Aggregation versus Selection Bias

1
Aggregation versus Selection Bias

• Hendrik Blockeel
• Maurice Bruynooghe
• K.U.Leuven

2
Mexican cocktails...

• Assume you try some of Mexicos many exotic
  cocktails
• If you drink too many, you may feel ill
  afterwards...
• If you drink cocktails with some specific
  ingredients, you may feel ill...
• If you drink too many cocktails with some
  specific ingredients, you may feel ill.
• Could our data mining systems detect the right
  pattern?

3
Handling Sets

• Observation
• The main difference between relational and
  propositional learning is in the ability to
  handle sets
• 1-1 and N-1 relations can be handled trivially
  by joining relations
• 1-N relation links to a tuple a set of other
  tuples, which may carry information
• So the question is how do we handle such sets?
• Currently two approaches
• Aggregating over the whole set
• Constructing a subset of elements with certain
  properties

4
Selection vs. Aggregation

• Given tuple t, collect set of tuples S linked to
  t
• Aggregation approach
• Augment t with Fi(S), with Fi aggregation
  functions
• Count, sum, average, min, max, ...
• Selection approach
• Given a tuple t, test existence of a tuple linked
  to t, with some specific properties
• Construct complex conditions Ci such that
  ?Ci(S)? has predictive power (or
  Count(?Ci(S))gt0)

5
Combining Selection and Aggregation

• General form Fi(?Cj(S))
• Are there any approaches that can (efficiently)
  learn this general form?
• Efficiently not by exhaustive enumeration

2
5
tequila
tequila
tequila
aggregation
selection
both
6
Possible approaches...

• Partial solution
• Assume some set of conditions partitions S
• Aggregates over S and all subsets in S almost as
  easily computable as aggregates over S
• Applying this recursively
• If set of conditions Cj imposes a recursive
  partitioning of S, little overhead involved in
  trying all combinations of Fi with Cj

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Illustration
?
A
B
C
?
?
?
?
?
?
?
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?
?
A1 A2 A3
B1 B2
C1 C2
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Possible approaches...

• A more general solution
• Use systems that learn aggregation and selection
  conditions at the same time
• Need some capacity for iterating over sets with
  any number of elements in any order
• One wild idea recurrent NNs
• Recurrent nodes allow to accumulate some property
  over any number of inputs
• Regular nodes identify specific properties of
  inputs
• Inspired by neural logic programs (Driessens,
  Ramon)
• Learning might be too difficult...

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Illustration
Recurrent (aggregating) node
Standard node
Input one vector
Input set of vectors, Presented consecutively