear_constraints.add(lin_expr = rows,",
"senses = my_senses, rhs = my_rhs,",
"names = my_rownames)\n",
)
)
)
cplex_script.write(
" ".join(
(
" prob.MIP_starts.add(cplex.SparsePair(ind =",
"[i for i in range(vars_num)], val = [1.0] * vars_num),",
"prob.MIP_starts.effort_level.auto)\n",
)
)
)
cplex_script.write(" prob.solve()\n")
cplex_script.write(
",".join(
(
" print (prob.solution.get_status()",
"prob.solution.status[prob.solution.get_status()]",
"prob.solution.MIP.get_best_objective()" "prob.solution.MIP.get_mip_relative_gap())\n",
)
)
)
cplex_script.write("except CplexError, exc:\n")
cplex_script.write(" print exc\n")
# Run script, solve optimization problem, extract solution
my_environ = os.environ
if "ILOG_LICENSE_FILE" not in my_environ:
my_environ["ILOG_LICENSE_FILE"] = "/local/projects/cplex/ilm/site.access.ilm"
try:
cplex_output_binary_str = subprocess.check_output(
["python2.6", tmpfile_name], env=my_environ, cwd=os.environ["PWD"]
)
except subprocess.CalledProcessError as err:
os.remove(tmpfile_name)
utils.error_exit("CPLEX exited with error code {}: {}\n".format(err.returncode, err.output))
# finally:
# os.remove(tmpfile_name)
cplex_output = cplex_output_binary_str.decode(locale.getpreferredencoding())
cplex_output_lines = cplex_output.split("\n")
cplex_solution_line = cplex_output_lines[-1 if len(cplex_output_lines[-1]) > 0 else -2]
try:
cplex_solution = eval(cplex_solution_line)
except Exception:
utils.error_exit("Error evaluating the CPLEX solution line: {}\n".format(cplex_solution_line))
sys.stderr.write("cplex_solution={}\n".format(cplex_solution))
sys.stderr.flush()
# if cplex_solution[0] not in (1, 101, 102):
# utils.error_exit("CPLEX didn't find the optimal solution: {} {}
# {}\n".format(cplex_solution[0], cplex_solution[1],
# cplex_solution[2]))
optimal_sol_upp_bound = int(math.floor(cplex_solution[2] * (1 + cplex_solution[3])))
stats["vcdim"] = int(math.floor(math.log2(optimal_sol_upp_bound))) + 1
if stats["vcdim"] > math.log2(len(candidates)):
sys.stderr.write("Lowering VC-dimension to maximum value\n")
sys.stderr.flush()
stats["vcdim"] = int(math.floor(math.log2(len(candidates))))
stats["epsilon_2_vc"] = epsilon.get_eps_vc_dim(lower_delta, stats["orig_size"], stats["vcdim"])
elif len(candidates) > 0 and vcdim > -1 and len(candidates_items) - 1 <= vcdim:
sys.stderr.write("Additional knowledge is useless\n")
sys.stderr.flush()
stats["vcdim"] = int(math.floor(math.log2(len(candidates))))
stats["epsilon_2_vc"] = epsilon.get_eps_vc_dim(lower_delta, stats["orig_size"], stats["vcdim"])
elif len(candidates) > 0 and vcdim == -1:
sys.stderr.write("Not using additional knowledge\n")
sys.stderr.flush()
stats["vcdim"] = int(math.floor(math.log2(len(candidates))))
stats["epsilon_2_vc"] = epsilon.get_eps_vc_dim(lower_delta, stats["orig_size"], stats["vcdim"])
else:
sys.stderr.write("There are no candidates\n")
sys.stderr.flush()
stats["vcdim"] = 0
stats["epsilon_2_vc"] = 0
# Loop to compute empirical VC-dimension using lengths distribution
capacity_str_len = len(str(capacity))
longer_equal = 0
lengths_dict = ds_stats["lengths"]
lengths = sorted(lengths_dict.keys(), reverse=True)
start_len_idx = 0
while start_len_idx < len(lengths):
if lengths[start_len_idx] > len(candidates_items) - 1:
longer_equal += lengths_dict[start_len_idx]
start_len_idx += 1
else:
break
for i in range(start_len_idx, len(lengths)):
cand_len = lengths[i]
longer_equal += lengths_dict[cand_len]
# Modify the script to use the new capacity.
with open(tmpfile_name, "r+t") as cplex_script:
cplex_script.seek(0)
cplex_script.write("capacity = {}\n".format(str(cand_len).ljust(capacity_str_len)))
# Run the script, solve optimization problem, extract solution
my_environ = os.environ
if "ILOG_LICENSE_FILE" not in my_environ:
my_environ["ILOG_LICENSE_FILE"] = "/local/projects/cplex/ilm/site.access.ilm"
try:
cplex_output_binary_str = subprocess.check_output(
["python2.6", tmpfile_name], env=my_environ, cwd=os.environ["PWD"]
)
except subprocess.CalledProcessError as err:
os.remove(tmpfile_name)
utils.error_exit("CPLEX exited with error code {}: {}\n".format(err.returncode, err.output))
# finally:
# os.remove(tmpfile_name)
cplex_output = cplex_output_binary_str.decode(locale.getpreferredencoding())
cplex_output_lines = cplex_output.split("\n")
cplex_solution_line = cplex_output_lines[-1 if len(cplex_output_lines[-1]) > 0 else -2]
try:
cplex_solution = eval(cplex_solution_line)
except Exception:
utils.error_exit("Error evaluating the CPLEX solution line: {}\n".format(cplex_solution_line))
sys.stderr.write("{}\n".format(cplex_solution))
# if cplex_solution[0] not in (1, 101, 102):
# utils.error_exit("CPLEX didn't find the optimal solution: {} {}
# {}\n".format(cplex_solution[0], cplex_solution[1],
# cplex_solution[2]))
# if cplex_solution[0] == 102:
optimal_sol_upp_bound_emp = int(math.floor(cplex_solution[2] * (1 + cplex_solution[3])))
# else:
# optimal_sol_upp_bound_emp = cplex_solution[0]
stats["emp_vc_dim"] = int(math.floor(math.log2(optimal_sol_upp_bound_emp))) + 1
if stats["emp_vc_dim"] > math.log2(len(negative_border)):
sys.stderr.write("Lowering VC-dimension to maximum value\n")
stats["emp_vc_dim"] = int(math.floor(math.log2(len(negative_border))))
sys.stderr.write(
" ".join(
(
"cand_len={}".format(cand_len),
"longer_equal={}".format(longer_equal),
"emp_vc_dim={}".format(stats["emp_vc_dim"]),
"optimal_sol_upp_bound_emp={}\n".format(optimal_sol_upp_bound_emp),
)
)
)
sys.stderr.flush()
# If stopping condition is satisfied, exit.
if stats["emp_vc_dim"] <= longer_equal:
break
os.remove(tmpfile_name)
# Compute the bound to the shatter coefficient, which we use to compute
# epsilon
bound = min(
(math.log(len(candidates)), stats["emp_vc_dim"] * math.log(math.e * stats["eval_size"] / stats["emp_vc_dim"]))
)
# Compute second candidate to epsilon_2
emp_epsilon_2 = epsilon.get_eps_shattercoeff_bound(lower_delta, stats["eval_size"], bound, max_freq_base_set)
sys.stderr.write(
"cand_len={} opt_sol_upp_bound_emp={} emp_vc_dim={} bound={} max_freq_base_set={} emp_e2={}\n".format(
cand_len, optimal_sol_upp_bound_emp, stats["emp_vc_dim"], bound, max_freq_base_set, emp_epsilon_2
)
)
sys.stderr.flush()
sys.stderr.write("not_emp_e2={}, emp_e2={}\n".format(stats["epsilon_2_vc"], emp_epsilon_2))
sys.stderr.flush()
stats["epsilon_2"] = min(emp_epsilon_2, stats["epsilon_2_vc"])
if len(candidates) > 0:
sys.stderr.write("Computing the candidates that are TFIs...")
sys.stderr.flush()
freq_bound = min_freq + stats["epsilon_2"]
eval_res_itemsets = frozenset(eval_res.keys())
for itemset in sorted(frozenset(candidates) & eval_res_itemsets, key=lambda x: eval_res[x], reverse=True):
if eval_res[itemset] >= freq_bound:
trueFIs[itemset] = eval_res[itemset]
sys.stderr.write("done\n")
sys.stderr.flush()
return (trueFIs, stats)
