For each of the remaining feature vectors in

Mixture ID (mt) For each feature vector in a segment, given the cluster label CM and the hidden state index st, the derivation of the conditional posterior probability of its mixture ID is straightforward:

where mm is the set of mixture IDs of feature vectors that belong to state 8 of HMM c. The mth entry of fl’ is fl + themcqs 6(mt, m), where we use

Given the cluster label, choose a hidden state for each feature vector :13; in the segment.

Use the chosen Gaussian mixture to generate the observed feature vector

2, where the shaded circle denotes the observed feature vectors , and the squares denote the hyperparameters of the priors used in our model.

1 illustrates how the speech signal of a single word utterance banana is converted to a sequence of feature vectors to £13711.

Segment (p;- k) We define a segment to be composed of feature vectors between two boundary frames.

Hidden State (8%) Since we assume the observed data are generated by HMMs, each feature vector , 30%, has an associated hidden state index.

From every image in a dataset, relevant areas are identified and a low-level feature vector (called a “descriptor”) is built to represent each area.

Now, given a new image, the nearest visual word is identified for each descriptor extracted from it, such that the image can be represented as a BoVW feature vector , by counting the instances of each visual word in the image (note that an occurrence of a low-level descriptor vector in an image, after mapping to the nearest cluster, will increment the count of a single dimension of the higher-level BoVW vector).

We extract descriptor features of two types.6 First, the standard Scale-Invariant Feature Transform (SIFT) feature vectors (Lowe, 1999; Lowe, 2004), good at characterizing parts of objects.

The feature vector qb consists of the following features:

We construct the design matrix (I) with one column for each feature vector qbct corresponding to each combination of training configuration 0 and test set If.

For a new unseen configuration with feature vector gbu, we determine the parameters 6., of the corresponding learning curve as:

Algorithms 2 and 3 were infeasible to run on Europarl data beyond one epoch because features vectors grew too large to be kept in memory.

The simple but effective idea is to randomly divide training data into evenly sized shards, use stochastic learning on each shard in parallel, while performing 61/62 regularization for joint feature selection on the shards after each epoch, before starting a new epoch with a reduced feature vector averaged across shards.

Let each translation candidate be represented by a feature vector x 6 RD where preference pairs for training are prepared by sorting translations according to smoothed sentence-wise BLEU score (Liang et al., 2006a) against the reference.

Parameter mixing by averaging will help to ease the feature sparsity problem, however, keeping feature vectors on the scale of several million features in memory can be prohibitive.

We assume a function u that maps outside trees 0 to feature vectors 2M0) 6 Rd].

For example, the feature vector might track the rule directly above the node in question, the word following the node in question, and so on.

We also assume a function gb that maps inside trees 75 to feature vectors gb(t) 6 Rd.