Further, these approaches typically depend on specific semantic signals such as sentiment- or topic-labels for their objective functions .

This results in the following objective function:

The objective function in Equation 2 could be coupled with any two given vector composition functions f, g from the literature.

To summarize, we have presented a novel method for learning multilingual word embeddings using parallel data in conjunction with a multilingual objective function for compositional vector models.

We describe a multilingual objective function that uses a noise-contrastive update between semantic representations of different languages to learn these word embeddings.

SUMMA hierarchically clusters the sentences by time, and then summarizes the clusters using an objective function that optimizes salience and coherence.

4.4 Objective Function

Having estimated salience, redundancy, and two forms of coherence, we can now put this information together into a single objective function that measures the quality of a candidate hierarchical summary.

Intuitively, the objective function should balance salience and coherence.

Next, we modify the objective function in Eq. '

Thus the new objective function consists of a sun of L x M 2 terms, each corresponding to a differen combination of inside and outside features.

2) Optimization of a convex objective function using EM.

Step 2: Use the EM algorithm to find 75 values that maximize the objective function in Eq.

For a given value of 6 we solve the NNSE(Text) and J NNSE(Brain+Text) objective function as detailed in Equation 1 and 4 respectively.

new objective function is:

With A or D fixed, the objective function for NNSE(Text) and JNNSE(Brain+Text) is convex.

NNSE solves the following objective function:

The weights are estimated by minimizing the objective function

(2013), however, our objective function yielded consistently better results in all experimental settings.

8For this post-hoc analysis, we include a sparsity parameter in the objective function of Equation 5 in order to get more interpretable results; hidden units are therefore maximally activated by a only few concepts.

The adaptation of NN is straightforward; the new objective function is derived as

For projective parsing, several algorithms (McDonald and Pereira, 2006; Carreras, 2007; Koo and Collins, 2010; Ma and Zhao, 2012) have been proposed to solve the model training problems (calculation of objective function and gradient) for different factorizations.

We introduce a multiplier 7 as a tradeoff between the two contributions (parallel and unsupervised) of the objective function K, and the final objective function K I has the following form:

To train our parsing model, we need to find out the parameters A that minimize the objective function K I in equation (11).

objective function and the gradient of the objective function .

In this section, we briefly review regularizers and then add two regularizers, inspired by Gaussian (L2, Section 3.1) and Dirichlet priors (Beta, Section 3.2), to the anchor objective function (Equation 3).

Instead of optimizing a function just of the data cc and parameters 6, f (cc, 6), one optimizes an objective function that includes a regularizer that is only a function of parameters: f (w, 6) + 716).

This requires including the topic matrix as part of the objective function .

Once we have established the anchor objective function, in the next section we regularize the objective function .

Given a sentence e of length |e| = I and a sentence f of length |f| = J, our goal is to find the best bidirectional alignment between the two sentences under a given objective function .

The HMM objective function f : X —> R can be written as a linear function of :c

Similarly define the objective function

Similar to the traditional maximum margin based Support Vector Machine (SVM) formulation, our model’s objective function is defined as:

Replacing the term fw (253,193) with the contents of Equation 1 in the minimization objective above, reveals the key difference from the traditional SVM formulation - the objective function has a maximum term inside the global minimization problem making it non-convex.

The algorithm then performs two step iteratively - first it determines the structural assignments for the negative examples, and then optimizes the fixed objective function using a cutting plane algorithm.

For MT feature weight optimization, we use iterative k-best optimization with an Expected-BLEU objective function (Rosti et al., 2010).

While we cannot train a neural network with this guarantee, we can explicitly encourage the log-softmaX normalizer to be as close to 0 as possible by augmenting our training objective function:

Note that 04 = 0 is equivalent to the standard neural network objective function .

The score of graph G (encoded as 2) can be written as the objective function quz, where gbe = ¢Tg(e).

To handle the constraint Az g b, we introduce multipliers p 2 0 to get the Lagrangian relaxation of the objective function:

L(z) is an upper bound on the unrelaxed objective function quz, and is equal to it if and only if the constraints AZ g b are satisfied.

Due to this discrepancy, the objective function in Eq.

For this model, we also introduce a hyperparameter 6 that weights the error at annotated nodes (1 — 6) higher than the error at unannotated nodes (6); since we have more confidence in the annotated labels, we want them to contribute more towards the objective function .

This induces a supervised objective function over all sentences: a regularized sum over all node losses normalized by the number of nodes N in the training set,

We next define our objective function .

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

Finding the best assignments to unobserved variables in our objective function is the inference problem.

However, to go beyond tuning weights in the loglinear SMT model, a cross-lingual objective function that can deeply integrate semantic frame criteria into the MT training pipeline is needed.

While monolingual MEANT alone accurately reflects adequacy via semantic frames and optimizing SMT against MEANT improves translation, the new cross-lingual XMEANT semantic objective function moves closer toward deep integration of semantics into the MT training pipeline.

In order to continue driving MT towards better translation adequacy by deeply integrating semantic frame criteria into the MT training pipeline, it is necessary to have a cross-lingual semantic objective function that assesses the semantic frame similarities of input and output sentences.

After that, we introduce the BRAE on the network structure, objective function and parameter inference.

In the semi-supervised RAE for phrase embedding, the objective function over a (phrase, label) pair (av, 25) includes the reconstruction error and the prediction error, as illustrated in Fig.

3.3.1 The Objective Function