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in Machine Learning by (19k points)

I'm sure there is a post on this, but I couldn't find one asking this exact question. Consider the following:

We have a word dictionary available

We are fed many paragraphs of words, and I wish to be able to predict the next word in a sentence given this input.

Say we have a few sentences such as "Hello my name is Tom", "His name is jerry", "He goes where there is no water". We check a hash table if a word exists. If it does not, we assign it a unique id and put it in the hash table. This way, instead of storing a "chain" of words as a bunch of strings, we can just have a list of uniqueID's.

Above, we would have for instance (0, 1, 2, 3, 4), (5, 2, 3, 6), and (7, 8, 9, 10, 3, 11, 12). Note that 3 is "is" and we added new unique id's as we discovered new words. So say we are given a sentence "her name is", this would be (13, 2, 3). We want to know, given this context, what the next word should be. This is the algorithm I thought of, but I dont think its efficient:

We have a list of N chains (observed sentences) where a chain may be ex. 3,6,2,7,8.

Each chain is on average size M, where M is the average sentence length

We are given a new chain of size S, ex. 13, 2, 3, and we wish to know what is the most probable next word?

Algorithm:

First scan the entire list of chains for those who contain the full S input(13,2,3, in this example). Since we have to scan N chains, each of length M, and compare S letters at a time, its O(N*M*S).

If there are no chains in our scan which have the full S, next scan by removing the least significant word (ie. the first one, so remove 13). Now, scan for (2,3) as in 1 in worst case O(N*M*S) which is really S-1.

Continue scanning this way until we get results > 0 (if ever).

Tally the next words in all of the remaining chains we have gathered. We can use a hash table which counts every time we add, and keeps track of the most added word. O(N) worst case build, O(1) to find max word.

The max word found is the the most likely, so return it.

Each scan takes O(M*N*S) worst case. This is because there are N chains, each chain has M numbers, and we must check S numbers for overlaying a match. We scan S times worst case (13,2,3,then 2,3, then 3 for 3 scans = S). Thus, the total complexity is O(S^2 * M * N).

So if we have 100,000 chains and an average sentence length of 10 words, we're looking at 1,000,000*S^2 to get the optimal word. Clearly, N >> M, since sentence length does not scale with number of observed sentences in general, so M can be a constant. We can then reduce the complexity to O(S^2 * N). O(S^2 * M * N) may be more helpful for analysis though, since M can be a sizeable "constant".

This could be the complete wrong approach to take for this type of problem, but I wanted to share my thoughts instead of just blatantly asking for assitance. The reason im scanning the way I do is because I only want to scan as much as I have to. If nothing has the full S, just keep pruning S until some chains match. If they never match, we have no idea what to predict as the next word! Any suggestions on a less time/space complex solution? Thanks!

1 Answer

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by (33.1k points)

It is a common problem of language modeling. You need is a hash table mapping fixed-length chains of words.

You should break the input into (k+1)-grams using a sliding window method. 

You should generate, for k=2,

For example:

START START the

START the wrath

the wrath sing

wrath sing goddess

goddess of peleus

of peleus son

peleus son achilles

For each 3-gram, tally the third word follows the first two.

Finally, loop through the hash table and for each key (2-gram) keep only the most commonly occurring third word. 

At the time of prediction, look only at the k (2) last words and then predict the next word. This takes only constant time, then it's just a hash table lookup.

Hope this answer helps. For more details on Word Prediction, study Machine Learning Algorithms. Also, go through Machine Learning Tutorial to go through this particular domain.

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