def label_mmr_score(self,
which_topic,
chosen_labels,
label_scores,
label_models):
"""
Maximal Marginal Relevance score for labels.
It's computed only when `apply_intra_topic_coverage` is True
Parameters:
--------------
which_topic: int
the index of the topic
chosen_labels: list<int>
indices of labels that are already chosen
label_scores: numpy.ndarray<#topic, #label>
label scores for each topic
label_models: numpy.ndarray<#label, #words>
the language models for labels
Returns:
--------------
numpy.ndarray: 1D of length #label - #chosen_labels
the scored label indices
numpy.ndarray: same length as above
the scores
"""
chosen_len = len(chosen_labels)
if chosen_len == 0:
# no label is chosen
# return the raw scores
return (np.arange(label_models.shape[0]),
label_scores[which_topic, :])
else:
kl_m = np.zeros((label_models.shape[0]-chosen_len,
chosen_len))
# the unchosen label indices
candidate_labels = list(set(range(label_models.shape[0])) -
set(chosen_labels))
candidate_labels = np.sort(np.asarray(candidate_labels))
for i, l_p in enumerate(candidate_labels):
for j, l in enumerate(chosen_labels):
kl_m[i, j] = kl_divergence(label_models[l_p],
label_models[l])
sim_scores = kl_m.max(axis=1)
mml_scores = (self._alpha *
label_scores[which_topic, candidate_labels]
- (1 - self._alpha) * sim_scores)
return (candidate_labels, mml_scores)
def jsd_divergence(p: np.array,
q: np.array) -> np.float:
"""
Calculate the Jensen-Shannon Divergence between two PDFs
Parameters
-----------
p: Numpy.array
discrete probability distribution, p
q: Numpy.array
discrete probability distribution, q
Returns
--------
Numpy.float
Jenson-Shannon Divergence
"""
m = (p + q)/2
divergence = (kl_divergence(p, m) + kl_divergence(q, m)) / 2
return np.sqrt(divergence)
def label_mmr_score(self, which_topic, chosen_labels, label_scores,
label_models):
"""
Maximal Marginal Relevance score for labels.
It's computed only when `apply_intra_topic_coverage` is True
Parameters:
--------------
which_topic: int
the index of the topic
chosen_labels: list<int>
indices of labels that are already chosen
label_scores: numpy.ndarray<#topic, #label>
label scores for each topic
label_models: numpy.ndarray<#label, #words>
the language models for labels
Returns:
--------------
numpy.ndarray: 1D of length #label - #chosen_labels
the scored label indices
numpy.ndarray: same length as above
the scores
"""
chosen_len = len(chosen_labels)
if chosen_len == 0:
# no label is chosen
# return the raw scores
return (np.arange(label_models.shape[0]),
label_scores[which_topic, :])
else:
kl_m = np.zeros((label_models.shape[0] - chosen_len, chosen_len))
# the unchosen label indices
candidate_labels = list(
set(range(label_models.shape[0])) - set(chosen_labels))
candidate_labels = np.sort(np.asarray(candidate_labels))
for i, l_p in enumerate(candidate_labels):
for j, l in enumerate(chosen_labels):
kl_m[i, j] = kl_divergence(label_models[l_p],
label_models[l])
sim_scores = kl_m.max(axis=1)
mml_scores = (
self._alpha * label_scores[which_topic, candidate_labels] -
(1 - self._alpha) * sim_scores)
return (candidate_labels, mml_scores)
def kullback_leibler_divergence(d1, d2):
"""Computes the Kullback-Leibler dissimilarity between two probability distributions.
Args:
d1 (dict): First probability distribution.
d2 (dict): Second probability distribution.
Returns:
The Kullback-Leibler dissimilarity value.
Note:
* The KL divergence is not a true "distance" because it is asymmetric and, it does not satisfy the triangle inequality.
"""
# validating distributions
if not isinstance(d1, dict) or not isinstance(d2, dict):
raise ValueError('Distributions must be dictionaries.')
# insignificant value
eps = 1e-6
# declaring probability density functions
pdf1 = []
pdf2 = []
# for each 'event' in distribution 1
for k1 in d1:
# adding p(k1) to pdf1
pdf1.append(d1[k1])
# if event 'k1' also occurs in d2
if k1 in d2.keys():
pdf2.append(d2[k1])
else:
pdf2.append(0)
# for events only occurring in d2
for k2 in d2:
# if event k2 only occurs in d2
if k2 not in d1.keys():
pdf1.append(0)
pdf2.append(d2[k2])
# building array distributions
arr_pdf1 = np.array(pdf1) + eps
arr_pdf2 = np.array(pdf2) + eps
# computing the distance between the 2 probability density functions
return kl_divergence(arr_pdf1, arr_pdf2)
def dice_func_entropy_conditioned(dist: Dict[int, int], dpmf: DicePmf):
"""Calls scipy.stats.entropy, but avoids result being inf"""
def condition_pk(pk_raw):
length = pk_raw.shape[0]
idx_zeros = [
k for k in range(length) if dist.get(k + dpmf.low, 0) == 0
]
min_val = min(
[pk_raw[k] for k in range(length) if k not in idx_zeros])
extra = min_val * len(idx_zeros)
scale = 1 / (1 + extra)
pk = np.array([
min_val if k in idx_zeros else scale * pk_raw[k]
for k in range(length)
])
return pk
pk_raw, pmf = DiceUtil.dice_comparable_arrays(dist, dpmf)
pk = condition_pk(pk_raw)
return kl_divergence(pk, pmf)
def dice_func_entropy(dist: Dict[int, int], dpmf: DicePmf):
"""Calls scipy.stats.entropy (i.e., Kullman-Leibler divergence)"""
pk, pmf = DiceUtil.dice_comparable_arrays(dist, dpmf)
return kl_divergence(pk, pmf)
