Intelligent Search

Intelligent Search

Intelligent Search(or at least really clever)

Some Preliminaries

• Text retrieval = matrix multiplication

A: our corpusdocuments are rowsterms are columns

Some Preliminaries

• Text retrieval = matrix multiplication

for each document d:for each term t:sd += adt qt

A: our corpusdocuments are rowsterms are columns

Some Preliminaries

• Text retrieval = matrix multiplication

A: our corpusdocuments are rowsterms are columns

sd = Σt adt qt

Some Preliminaries

• Text retrieval = matrix multiplication

A: our corpusdocuments are rowsterms are columns

s = A q

More Preliminaries

• Recommendation = Matrix multiply

A: our users’ historiesusers are rowsitems are columns

More Preliminaries

• Recommendation = Matrix multiply

A: our users’ historiesusers are rowsitems are columns

Users who bought itemsin the list h also bought items in the list r

More Preliminaries

• Recommendation = Matrix multiply

for each user u:for each item t1:for each item t2:

rt1 += au,t1 au,t2 ht2

A: our users’ historiesusers are rowsitems are columns

More Preliminaries

• Recommendation = Matrix multiply

A: our users’ historiesusers are rowsitems are columns

sd = Σt2 Σu au,t1 au,t2 qt2

More Preliminaries

• Recommendation = Matrix multiply

A: our users’ historiesusers are rowsitems are columns

s = A’ (A q)

More Preliminaries

• Recommendation = Matrix multiply

A: our users’ historiesusers are rowsitems are columns

s = (A’ A) q

More Preliminaries

• Recommendation = Matrix multiply

A: our users’ historiesusers are rowsitems are columns

s = (A’ A) q ish!

Why so ish?

• In real life, ish happens because:

• Big data ... so we selectively sample

• Sparse data ... so we smooth

• Finite computers ... so we sparsify

• Top-40 effect ... so we use some stats

The same in spite of ish

• The shape of the computation is unchanged

• The cost of the computation is unchanged

• Broad algebraic conclusions still hold

Back to recommendations ...

Dyadic Structure● Functional

– Interaction: actor -> item*● Relational

– Interaction ⊆ Actors x Items● Matrix

– Rows indexed by actor, columns by item– Value is count of interactions

● Predict missing observations

Fundamental Algorithmics● Cooccurrence

● A is actors x items, K is items x items● Product has general shape of matrix ● K tells us “users who interacted with x also

interacted with y”

Fundamental Algorithmic Structure● Cooccurrence

● Matrix approximation by factoring

● LLR

But Wait ...

But Wait ...

Does it have to be that way?

What we have:

For a user who watched/bought/listened to this

What we have:

For a user who watched/bought/listened to this

Sum over all other users who watched/bought/...

What we have:

For a user who watched/bought/listened to this

Sum over all other users who watched/bought/...

Add up what they watched/bought/listened to

What we have:

For a user who watched/bought/listened to this

Sum over all other users who watched/bought/...

Add up what they watched/bought/listened to

And recommend that

What we have:

For a user who watched/bought/listened to this

Sum over all other users who watched/bought/...

Add up what they watched/bought/listened to

And recommend that

ish

What we have:

Add up what they watched/bought/listened to

What we have:

Add up what they watched/bought/listened to

But wait, we can do that faster

What we have:

Add up what they watched/bought/listened to

But wait, we can do that faster

But why not ...

But why not ...

But why not ...

Why just dyadic learning?

But why not ...

Why just dyadic learning?

Why not triadic learning?

But why not ...

Why just dyadic learning?

Why not p-adic learning?

For example● Users enter queries (A)

– (actor = user, item=query) ● Users view videos (B)

– (actor = user, item=video)● AʼA gives query recommendation

– “did you mean to ask for”● BʼB gives video recommendation

– “you might like these videos”

The punch-line● BʼA recommends videos in response to a query

– (isnʼt that a search engine?)– (not quite, it doesnʼt look at content or meta-data)

Real-life example● Query: “Paco de Lucia”● Conventional meta-data search results:

– “hombres del paco” times 400– not much else

● Recommendation based search:– Flamenco guitar and dancers– Spanish and classical guitar– Van Halen doing a classical/flamenco riff

Real-life example

Real-life example

System Diagram

Viewing Logs t user video

Search Logs t user query-term

selective sampler

selective sampler

count

count

join on user

count

Related videos v => v1 v2...

Related terms v => t1 t2...

llr + sparsify

Hadoop

Indexing

Related videos v => v1 v2...

Video meta v => url title...

join on video

Lucene Index

Related terms v => t1 t2...

Hadoop Lucene (+Katta?)

Hypothetical Example● Want a navigational ontology?● Just put labels on a web page with traffic

– This gives A = users x label clicks● Remember viewing history

– This gives B = users x items● Cross recommend

– BʼA = click to item mapping● After several users click, results are whatever

users think they should be

Resources● My blog

– http://tdunning.blogspot.com/● The original LLR in NLP paper

– Accurate Methods for the Statistics of Surprise and Coincidence (check on citeseer)

● Source code– Mahout project– contact me ([email protected])