We address the problem of aligning multiple medical event sequences, corresponding to different clinical narratives, comparing the following approaches: (1) A novel weighted finite state transducer representation of medical event sequences that enables composition and search for decoding, and (2) Dynamic programming with iterative pairwise alignment of multiple sequences using global and local alignment algorithms.

We present results using both approaches and observe that the finite state transducer approach performs performs significantly better than the dynamic programming one by 6.8% for the problem of multiple-sequence alignment.

As a contrast, we adapt dynamic programming algorithms (Needleman et al., 1970, Smith and Waterman, 1981) used to produce global and local alignments for aligning sequences of medical events across narratives.

dynamic programming or other ILP-based methods proposed in literature.

We propose a novel WFST—based representation that enables accurate decoding for MSA when compared to popularly used dynamic programming algorithms (Needleman et al., 1970, Smith and Waterman, 1981) or other state of the art methods (Do et al., 2012).

These scores are used in both the WFST—based representation and decoding, as well as for dynamic programming .

We also use popular dynamic programming algorithms (Needleman et al., 1970, Smith and Waterman, 1981) for sequence alignment of medical events across narratives and compare it to the WFST-based representation and decoding.

Dynamic programming algorithms have been popularly leveraged to produce pairwise and global genetic alignments, where edit distance based metrics are used to compute the cost of insertions, deletions and substitutions.

We use dynamic programming to compute the best alignment, given the temporal and coreference information between medical events across these sequences.

We demonstrate that the WFST—based approach outperforms popularly used dynamic programming algorithms for multiple sequence alignment.

(2) find the highest scoring derivation using dynamic programming

Steps 1 and 2 can be performed efficiently; in particular, we avoid the classical dynamic programming intersection, instead relying on dynamic programming over the original, simple hypergraph.

0 Using dynamic programming , find values for the yv and ye variables that form a valid derivation, and that maximize

The approach uses Lagrangian relaxation to decompose the decoding problem into tractable sub-problems, thereby avoiding exhaustive dynamic programming .

Exact dynamic programming algorithms for the problem are well known (Bar-Hillel et al., 1964), but are too expensive to be used in practice.2 Previous work on decoding for syntax-based SMT has therefore been focused primarily on approximate search methods.

Dynamic programming over the weighted hypergraph.

We do this by gradually introducing constraints to step 1 ( dynamic programming over the hypergraph), while still maintaining efficiency.

The second step involves simple dynamic programming over the hypergraph (V, E) (it is simple to integrate the 68 terms into this algorithm).

The main steps of the algorithm are: 1) construction of the graph (8, T); 2) at each iteration, dynamic programming over the hypergraph (V, E); 3) at each iteration, all-pairs shortest path algorithms over the graph (8, T).

steps—hypergraph dynamic programming , and all-pairs shortest path—are widely known algorithms that are simple to implement.

Our algorithm is another dynamic programming decoding pass on the trigram forest, and is similar to the parsing algorithm for maximizing expected labelled recall presented by Goodman (1996).

The expression can be factorized and computed using dynamic programming on the forest.

We can also use the dynamic programming hook trick.

From a dynamic programming point of view, the DP states are X [i, j], where X ranges over all possible nonterminals and i and j range over 0 to the input string length Each state stores the best translations obtainable.

Thus, to preserve the dynamic programming property, we need to refine the states by adding the boundary words into the parameterization.

(2005) factor-izes the dynamic programming steps and lowers the asymptotic complexity of the n-gram integrated decoding, but has not been implemented in large-scale systems where massive pruning is present.

(2007) also take a two-pass decoding approach, with the first pass leaving the language model boundary words out of the dynamic programming state, such that only one hypothesis is retained for each span and grammar symbol.

While dynamic programming is viable for bigram-based sentence compression, finding optimal compressed trees within graphs is NP-hard.

0 DP: The bigram-based dynamic program of McDonald (2006) described in §2.3.9

However, while the former problem can be solved efficiently using the dynamic programming approach of McDonald (2006), there are no efficient algorithms to recover maximum weighted non-projective subtrees in a general directed graph.

Following this, §2.3 discusses a dynamic program to find maximum weight bigram subsequences from the input sentence, while §2.4 covers LP relaxation-based approaches for approximating solutions to the problem of finding a maximum-weight subtree in a graph of potential output dependencies.

McDonald (2006) provides a Viterbi-like dynamic programming algorithm to recover the highest-scoring sequence of order-preserving bigrams from a lattice, either in unconstrained form or with a specific length constraint.

The latter requires a dynamic programming table [T] which represents the best score for a compression of length 7“ ending at token i.

We perform inference under this model using Markov Chain Monte Carlo and dynamic programming .

Additionally, a computational advantage of this formalism is that the marginalized probability over all possible alignments for any two trees can be efficiently computed with a dynamic program in linear time.

We sample pairs of trees and then compute marginalized probabilities over all possible alignments using dynamic programming .

Fortunately, for any given pair of trees T1 and T2 this marginalization can be computed using a dynamic program in time O(|T1||T2|).

A dynamic program builds this table from the bottom up: For each node pair 711,712, we sum the probabilities of all local alignment configurations, each multiplied by the appro-

This algorithm is an adaptation of the dynamic program presented in (J iang et al., 1995) for finding minimum cost alignment trees (Fig.

We also devised a dynamic programming algorithm for forest oracles, an interesting problem by itself.

We will present a dynamic programming algorithm for this problem in Sec.

Analogous to the language model cost in forest rescoring, the unit feature cost here is a non-monotonic score in the dynamic programming backbone, and the derivations may thus be extracted oat-of-order.

Alternatively, discriminative parsing is tractable with exact and efficient search based on dynamic programming (DP) if all features are restricted to be local, that is, only looking at a local window within the factored search space (Taskar et al., 2004; McDonald et al., 2005).

We instead propose a dynamic programming algorithm which optimizes the number of matched brackets for a given number of test brackets.

We restrict the target side to the so called well-formed dependency structures, in order to cover a large set of non-constituent transfer rules (Marcu et al., 2006), and enable efficient decoding through dynamic programming .

tation and make it hard to employ shared structures for efficient dynamic programming .

In this paper, we propose a new Bayesian model for fully unsupervised word segmentation and an efficient blocked Gibbs sampler combined with dynamic programming for inference.

With a combination of dynamic programming and an accurate spelling model from a Bayesian perspective, our model significantly outperforms the previous reported results, and the inference is very efficient.

Instead, we propose a sentence-wise Gibbs sampler of word segmentation using efficient dynamic programming , as shown in Figure 3.

Section 4 describes an efficient blocked Gibbs sampler that leverages dynamic programming for inference.

To segment a string into “words”, we used efficient dynamic programming combined with MCMC, as described in the next section.

First, we implement a chart-based dynamic programming parser for the 2nd-0rdered MST model, and develop a training procedure based on the perceptron algorithm with averaged parameters (Collins, 2002).

J iang and Liu (2009) resort to a dynamic programming procedure to search for a completed projected tree.

Jiang and Liu (2009) refer to alignment matrix and a dynamic programming search algorithm to obtain better projected dependency trees.

Follow the edge based factorization method (Eisner, 1996), we factorize the score of a dependency tree s(x, y) into its dependency edges, and design a dynamic programming algorithm to search for the candidate parse with maximum score.

In this work, however, we still adopt the more general, bottom-up dynamic programming algorithm Algorithm 1 in order to facilitate the possible expansions.

The problem is formulated in terms of obtaining the minimum description length of a text, and the proposed solution finds the segments and their languages through dynamic programming .

An actual procedure for obtaining an optimal result through dynamic programming was proposed.

We can straightforwardly implement this recur—sive computation through dynamic programming , by managing a table of size |X | x To fill a cell of this table, formula (4) suggests referring to t x |£| cells and calculating the description length of the rest of the text for O( |X | —t) cells for each language.

Nevertheless, since we use a uniform amount of training data for every language, and since varying 7 would prevent us from improving the efficiency of dynamic programming , as explained in §4, in this article we set 7 to a constant obtained empirically.

By applying the above methods, we propose a solution to formula (1) through dynamic programming .

8 efficiently with dynamic programming (using the Viterbi algorithm for trees); the total cost is linear in Ln.

8; this can be done in 0(Ln) time with dynamic programming , as discussed in §3.2.

This can be computed exactly in time 0(B 25:1 Lnk ) , through dynamic programming .

For example, such solvers are unable to take advantage of efficient dynamic programming routines for sentence compression (McDonald, 2006).

9 can be used for the maximization above: for tasks #1—#2, we solve a relaxation by running AD3 without rounding, and for task #3 we use dynamic programming ; see Table 1.

The first line is a baseline HMM using exact posterior computation and inference with the standard dynamic programming algorithms.

For the standard HMM, there is a dynamic programming algorithm to compute the posterior probability over word alignments Pr(a|e, f These are the sufficient statistics gathered in the E step of EM.

The structure of the fertility model violates the Markov assumptions used in this dynamic programming method.

Rather than maximizing each row totally independently, we keep track of the best configurations for each number of words generated in each row, and then pick the best combination that sums to J: another straightforward exercise in dynamic programming .

Consequently the task of sentence alignment becomes handily solvable by means of such basic techniques as dynamic programming .

Note that it is relatively straightforward to identify the type of many-to-many alignment in monotonic alignment using techniques such as dynamic programming if there is no scrambled pairing or the scrambled pairings are local, limited to a short distance.

Both use dynamic programming to search for the best alignment.

(2007), a generative model is proposed, accompanied by two specific alignment strategies, i.e., dynamic programming and divisive clustering.

We shall describe our model to solve the first problem in 3.1 and our dynamic programming approach to make the inference tractable in 3.2.

We will show that dynamic programing can be used to make this problem tractable, using Model 1.

an iterative approach to compute the Viterbi word alignments for IBM Model 1 using dynamic programming .

We employed dynamic programming on hierarchies of indicators to compute the feature space providing the best pairwise classifications efficiently.

Now selecting the best space for one of these measures can be achieved by using dynamic programming techniques.

We use a dynamic programming technique to compute the best hierarchy by cutting this tree and only keeping classifiers situated at the leaf.

hierarchies with dynamic programming .

We pick the subtree which has the higher probability in the two dynamic programming tables.

If the sentence has the same number of sub-trees in both DTp and DTn, we pick the one with higher probability in the dynamic programming tables.

Following (Joty et al., 2012), we implement a probabilistic CKY—like bottom-up algorithm for computing the most likely parse using dynamic programming .

Specifically, with n discourse units, we use the upper-triangular portion of the n><n dynamic programming table D. Given U$(0) and U$(1) are the start and end EDU Ids of unit U95:

Beam sampling limits the number of possible state transitions for each node to a finite number using slice sampling (Neal, 2003), and then efficiently samples whole hidden state transitions using dynamic programming .

We can parallelize procedures in sampling u and z because the slice sampling for u and the dynamic programing for z are independent for each sentence.

,T) using dynamic programming as follows: In the joint model, p(zt|:c0(t), no.0») oc

Inference is efficiently carried out by beam sampling (Gael et al., 2008), which combines slice sampling and dynamic programming .

General algorithms for parsing LCFRSs build a dynamic programming chart of recognized nonterminals bottom-up, in a manner analogous to the CKY algorithm for CFGs (Hopcroft and Ullman, 1979), but with time and space complexity that are dependent on the rank and fanout of the grammar rules.

Whenever it is possible, binarization of LCFRS rules, or reduction of rank to two, is therefore important for parsing, as it reduces the time complexity needed for dynamic programming .

Existing parsing algorithms for LCFRSs exploit dynamic programming .

AS an example, in the case of parsing based on CFGS, nonterminals as well as partial parses all have fanout one, resulting in the standard time complexity of O(|w|3) of dynamic programming methods.

The preferred sequence is determined by using dynamic programming and beam search.

Our algorithm efficiently searches for the best sequence of sentences by using dynamic programming and beam search.

To alleviate this, we find an approximate solution by adopting the dynamic programming technique of the Held and Karp Algorithm (Held and Karp, 1962) and beam search.

In the search procedure, our dynamic programming based algorithm retains just the hypothesis with maximum score among the hypotheses that have the same sentences and the same last sentence.

Our approach finds the highest-scoring b and c using a dynamic programming algorithm: the zeroth-order case of inference under a semi-Markov model (Janssen and Limnios, 1999).

The approach can be understood as an alternative to parsing approaches using graph transducers such as (synchronous) hyperedge replacement grammars (Chiang et al., 2013; Jones et al., 2012; Drewes et al., 1997), in much the same way that spanning tree algorithms are an alternative to using shift-reduce and dynamic programming algorithms for dependency parsing.1 While a detailed

chart-based dynamic programming for inference.

While prior feature-based dynamic programming parsers have restricted training and evaluation to artificially short sentences, we present the first general, feature-rich discriminative parser, based on a conditional random field model, which has been successfully scaled to the full WSJ parsing data.

We have presented a new, feature-rich, dynamic programming based discriminative parser which is simpler, more effective, and faster to train and test than previous work, giving us new state-of-the-art performance when training and testing on sentences of length g 15 and the first results for such a parser trained and tested on sentences of length g 40.

This paper extends the third thread of work, where joint inference via dynamic programming algorithms is used to train models and to attempt to find the globally best parse.

P(.7-",f/|.7:, M) is the marginal probability of all the possible F E .7: that contain .735, as a word, which can be calculated efficiently through dynamic programming (the process is similar to the foreward-backward algorithm in training a hidden Markov model (HMM) (Rabiner, 1989)):

Then, the previous dynamic programming method can be extended to the bilingual expectation

where K is the number of characters in .73, and the k-th character is the start of the word fj, since 7' and J are unknown during the computation of dynamic programming .

Coupled with dynamic programming , transition-based dependency parsing with beam search can be done very efficiently and gives significant improvement to parsing accuracy.

Huang and Sagae (2010) later applied dynamic programming to this approach and showed improved efficiency.

which can be done very efficiently when it is coupled with dynamic programming (Zhang and Clark, 2008; Huang and Sagae, 2010; Zhang and Nivre, 2011; Huang et a1., 2012; Bohnet and Nivre, 2012).

In the figure, phone bigram TF—IDF is labeled p2; phonetic alignment with dynamic programming is labeled DP.

The feature selection experiments in Figure 2 shows that the TF—IDF features alone are quite weak, while the dynamic programming alignment features alone are quite good.

Given (13,10), we use dynamic programming to align the surface form 1‘9 with all of the baseforms of w. Following (Riley et al., 1999), we encode a phoneme/phone with a 4-tuple: consonant manner, consonant place, vowel manner, and vowel place.

The 1-1 alignment problem can be formulated as a dynamic programming problem to find the maximum score of alignment, given a probability table of aligning letter and phoneme as a mapping function.

The dynamic programming recursion to find the most likely alignment is the following:

It combines a dynamic programming alignment algorithm with an appropriate scoring scheme for computing phonetic similarity on the basis of multivalued features.

The trick is to parameterize q as a factorized distribution such that the estimation of q* and decoding using q* are both tractable through efficient dynamic programs .

(2008) effectively do take n = 00, by maintaining the whole translation string in the dynamic programming state.

Figure 4: Dynamic programming estimation of q*.

We next describe a dynamic programming solution for calculating p(7't | Gp(7's)).

3.3 Dynamic Programming

Thus every word generated under G0 aligns to null, and we can simplify the dynamic programming algorithm that scores a tree 7'5 under G0: