def calc_entropy(comms, n_comm):
# Calculates the entropy of the communication distribution
# p(c) is calculated by averaging over episodes
comms = [U.to_int(m) for m in comms]
eps = 1e-9
p_c = U.probs_from_counts(comms, n_comm, eps=eps)
entropy = 0
for c in range(n_comm):
entropy += -p_c[c] * math.log(p_c[c])
return entropy
def calc_context_indep(acts, comms, n_acts, n_comm):
# Calculates the context independence (Bogin et al., 2018)
comms = [U.to_int(m) for m in comms]
acts = [U.to_int(a) for a in acts]
eps = 1e-9
p_a = U.probs_from_counts(acts, n_acts, eps=eps)
p_c = U.probs_from_counts(comms, n_comm, eps=eps)
p_ac = U.bin_acts(comms, acts, n_comm, n_acts)
p_ac /= np.sum(p_ac)
p_a_c = np.divide(p_ac, np.reshape(p_c, (-1, 1)))
p_c_a = np.divide(p_ac, np.reshape(p_a, (1, -1)))
ca = np.argmax(p_a_c, axis=0)
ci = 0
for a in range(n_acts):
ci += p_a_c[ca[a]][a] * p_c_a[ca[a]][a]
ci /= n_acts
return ci
def calc_mutinfo(acts, comms, n_acts, n_comm): # Calculate mutual information between actions and messages # Joint probability p(a, c) is calculated by counting co-occurences, *not* by performing interventions # If the actions and messages come from the same agent, then this is the speaker consistency (SC) # If the actions and messages come from different agents, this is the instantaneous coordinatino (IC) comms = [U.to_int(m) for m in comms] acts = [U.to_int(a) for a in acts] # Calculate probabilities by counting co-occurrences p_a = U.probs_from_counts(acts, n_acts) p_c = U.probs_from_counts(comms, n_comm) p_ac = U.bin_acts(comms, acts, n_comm, n_acts) p_ac /= np.sum(p_ac) # normalize counts into a probability distribution # Calculate mutual information mutinfo = 0 for c in range(n_comm): for a in range(n_acts): if p_ac[c][a] > 0: mutinfo += p_ac[c][a] * math.log(p_ac[c][a] / (p_c[c] * p_a[a])) return mutinfo