Incorrect IDF in MultiPhraseQuery and SpanOrQuery [LUCENE-8943]

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I recently stumbled across a very old bug in the IDF computation for MultiPhraseQuery and SpanOrQuery.

BM25Similarity and TFIDFSimilarity / ClassicSimilarity have a method for combining IDF values from more than on term / TermStatistics.

I mean the method:

Explanation idfExplain(CollectionStatistics collectionStats, TermStatistics termStats[])

It simply adds up the IDFs from all termStats[].

This method is used e.g. in PhraseQuery where it makes sense. If we assume that for the phrase "New York" the occurrences of both words are independent, we can multiply their probabilitis and since IDFs are logarithmic we add them up. Seems to be a reasonable approximation. However, this method is also used to add up the IDFs of all terms in a MultiPhraseQuery as can be seen in:

Similarity.SimScorer getStats(IndexSearcher searcher)

A MultiPhraseQuery is actually a PhraseQuery with alternatives at individual positions. IDFs of alternative terms for one position should not be added up. Instead we should use the minimum value as an approcimation because this corresponds to the docFreq of the most frequent term and we know that this is a lower bound for the docFreq for this position.

In SpanOrQuerry we have the same problem It uses buildSimWeight(...) from SpanWeight and adds up all IDFs of all OR-clauses.

If my arguments are not convincing, look at SynonymQuery / SynonymWeight in the constructor:

SynonymWeight(Query query, IndexSearcher searcher, ScoreMode scoreMode, float boost)

A SynonymQuery is also a kind of OR-query and it uses the maximum of the docFreq of all its alternative terms. I think this is how it should be.

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Migrated from LUCENE-8943 by Christoph Goller, updated Apr 09 2020

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Christoph Goller (migrated from JIRA)

Why is this an issue?

Because IDFs of SpanOrQueriy and MultiPhraseQuery can get gigantic meaning that such queries have an unexpectedly high impact on the final score.

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Alan Woodward (@romseygeek) (migrated from JIRA)

Thanks for opening this issue Christoph. MultiPhraseQuery we can solve this for pretty easily, SpanOr will be slightly trickier I think but will be helped once #9955 is merged and we can simplify SpanWeight.buildSimWeight()

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Christoph Goller (migrated from JIRA)

Thanks for your quick response Alan. I've been doing some thinking about adding up IDF values in case of simple phrase queries and I no longer think that is the way we should do it.

The problem is that we can get very high IDF values, i.e. values that are considerably higher than the maximum IDF value for a single term!

Consider an index with 10 million docs. The maximum IDF value (BM25) for a single term is 16.8. Assume we have 10 docs containing "wifi" and 10 docs containing "wi-fi" which is split by our tokenizer into 2 tokens. The IDF value for "wifi" will be 13.77. If we assume that "wi" and "fi" both occur only in "wi-fi" docs, we get an IDF of 27.5 for the "wi fi" phrase query which wee need in order to find our 10 "wi-fi" docs. If we search for wifi OR "wi fi" the docs containing "wi-fi" will score much higher!

Admittedly, it is easy to construct examples in which adding the IDF values of phrase parts yields values that are too high. The assumption of independence of phrase parts does not normally apply. But BM25 has a saturation for IDF values and adding up IDF values breaks it. This seems to be a serious drawback.

I propose to switch from combining IDF-values to calculating / approximating docFreq. For the OR-case SynonymQuery does this already. It uses the maximum. For the AND-case we could use something like

docFreqPhrase = (docFreq1 * docFreq2) / docCount

The intuition behind this is again independence of phrase parts. But by computing a docFreq we can guarantee the saturation for IDF.

For the "wi fi" example we get docFreqPhrase of 10^-5 leading to an IDF of 16.8 (saturation) and the difference to the IDF of wifi is considerably smaller compared to adding up IDFs. If phrase parts are rare, we quickly run into saturation of the IDF. But we also get some reasonable values. Consider the phrase "New York". If we assume that 100,000 docs contain "new" and 10,000 docs contain "york". By applying the formula from above we get and IDF for the phrase "New York" of 11.5 which is roughly the number we get when we add up the IDFs of the parts (current Lucene behavior).

We could even have some simple adjustments for the fact that usually the independence assumption is not correct. For both the OR-case and the AND-case we could make values a little bit higher. The exact way for approximating docFreq for the AND-case and the OR-case could be defined in the Similarity and it could be configurable.

I also did some research with Google:

(multiword OR N-gram) AND BM25 AND IDF

Unfortunately I did not find anything that helps.

Do you know about the benchmarks used to evaluate scoring in Lucene? Are there any phrase queries involved?
Robert told me it’s very Trek-like, so probably no phrase queries?

In my opinion something like BM25 can only get us to a certain level of relevance. Of course, we have to get it right. IDF values of phrases / SpanQueries should not have such a big effect on the score simply because they get too high IDF-values. We have to do something reasonable. But for real break-through improvements we need something like query segmentation or even query interpretation and proximity of query terms in documents should have a high impact on the score. That's why I think it is important to integrate PhraseQueries and SpanQueries properly into BM25.

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Jim Ferenczi (@jimczi) (migrated from JIRA)

I don't think we can realistically approximate the doc freq of phrases, especially if you consider more than 2 terms. The issue with the score difference of "wifi" (single term) vs "wi fi" (multiple terms) is more a synonym issue where the association between these terms is made at search time. Currently BM25 similarity sums the idf values but this was done to limit the difference with the classic (tfidf) similarity. The other similarities take a simpler approach that just sum the score of each term that appear in the query like a boolean query would do (see MultiSimilarity). It's difficult to pick one approach over the other here but the context is important. For single term synonym (terms that appear at the same position) we have the SynonymQuery that is used to blend the score of such terms. I tend to agree that the MultiPhraseQuery should take the same approach so that each position can score once instead of per terms. However it is difficult to expand this strategy to variable length multi words synonyms. We could try with a specialized MultiWordsSynonymQuery that would apply some strategy (approximation of the doc count like you propose or anything that makes sense here ;) ) to make sure that all variations are scored the same. Does this makes sense ?

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Christoph Goller (migrated from JIRA)

I agree, we cannot realistically approximate the doc freq of phrases.
And yes, actually the scoring problem I brought up is a kind of synonym issue.

Usually, if we are using synonyms we want to score exact query matches higher than synonym matches. That's probably one of the reasons why SynonymQuery allows to specify boosts.

I am having lots of multiword synonyms. W2k16 e.g. is a synonym for "Windows Server 2016". Different boosts for multiword synonyms don't work reliably since matches for "Windows Server 2016" may score much higher than those of W2k16 due to huge IDFs.

I am not so much looking for an optimal BM25 scoring for Phrases / Multiphrases / Spans. Instead I  am looking for a
way to score them within BM25 so that boosts work as expected.

One step into this direction would be to limit IDF values in case of Phrases / Multiphrases / Spans. In BM25 it seems to be very important that IDF saturates and currently the behavior of Phrases / Multiphrases / Spans contradicts that. With the solution I proposed we can get rid of huge IDF values for Phrases / Multiphrases / Spans. Therefore I still think we should do it. Plus it would make scores more camparable and boosts would work more reliable.

Your post made me think of the problem in another way. If we had something like MultiWordsSynonymQuery, we could have even more control. Similar to SynonymQuery we could use one IDF value for all synonyms. Synonym boost would work much more reliably.

MultiWordsSynonymQuery could be very general. In my last post I suggested to approximate docFreq instead of IDFs in order to gurantee saturation. For implementing it, I thought about adding a member variable pseudoStats (TermStatistics) to Weight, which would be used for computing SimScorer. Usually the values for pseudoStats would be computed bottom up (SpanWeight, PhraseWeight) from the subqueries. But we could implement a general MultiWordsSynonymQuery as subclass of BooleanQuery (only allowing disjunction) which would set (adapt) pseudoStats in all its subweights (docFreq as max docFreq of all synonyms just as SynonymQuery currently does).

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Jim Ferenczi (@jimczi) (migrated from JIRA)

Your post made me think of the problem in another way. If we had something like MultiWordsSynonymQuery, we could have even more control. Similar to SynonymQuery we could use one IDF value for all synonyms. Synonym boost would work much more reliably.

 

Yes, that's what I tried to explain in my post. It is a specific issue with multi-words synonyms so we should have a dedicated query. 

 

Usually the values for pseudoStats would be computed bottom up (SpanWeight, PhraseWeight) from the subqueries. But we could implement a general MultiWordsSynonymQuery as subclass of BooleanQuery (only allowing disjunction) which would set (adapt) pseudoStats in all its subweights (docFreq as max docFreq of all synonyms just as SynonymQuery currently does).

 

+1, that's how I'd start with this. We don't need to handle all type of queries though, only Term (e.g.: body:ny), conjunction of Term queries (e.g.: body:new AND body:york) and phrase queries (e.g.: "new york") should be accepted.

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Christoph Goller (migrated from JIRA)

In the meanwhile I worked on the problem of the MultiWordsSynonymQuery a little bit.

I think queries that are allowed as synonym-clauses within the MultiWordsSynonymQuery we need two additional properties.

1. Their weights should deliver a pseudo-statistics so that we can compute a combined IDF value for all the synonyms.
   I implemented a prototype for SpanQueries already. I did this by adding an interface PseudoStatistics which may be implemented by Weights.
2. They have to provide frequencies so that we can add up all frequencies just as SynonymQuery currently does for terms. We could also have an additional Interface for that that could be implemented by some Scorers or we could add a new ScoreMode COMPLETE_FREQUENCIES and Scorers could deliver frequencies instead of scores for this ScoreMode.

Instead of implementing MultiWordsSynonymQuery as a subclass of BooleanQuery I would rather implement it as a mor generalized version of SynonymQuery with lots of core copied from there.