Both parallel and monolingual corpora are used to obtain these probability distributions over target phrases.

If a source phrase is found in the baseline phrase table it is called a labeled phrase: its conditional empirical probability distribution over target phrases (estimated from the parallel data) is used as the label, and is sub-

We then propagate by deriving a probability distribution over these target phrases using graph propagation techniques.

We then limit the set of translation options for each unlabeled source phrase (§2.3), and using a structured graph propagation algorithm, where translation information is propagated from labeled to unlabeled phrases proportional to both source and target phrase similarities, we estimate probability distributions over translations for

Draw a word: wdm N Multinomial(zd,n) Where, T is the number of topics, 9b,; is the word probabilities for topic 75, 6d is the topic probability distribution , 2d,“, is topic assignment and wdm is word assignment for nth word position in document d respectively.

(a) Infer a probability distribution 0d over class labels using M D using Equation 3.

We use the labeled topics to find probability distribution of each training document over the class labels.

We use this new model to infer the probability distribution of each unlabeled training document over the class labels.

While classifying a test document, its probability distribution over class labels is inferred using TS-LDA model and it is classified to its most probable class label.

The word2vec toolkit implements two efficient alternatives to the standard computation of the output word probability distributions by a softmax classifier.

Hierarchical softmax is a computationally efficient way to estimate the overall probability distribution using an output layer that is proportional to log(unigram.perplexity(W)) instead of W (for W the vocabulary size).

Allocation (LDA) models (Blei et al., 2003; Griffiths et al., 2007), where parameters are set to optimize the joint probability distribution of words and documents.

MLNs define a probability distribution over possible worlds, where a world’s probability increases exponentially with the total weight of the logical clauses that it satisfies.

Given a set of weighted logical formulas, PSL builds a graphical model defining a probability distribution over the continuous space of values of the random variables in the model.

Using distance to satisfaction, PSL defines a probability distribution over all possible interpretations I of all ground atoms.

and x to observed ones X (variables with known labels, if any), our objective function is associated with the following joint probability distribution

A message mizj is sent from node i to node j and captures the belief of 2' about j, which is the probability distribution over the labels of j; i.e.

what i “thinks” j’s label is, given the current label of i and the type of the edge that connects i and j. Beliefs refer to marginal probability distributions of nodes over labels; for example denotes the belief of node 2' having label 3),.

In the E step of EM, we compute a probability distribution (according to the current model) over all possible completions of the observed data, and the expected counts of all types, which may be fractional.

The IBM models and related models define probability distributions p(a, f | e, 6), which model how likely a French sentence f is to be generated from an English sentence e with word alignment a.

Different models parameterize this probability distribution in different ways.