Ando and Zhang (2005) defined an objective function that combines the original problem on the labeled data with a set of auxiliary problems on unlabeled data.

The combined objective function is then alternatingly optimized with the labeled and unlabeled data.

The learning algorithm then optimizes a regularized, convex objective function that is expressed in terms of these features.

distributed clustering algorithm with a similar objective function as the Brown algorithm.

We made a small modification to the objective function for logistic regression to take into account the prior distribution and to use 50% as a uniform decision boundary for all the classes.

When training the classifier for a class with [9 positive examples out of a total of n examples, we change the objective function to:

We suspect that such features make the optimization of the objective function much more difficult.

Also, SGD is very easy to implement because it does not need to use the Hessian information on the objective function .

SGD uses a small randomly-selected subset of the training samples to approximate the gradient of the objective function given by Equation 2.

The learning rate parameters for SGD were then tuned in such a way that they maximized the value of the objective function in 30 passes.

Figure 3 shows how the value of the objective function changed as the training proceeded.

Model parameters are estimated using a generalized expectation (GE) objective function that penalizes the mismatch between model predictions and linguistic expectation constraints.

Generalized expectation criteria (Mann and McCallum, 2008; Druck et al., 2008) are terms in a parameter estimation objective function that express a preference on the value of a model expectation.

2In general, the objective function could also include the likelihood of available labeled data, but throughout this paper we assume we have no parsed sentences.

With GE we may add a term to the objective function that encourages a feature-rich CRF to match this expectation on unlabeled data, and in the process learn about related features.

We learn the optimal weight vectors {fikfifzv fiT and 3 by optimizing the following objective function:

The objective function follows standard empirical risk minimization with regularization.

Recall that we impose a constraint FV = 0 when optimizing the objective function .

In MDL, there is a single objective function to (1) maximize the likelihood of observing the data, and at the same time (2) minimize the length of the model description (which depends on the model size).

However, the search procedure for MDL is usually nontrivial, and for our task of unsupervised tagging, we have not found a direct objective function which we can optimize and produce good tagging results.

Finally, we add an objective function that minimizes the number of grammar variables that are assigned a value of 1.

objective function value of 459.3

This goal is formalized by the following objective function:

The nonnegative weights ad reflect the importance of the different translation tasks and 2d ad 2 l. AL-SMT formulation for single language pair is a special case of this formulation where only one of the ad’s in the objective function (1) is one and the rest are zero.

The goal is to optimize the objective function (1) with minimum human effort in providing the translations.

Based on the graphical model representation in Figure 3, we derive the log-likelihood objective function , in a similar way as in (Cohn and Hofmann, 2000), as follows

objective function ignores all the biases from the

points based on the objective function £ in Equation (5).

SMT comparably or better than the state-of-the-art beam-search strategy, converging on solutions with higher objective function in a shorter time.

Both algorithms do not show any clear score improvement with increasing running time which suggests that the decoder’s objective function is not very well correlated with the BLEU score on this corpus.

LK works by generating an initial random feasible solution for the TSP problem, and then repeatedly identifying an ordered subset of k edges in the current tour and an ordered subset of k edges not included in the tour such that when they are swapped the objective function is improved.

In SMT, however, the optimization objective function in MERT is the MT evaluation criteria, such as BLEU.

We therefore introduce a new optimization objective function in this paper.

Replacement f-measure (rf): We use rf as the optimization objective function in MERT, which is similar to the conventional f-measure and lever-agesrp and rr: 7“f = (2 X 7”]?