def compositional_disjunction():
lexica = Lexica(baselexicon={
p: [w1, w2],
q: [w1, w3],
pandq: [w1]
},
costs={
p: 0.0,
q: 0.0,
pandq: 1.0
},
join_closure=True,
nullsem=True,
nullcost=5.0,
disjunction_cost=1.0)
lexica.display()
mod = Pragmod(lexica=lexica.lexica2matrices(),
messages=lexica.messages,
states=lexica.states,
costs=lexica.cost_vector(),
prior=np.repeat(1.0 / len(lexica.states),
len(lexica.states)),
lexprior=np.repeat(1.0 / len(lexica), len(lexica)),
temperature=1.0,
alpha=1.0,
beta=1.0)
mod.run_expertise_model(n=2, display=True, digits=2)
def basic_scalar():
lexica = [np.array([[1.0,1.0], [1.0, 0.0], [1.0, 1.0]]),
np.array([[1.0,0.0], [1.0, 0.0], [1.0, 1.0]]),
np.array([[0.0,1.0], [1.0, 0.0], [1.0, 1.0]])]
mod = Pragmod(lexica=lexica,
messages=['cheap', 'free', NULL_MSG],
states=[w1, w2],
costs=np.array([0.0, 0.0, 5.0]),
prior=np.repeat(1.0/2.0, 2),
lexprior=np.repeat(1.0/3.0, 3),
temperature=1.0,
alpha=1.0,
beta=2.0)
for lex in lexica:
print("=" * 70)
print(mod.lex2str(lex))
mod.run_base_model(lex, n=2, display=True, digits=2)
mod.run_expertise_model(n=3, display=True, digits=2)
def generic_disjunction_example(alpha=1.0,
beta=1.0,
disjunction_cost=1.0,
n=2,
fulldisplay=False,
unknown_word=None):
"""Common code for our two illustrative examples, which
differ only in the above keyword parameters. Increase n to see
greater depths of recursion. use fulldisplay=True to see more
details."""
# Use the lexicon generation convenience function to
# generate all the join-closure lexica and calculate
# the necessary message costs:
lexica = Lexica(baselexicon={
'A': ['1'],
'B': ['2'],
'X': ['1', '2']
},
costs={
'A': 0.0,
'B': 0.0,
'X': 0.0
},
join_closure=True,
nullsem=True,
nullcost=5.0,
disjunction_cost=disjunction_cost,
unknown_word=unknown_word)
# Lexical matrices:
lexmats = lexica.lexica2matrices()
# Pragmatic models for the above lexical space.
mod = Pragmod(lexica=lexmats,
messages=lexica.messages,
states=lexica.states,
costs=lexica.cost_vector(),
prior=np.repeat(1.0 / len(lexica.states),
len(lexica.states)),
lexprior=np.repeat(1.0 / len(lexmats), len(lexmats)),
temperature=1.0,
alpha=alpha,
beta=beta)
if fulldisplay:
lexica.display()
# Run the base model on the individual lexica so we can show
# those lower steps:
for lex in lexmats:
print("=" * 70)
print(mod.lex2str(lex))
mod.run_base_model(lex, n=2, display=True, digits=2)
## Run the anxious experts model - fulldisplay=True for a fuller picture:
langs = mod.run_expertise_model(n=n, display=fulldisplay, digits=2)
# Look at the specific table we care about:
msg_index = mod.messages.index('A v X')
final_listener = langs[-1]
mod.display_joint_listener(final_listener[msg_index], digits=2)
return langs
def compositional_disjunction():
lexica = Lexica(
baselexicon={p: [w1, w2], q: [w1, w3], pandq:[w1]},
costs={p:0.0, q:0.0, pandq:1.0},
join_closure=True,
nullsem=True,
nullcost=5.0,
disjunction_cost=1.0)
lexica.display()
mod = Pragmod(
lexica=lexica.lexica2matrices(),
messages=lexica.messages,
states=lexica.states,
costs=lexica.cost_vector(),
prior=np.repeat(1.0/len(lexica.states), len(lexica.states)),
lexprior=np.repeat(1.0/len(lexica), len(lexica)),
temperature=1.0,
alpha=1.0,
beta=1.0)
mod.run_expertise_model(n=2, display=True, digits=2)
def basic_scalar():
lexica = [
np.array([[1.0, 1.0], [1.0, 0.0], [1.0, 1.0]]),
np.array([[1.0, 0.0], [1.0, 0.0], [1.0, 1.0]]),
np.array([[0.0, 1.0], [1.0, 0.0], [1.0, 1.0]])
]
mod = Pragmod(lexica=lexica,
messages=['cheap', 'free', NULL_MSG],
states=[w1, w2],
costs=np.array([0.0, 0.0, 5.0]),
prior=np.repeat(1.0 / 2.0, 2),
lexprior=np.repeat(1.0 / 3.0, 3),
temperature=1.0,
alpha=1.0,
beta=2.0)
for lex in lexica:
print("=" * 70)
print(mod.lex2str(lex))
mod.run_base_model(lex, n=2, display=True, digits=2)
mod.run_expertise_model(n=3, display=True, digits=2)
def explore_listener_parameters(self):
"""Explore a large parameter space, classifying the parameter vectors
based on the max listener <world,lex> inference given self.msg"""
results = defaultdict(list)
for dcost, alpha, beta, depth in product(self.dcosts,
self.alphas,
self.betas,
self.depths):
params = {'alpha': alpha,
'beta': beta,
'depth': depth,
'disjunction_cost': dcost}
lexica = Lexica(
baselexicon=self.baselexicon,
costs=self.lexical_costs,
join_closure=True,
nullsem=True,
nullcost=5.0,
disjunction_cost=dcost,
unknown_word=self.unknown_word)
lexmats = lexica.lexica2matrices()
mod = Pragmod(
lexica=lexmats,
messages=lexica.messages,
states=lexica.states,
costs=lexica.cost_vector(),
prior=np.repeat(1.0/len(lexica.states), len(lexica.states)),
lexprior=np.repeat(1.0/len(lexmats), len(lexmats)),
temperature=1.0,
alpha=alpha,
beta=beta)
# Run the model:
langs = mod.run_expertise_model(n=depth, display=False)
# Get the listener's joint probability table for this message:
msg_index = mod.messages.index(self.msg)
prob_table = langs[-1][msg_index]
sorted_probs = sorted(prob_table.flatten())
max_pair = None
max_prob = sorted_probs[-1]
# No ties allowed!
if max_prob != sorted_probs[-2]:
for i, j in product(list(range(prob_table.shape[0])),
list(range(prob_table.shape[1]))):
if prob_table[i, j] == max_prob:
max_pair = (i, mod.states[j])
# Add the target probability:
params['prob'] = max_prob
# Print to show progress:
print(max_pair, params)
# Store this dictionary of results -- parameters plus the predicted probability
# max_pair is a lexicon index and state name.
results[max_pair].append(params)
return results
def explore_listener_parameters(self):
"""Explore a large parameter space, classifying the parameter vectors
based on the max listener <world,lex> inference given self.msg"""
results = defaultdict(list)
for dcost, alpha, beta, depth in product(self.dcosts, self.alphas,
self.betas, self.depths):
params = {
'alpha': alpha,
'beta': beta,
'depth': depth,
'disjunction_cost': dcost
}
lexica = Lexica(baselexicon=self.baselexicon,
costs=self.lexical_costs,
join_closure=True,
nullsem=True,
nullcost=5.0,
disjunction_cost=dcost,
unknown_word=self.unknown_word)
lexmats = lexica.lexica2matrices()
mod = Pragmod(lexica=lexmats,
messages=lexica.messages,
states=lexica.states,
costs=lexica.cost_vector(),
prior=np.repeat(1.0 / len(lexica.states),
len(lexica.states)),
lexprior=np.repeat(1.0 / len(lexmats), len(lexmats)),
temperature=1.0,
alpha=alpha,
beta=beta)
# Run the model:
langs = mod.run_expertise_model(n=depth, display=False)
# Get the listener's joint probability table for this message:
msg_index = mod.messages.index(self.msg)
prob_table = langs[-1][msg_index]
sorted_probs = sorted(prob_table.flatten())
max_pair = None
max_prob = sorted_probs[-1]
# No ties allowed!
if max_prob != sorted_probs[-2]:
for i, j in product(list(range(prob_table.shape[0])),
list(range(prob_table.shape[1]))):
if prob_table[i, j] == max_prob:
max_pair = (i, mod.states[j])
# Add the target probability:
params['prob'] = max_prob
# Print to show progress:
print(max_pair, params)
# Store this dictionary of results -- parameters plus the predicted probability
# max_pair is a lexicon index and state name.
results[max_pair].append(params)
return results
def generic_disjunction_example(
alpha=1.0,
beta=1.0,
disjunction_cost=1.0,
n=2,
fulldisplay=False,
unknown_word=None):
"""Common code for our two illustrative examples, which
differ only in the above keyword parameters. Increase n to see
greater depths of recursion. use fulldisplay=True to see more
details."""
# Use the lexicon generation convenience function to
# generate all the join-closure lexica and calculate
# the necessary message costs:
lexica = Lexica(
baselexicon={'A': ['1'], 'B': ['2'], 'X':['1', '2']},
costs={'A':0.0, 'B':0.0, 'X':0.0},
join_closure=True,
nullsem=True,
nullcost=5.0,
disjunction_cost=disjunction_cost,
unknown_word=unknown_word)
# Lexical matrices:
lexmats = lexica.lexica2matrices()
# Pragmatic models for the above lexical space.
mod = Pragmod(
lexica=lexmats,
messages=lexica.messages,
states=lexica.states,
costs=lexica.cost_vector(),
prior=np.repeat(1.0/len(lexica.states), len(lexica.states)),
lexprior=np.repeat(1.0/len(lexmats), len(lexmats)),
temperature=1.0,
alpha=alpha,
beta=beta)
if fulldisplay:
lexica.display()
# Run the base model on the individual lexica so we can show
# those lower steps:
for lex in lexmats:
print("=" * 70)
print(mod.lex2str(lex))
mod.run_base_model(lex, n=2, display=True, digits=2)
## Run the anxious experts model - fulldisplay=True for a fuller picture:
langs = mod.run_expertise_model(n=n, display=fulldisplay, digits=2)
# Look at the specific table we care about:
msg_index = mod.messages.index('A v X')
final_listener = langs[-1]
mod.display_joint_listener(final_listener[msg_index], digits=2)
return langs
def I_implicature_simulation_datapoint(common_ref_prob,
dcost=1.0,
alpha=2.0):
# Values to obtain:
is_max = False
listener_val = None
speaker_val = None
# Set-up:
lexica = Lexica(baselexicon=BASELEXICON,
costs=LEXICAL_COSTS,
join_closure=True,
nullsem=True,
nullcost=5.0,
disjunction_cost=dcost)
ref_probs = np.array([
common_ref_prob, (1.0 - common_ref_prob) / 2.0,
(1.0 - common_ref_prob) / 2.0
])
lexprior = np.repeat(1.0 / len(lexica.lexica2matrices()),
len(lexica.lexica2matrices()))
# Run the model:
mod = Pragmod(lexica=lexica.lexica2matrices(),
messages=lexica.messages,
states=lexica.states,
costs=lexica.cost_vector(),
lexprior=lexprior,
prior=ref_probs,
alpha=alpha)
langs = mod.run_expertise_model(n=3, display=False, digits=2)
# Get the values we need:
speaker = mod.speaker_lexical_marginalization(langs[-2])
listener = mod.listener_lexical_marginalization(langs[-3])
superkind_term_index = mod.messages.index(SUPERKIND_MSG)
common_state_index = mod.states.index(COMMON_REF)
disj_term_index = mod.messages.index(DISJ_MSG)
disj_state_index = mod.states.index(DISJ_REF)
# Fill in listener_val and speaker_val:
listener_val = listener[superkind_term_index, common_state_index]
speaker_val = speaker[disj_state_index, disj_term_index]
# Determine whether max, with a bit of rounding to avoid
# spurious mismatch diagnosis:
maxspkval = np.max(speaker[disj_state_index])
is_max = np.round(speaker_val, 10) == np.round(maxspkval, 10)
# Return values:
return (listener_val, speaker_val, is_max)
def I_implicature_simulation_datapoint(
common_ref_prob, dcost=1.0, alpha=2.0):
# Values to obtain:
is_max = False
listener_val = None
speaker_val = None
# Set-up:
lexica = Lexica(
baselexicon=BASELEXICON,
costs=LEXICAL_COSTS,
join_closure=True,
nullsem=True,
nullcost=5.0,
disjunction_cost=dcost)
ref_probs = np.array([common_ref_prob, (1.0-common_ref_prob)/2.0,
(1.0-common_ref_prob)/2.0])
lexprior = np.repeat(1.0/len(lexica.lexica2matrices()),
len(lexica.lexica2matrices()))
# Run the model:
mod = Pragmod(
lexica=lexica.lexica2matrices(),
messages=lexica.messages,
states=lexica.states,
costs=lexica.cost_vector(),
lexprior=lexprior,
prior=ref_probs,
alpha=alpha)
langs = mod.run_expertise_model(n=3, display=False, digits=2)
# Get the values we need:
speaker = mod.speaker_lexical_marginalization(langs[-2])
listener = mod.listener_lexical_marginalization(langs[-3])
superkind_term_index = mod.messages.index(SUPERKIND_MSG)
common_state_index = mod.states.index(COMMON_REF)
disj_term_index = mod.messages.index(DISJ_MSG)
disj_state_index = mod.states.index(DISJ_REF)
# Fill in listener_val and speaker_val:
listener_val = listener[superkind_term_index, common_state_index]
speaker_val = speaker[disj_state_index, disj_term_index]
# Determine whether max, with a bit of rounding to avoid
# spurious mismatch diagnosis:
maxspkval = np.max(speaker[disj_state_index])
is_max = np.round(speaker_val, 10) == np.round(maxspkval, 10)
# Return values:
return (listener_val, speaker_val, is_max)
def Q_implicature_simulation_datapoint(specific_cost,
dcost=1.0,
alpha=2.0):
# Values to obtain:
is_max = False
listener_val = None
speaker_val = None
# Set-up:
lexica = Lexica(baselexicon=BASELEXICON,
costs={
GENERAL_MSG: 0.0,
SPECIFIC_MSG: specific_cost
},
join_closure=True,
nullsem=True,
nullcost=5.0,
disjunction_cost=dcost)
ref_probs = np.repeat(1.0 / len(lexica.states), len(lexica.states))
lexprior = np.repeat(1.0 / len(lexica.lexica2matrices()),
len(lexica.lexica2matrices()))
# Run the model:
mod = Pragmod(lexica=lexica.lexica2matrices(),
messages=lexica.messages,
states=lexica.states,
costs=lexica.cost_vector(),
lexprior=lexprior,
prior=ref_probs,
alpha=alpha)
langs = mod.run_expertise_model(n=3, display=False, digits=2)
# Get the values we need:
speaker = mod.speaker_lexical_marginalization(langs[-2])
listener = mod.listener_lexical_marginalization(langs[-3])
general_msg_index = lexica.messages.index(GENERAL_MSG)
general_only_state = lexica.states.index(GENERAL_ONLY_REF)
disj_state_index = lexica.states.index(DISJ_REF)
disj_msg_index = lexica.messages.index(DISJ_MSG)
speaker_val = speaker[disj_state_index, disj_msg_index]
listener_val = listener[general_msg_index, general_only_state]
# Determine whether max, with a bit of rounding to avoid spurious
# mismatch diagnosis:
maxspkval = np.max(speaker[disj_state_index])
is_max = np.round(speaker_val, 10) == np.round(maxspkval, 10)
# Return values:
return (listener_val, speaker_val, is_max)
def Q_implicature_simulation_datapoint(
specific_cost, dcost=1.0, alpha=2.0):
# Values to obtain:
is_max = False
listener_val = None
speaker_val = None
# Set-up:
lexica = Lexica(
baselexicon=BASELEXICON,
costs={GENERAL_MSG: 0.0, SPECIFIC_MSG: specific_cost},
join_closure=True,
nullsem=True,
nullcost=5.0,
disjunction_cost=dcost)
ref_probs = np.repeat(1.0/len(lexica.states), len(lexica.states))
lexprior = np.repeat(1.0/len(lexica.lexica2matrices()),
len(lexica.lexica2matrices()))
# Run the model:
mod = Pragmod(
lexica=lexica.lexica2matrices(),
messages=lexica.messages,
states=lexica.states,
costs=lexica.cost_vector(),
lexprior=lexprior,
prior=ref_probs,
alpha=alpha)
langs = mod.run_expertise_model(n=3, display=False, digits=2)
# Get the values we need:
speaker = mod.speaker_lexical_marginalization(langs[-2])
listener = mod.listener_lexical_marginalization(langs[-3])
general_msg_index = lexica.messages.index(GENERAL_MSG)
general_only_state = lexica.states.index(GENERAL_ONLY_REF)
disj_state_index = lexica.states.index(DISJ_REF)
disj_msg_index = lexica.messages.index(DISJ_MSG)
speaker_val = speaker[disj_state_index, disj_msg_index]
listener_val = listener[general_msg_index, general_only_state]
# Determine whether max, with a bit of rounding to avoid spurious
# mismatch diagnosis:
maxspkval = np.max(speaker[disj_state_index])
is_max = np.round(speaker_val, 10) == np.round(maxspkval, 10)
# Return values:
return (listener_val, speaker_val, is_max)