Parameter Tuning for Differential Mining of String Patterns

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Parameter Tuning for Differential Miningof
String Patterns

• J.Besson, C. Rigotti, I. Mitasiunaite and J.-F.
  Boulicaut

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Tuning extraction parameters

• Local pattern mining itemsets, closed itemsets,
  episodes, seq. patterns, substrings
• . under constraints (monotonic or not or
  neither, pattern shapes, occurrence properties,
  measures )
• can select/focus .
• where to look in the parameter space ?
• often easy when a single threshold
• but when multiple constraints/multiple
  thresholds ?

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Two different kinds of tuning

• 1) exploratory stage find in parameter space
  promising areas
• 2) fine grain tuning ako greedy strategy by
  small local exploration of the parameter space

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Tools ?

• Best ever tool used in exploratory stage to find
  promising setting of the parameters in local
  pattern mining ???

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Tools

• GREP Word Count
• method manual mix
• count extracted patterns
• choose points in parameter space
• random walk
• try local greedy strategy
• having in mind known properties of the
  constraints (when applicable) and domain
  knowledge

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Tools

• when several parameters, several thresholds,
  e.g., minimal support and maximal support on
  another dataset
• perform more exhaustive exploration of pattern
  space
• draw curves depicting the extraction landscape

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Tools / landscape

• Examples

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Obtaining extraction landscapes

• use script - can need a lot of resources to
  execute - too much time needed to explore a large
  parameter space (several parameters)
• use a global model of the presence of the local
  patterns to estimate the number of patterns
• reuse/adapt a model - not so much exist
• develop a new global model - each kind of
  patterns and each conjunction of constraints can
  be a research problem in itself
• incorporate K of domain ? Global analytical
  model even more complex to exhibit

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What about sampling the pattern space ?

• sounds too naive, needing complicated frameworks
• how to sample ?
• size of the sample ?
• number of pattern in the sample that satisfy the
  constraints ?
• using domain knowledge ?
• how to estimate value for the whole pattern space
  ?

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What about simple choices ?

• sampling with replacement in pat. that satisfies
  the syntactic constraints (conjunction of
  constraints)
• number of patterns in the sample that satisfy the
  constraints
• compute probability to satisfy the constraints
  for each patterns (incorporate K of the domain)
  in the sample
• approx. number of patterns that sat. the
  constraints (in the sample)
• sample size growth the sample up to convergence
  of percentage of patterns satisfying the
  constraints
• estimate the number of patterns in the pattern
  space that satisfy the constraints percentage of
  the pat. that sat. syntactic constraints

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Whole process

• 1) built an initial sample of Psynt
• 2) comp. estimate of E(N) from the sample
• 3) add more patt. to the sample
• 4) comp. estimate of E(N) from the sample
• 5) if estimate changes a lot goto 3)

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Using it in freq. substring mining

• Two datasets R1 and R2 (two sets of strings)
• Constraints
• having size Z
• appearing at least min times in R1
• appearing no more than max times in R2
• Consider exact and approx. matching

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Pattern space and K of domain

• string over an alphabet of 4 or 8 symbols
• K of domain as three models of symbol
  distribution
• Me - independent symbols with equal frequency
• Md - independent symb. with different
  frequencies
• Mm - first order Markov model
• for given p, and Me or Md or Mm, we have the
  proba that exits at-least one occ. of p in a
  string
• from binomial distribution we have the proba that
  p sat. min and max support constraints

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Example / random data

• 4 symb. Md (0.4, 0.1, 0.2, 0.3) 100 strings of
  length 1000 in R1 and R2 , exact match

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Example / random data

• 4 symb. Mm, 100 strings of length 1000 in R1 and
  R2, exact and approx. match

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Example / gene promoter seq.

• 4 symb. A,C,G,T - Md, strings of 4000 symb., 29
  in R1 and 21 in R2 - approx. match

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Example / gene promoter seq.

• Estimate vs. extraction

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Conclusion

• Drawing extraction landscape for parameter
  tuning, in local pattern extraction, using
  pattern space sampling
• seems possible
• at-least in some cases
• using simple framework
• incorparating K of domain (to some extend -
  many works on proba of a given patt. to sat.
  constraints)
• simplier than building a global analytical model
• faster than running real extractions
• sufficient in exploratory stage ?
• companion software?

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Example / random data

• 8 symb. Me, 100 strings of length 30000 in R1 and
  R2, approx. match

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Pb - Sampling / estimate

• kind of sampling (with replacement ?)
• specific sampling (ako stratified sampling) for
  some constraints ?
• kinds of patterns ?
• quality of estimates occurrences of different
  patterns are not independent

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Pb - Other parameters added

• size of starting set
• convergence criterion ? 5 ?
• size of additional subsets
• not so hard to tune ?

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Number of patterns

• conjunction of constraints C
• patterns in patt. space PS
• for each patt. p, let var Xp1 if p sat. C or
  Xp0 if p not sat. C
• N nb of patt. that sat. C sum of Xp over PS
• E(N) sum of E(Xp) over PS
• E(Xp) proba that p sat. C
• Psynt patt. in PS that sat. syntactic
  constraint in C
• E(N) sum of E(Xp) over Psynt

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Number of patterns

• comp. NS sum of E(Xp) over a sample of Psynt
• comp. ratio NR NS/sample size
• use NR size of Psynt as an estimate of E(N)

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Example / gene promoter seq.

• Estimate vs. extraction

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Example / gene promoter seq.

• Estimate vs. extraction

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Often repeat exploratory stage

• redo exploratory stage after important changes
  as
• data selection (e.g., part of sequences)
• encoding (e.g., mapping on event types)
• discretization (e.g., threshold of binarization)