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From Noelia Osés Fernández <>
Subject Re: Log-likelihood based correlation test?
Date Tue, 21 Nov 2017 09:28:52 GMT

If I understood your explanation correctly, you say that some elements of
PtP are removed by the LLR (set to zero, to be precise). But the elements
that survive are calculated by matrix multiplication. The final PtP is put
into EleasticSearc and when we query for user recommendations ES uses KNN
to find the items (the rows in PtP) that are most similar to the user's

If the non-zero elements of PtP have been calculated by straight matrix
multiplication, and I'm assuming that the P matrix only has 0s and 1s to
indicate which items have been purchased by which user, then the elements
of PtP are either 0 or greater to or equal than 1. However, the scores I
get are below 1.

So is the KNN using cosine similarity as a metric to calculate the closest
neighbours? And is the results of this cosine similarity metric what is
returned as a 'score'?

If it is, when it is greater than 1, is this because the different cosine
similarities are added together i.e. PtP, PtL... ?

Thank you for all your valuable help!

On 17 November 2017 at 19:52, Pat Ferrel <> wrote:

> Mahout builds the model by doing matrix multiplication (PtP) then
> calculating the LLR score for every non-zero value. We then keep the top K
> or use a threshold to decide whether to keep of not (both are supported in
> the UR). LLR is a metric for seeing how likely 2 events in a large group
> are correlated. Therefore LLR is only used to remove weak data from the
> model.
> So Mahout builds the model then it is put into Elasticsearch which is used
> as a KNN (K-nearest Neighbors) engine. The LLR score is not put into the
> model only an indicator that the item survived the LLR test.
> The KNN is applied using the user’s history as the query and finding items
> the most closely match it. Since PtP will have items in rows and the row
> will have correlating items, this “search” methods work quite well to find
> items that had very similar items purchased with it as are in the user’s
> history.
> =============================== that is the simple explanation
> ========================================
> Item-based recs take the model items (correlated items by the LLR test) as
> the query and the results are the most similar items—the items with most
> similar correlating items.
> The model is items in rows and items in columns if you are only using one
> event. PtP. If you think it through, it is all purchased items in as the
> row key and other items purchased along with the row key. LLR filters out
> the weakly correlating non-zero values (0 mean no evidence of correlation
> anyway). If we didn’t do this it would be purely a “Cooccurrence”
> recommender, one of the first useful ones. But filtering based on
> cooccurrence strength (PtP values without LLR applied to them) produces
> much worse results than using LLR to filter for most highly correlated
> cooccurrences. You get a similar effect with Matrix Factorization but you
> can only use one type of event for various reasons.
> Since LLR is a probabilistic metric that only looks at counts, it can be
> applied equally well to PtV (purchase, view), PtS (purchase, search terms),
> PtC (purchase, category-preferences). We did an experiment using Mean
> Average Precision for the UR using video “Likes” vs “Likes” and “Dislikes”
> so LtL vs. LtL and LtD scraped from reviews and got a
> 20% lift in the MAP@k score by including data for “Dislikes”.
> occurences/
> So the benefit and use of LLR is to filter weak data from the model and
> allow us to see if dislikes, and other events, correlate with likes. Adding
> this type of data, that is usually thrown away is one the the most powerful
> reasons to use the algorithm—BTW the algorithm is called Correlated
> Cross-Occurrence (CCO).
> The benefit of using Lucene (at the heart of Elasticsearch) to do the KNN
> query is that is it fast, taking the user’s realtime events into the query
> but also because it is is trivial to add all sorts or business rules. like
> give me recs based on user events but only ones from a certain category, of
> give me recs but only ones tagged as “in-stock” in fact the business rules
> can have inclusion rules, exclusion rules, and be mixed with ANDs and ORs.
> BTW there is a version ready for testing with PIO 0.12.0 and ES5 here:
> Instructions
> in the readme and notice it is in the 0.7.0-SNAPSHOT branch.
> On Nov 17, 2017, at 7:59 AM, Andrew Troemner <>
> wrote:
> I'll echo Dan here. He and I went through the raw Mahout libraries called
> by the Universal Recommender, and while Noelia's description is accurate
> for an intermediate step, the indexing via ElasticSearch generates some
> separate relevancy scores based on their Lucene indexing scheme. The raw
> LLR scores are used in building this process, but the final scores served
> up by the API's should be post-processed, and cannot be used to reconstruct
> the raw LLR's (to my understanding).
> There are also some additional steps including down-sampling, which scrubs
> out very rare combinations (which otherwise would have very high LLR's for
> a single observation), which partially corrects for the statistical problem
> of multiple detection. But the underlying logic is per Ted Dunning's
> research and summarized by Noelia, and is a solid way to approach
> interaction effects for tens of thousands of items and including secondary
> indicators (like demographics, or implicit preferences).
> *ANDREW TROEMNER*Associate Principal Data Scientist |
> Office: 317.832.4404
> Mobile: 317.531.0216
> <>
> On Fri, Nov 17, 2017 at 9:55 AM, Daniel Gabrieli <
> > wrote:
>> Maybe someone can correct me if I am wrong but in the code I believe
>> Elasticsearch is used instead of "resulting LLR is what goes into the AB
>> element in matrix PtP or PtL."
>> By default the strongest 50 LLR scores get set as searchable values in
>> Elasticsearch per item-event pair.
>> You can configure the thresholds for significance using the configuration
>> parameters: maxCorrelatorsPerItem or minLLR.  And this configuration is
>> important because at default of 50 you may end up treating all "indicator
>> values" as significant.  More info here:
>> /ur_config
>> On Fri, Nov 17, 2017 at 4:50 AM Noelia Osés Fernández <
>>> wrote:
>>> Let's see if I've understood how LLR is used in UR. Let P be the matrix
>>> for the primary conversion indicator (say purchases) and Pt its transposed.
>>> Then, with a second matrix, which can be P again to make PtP or a matrix
>>> for a secondary indicator (say L for likes) to make PtL, we take a row from
>>> Pt (item A) and a column from the second matrix (either P or L, in this
>>> example) (item B) and we calculate the table that Ted Dunning explains on
>>> his webpage: the number of coocurrences that item A *AND* B have been
>>> purchased (or purchased AND liked), the number of times that item A *OR*
>>>  B have been purchased (or purchased OR liked), and the number of times
>>> that *neither* item A nor B have been purchased (or purchased or
>>> liked). With this counts we calculate LLR following the formulas that Ted
>>> Dunning provides and the resulting LLR is what goes into the AB element in
>>> matrix PtP or PtL. Correct?
>>> Thank you!
>>> On 16 November 2017 at 17:03, Noelia Osés Fernández <
>>> > wrote:
>>>> Wonderful! Thanks Daniel!
>>>> Suneel, I'm still new to the Apache ecosystem and so I know that Mahout
>>>> is used but only vaguely... I still don't know the different parts well
>>>> enough to have a good understanding of what each of them do (Spark, MLLib,
>>>> PIO, Mahout,...)
>>>> Thank you both!
>>>> On 16 November 2017 at 16:59, Suneel Marthi <> wrote:
>>>>> Indeed so. Ted Dunning is an Apache Mahout PMC and committer and the
>>>>> whole idea of Search-based Recommenders stems from his work and insights.
>>>>> If u didn't know, the PIO UR uses Apache Mahout under the hood and hence
>>>>> see the LLR.
>>>>> On Thu, Nov 16, 2017 at 3:49 PM, Daniel Gabrieli <dgabrieli@
>>>>>> wrote:
>>>>>> I am pretty sure the LLR stuff in UR is based off of this blog post
>>>>>> and associated paper:
>>>>>> Accurate Methods for the Statistics of Surprise and Coincidence
>>>>>> by Ted Dunning
>>>>>> On Thu, Nov 16, 2017 at 10:26 AM Noelia Osés Fernández <
>>>>>>> wrote:
>>>>>>> Hi,
>>>>>>> I've been trying to understand how the UR algorithm works and
>>>>>>> think I have a general idea. But I would like to have a *mathematical
>>>>>>> description* of the step in which the LLR comes into play. In
>>>>>>> CCO presentations I have found it says:
>>>>>>> (PtP) compares column to column using
>>>>>>> *log-likelihood based correlation test*
>>>>>>> However, I have searched for "log-likelihood based correlation
>>>>>>> in google but no joy. All I get are explanations of the likelihood-ratio
>>>>>>> test to compare two models.
>>>>>>> I would very much appreciate a math explanation of log-likelihood
>>>>>>> based correlation test. Any pointers to papers or any other literature
>>>>>>> explains this specifically are much appreciated.
>>>>>>> Best regards,
>>>>>>> Noelia
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Noelia Osés Fernández, PhD
Senior Researcher |
Investigadora Senior
+[34] 943 30 92 30
Data Intelligence for Energy and
Industrial Processes | Inteligencia
de Datos para Energía y Procesos


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