Merck ACSM Intern Presentation

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Merck ACSMIntern Presentation

• Xiangdong wen

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Projects

• Quality control on high throughput screening
• Active learning approach to this type of problems

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Quality control on high throughput screening (HTS)

• HTS quantitatively and qualitatively examining
  the interaction of synthetic molecules with
  proteins, identify target compounds for a
  potential drug.
• HTS plays an important role in pharmaceutical
  research and drug discovery.
• Technologies HTRF, SPA, FLIPR, BLA

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FlIPR system Fluorescent Imaging Plate reader

• 96,
• 384,
• 1536,
• 3456,
• More wells

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384 well FLIPR Assays

• 16 (rows) x 24 (columns)384 wells
• First 2 and last 2 columns are controls.
• 16x(24-2x2)320 wells.
• Two channels data, top and bottom, or max and min
  for the intensity value.
• we use the differences top-bottom.

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Data

• Min
• VGCCA1B_FLIPR_ANT_Block1_2904.txt
• Max
• VGCCA1B_FLIPR_ANT_Block1_2904.txt
• 2904 plates,
• experts fail 406 plates.
• Pass 2498 plates

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Quality control for flipr system

• Global quality control
• Median Polish method
• Local quality control
• a set of rules
• such as patch finder

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Median Polish

• µij µ µi µj eij
• µij the value at well (i, j)
• µ analog of the global mean, fixed overall
  effects.
• µi analog of the ith row mean, row effects
• µj analog of the jth column mean, column
  effects.
• eij random error term.

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Median Polish cont,

• Median polish needs 162036 features for 384
  flipr assays.
• Do QC by computing these 36 features and test
  whether they fall in some interval, if not we
  fail the plate.
• For now, global quality control using median
  polish features

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My Approach

• There are 320 well values for each assay.
• Sort these 320 values.
• Take the smallest N (2-35) of them.
• Compute the mean of these smallest N numbers
• Use the mean as a feature.
• Use rpart in R, get threshold values.
• Found optimum Ns. (N13,14,15)
• Explored more details on N13,14,15. get the
  corresponding optimum threshold.

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Find the optimum N
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Find the optimum threshold
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New rule

• If Mean_Of_15_Smallestgt5246.992
• Pass the plate
• Otherwise fail the plate.

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Results
Define Cost PF 0.5 FP Global QC (median
polish) cost292 0.5 65324.5 New rule
cost123 0.5 218232 Cost decreased
by (324.5-232)/324.528.5
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Other approaches

• Compute the mean and variance for each mn
  blocks, m(4-gt10), n(4-gt10). And use the results
  as features.
• Apply LDA in R.
• Use random Forest package in R.
• These methods did not get us better results.

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Active Learning

• Many manual tasks are tedious, repetitive, boring
  or even dangerous.
• We try to automate such kinds of tasks.
• Learning ask questions and learn from answers.
• Active learning if questions are cheap but
  answers are expensive, wed like to ask the
  most informative series of questions.

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Classification

• Input
• samples (x1,y1),(x2,y2),(xn, yn)
• Output
• a classification rule c. Such that the error
  rate err(c) is as small as possible.

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Sequential sampling

• When labels are expensive, we would like to
  economize.
• Select examples which will result in the best
  classifier.
• We can hope for extra efficiency if we permit
  sampling to depend on previous samples and labels.

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Query by CommitteeHow to do sequential sampling?

• Let Sn be the labeled sample at stage n.
• Let VnC(Sn) be the version space at stage n,
  relative to the current sample.
• (version space the set of all classifiers
  which agree with the samples.)
• Define the information in Vn as logp(Vn)
• Given an unlabelled example x, measure its
  potential information by the expected
  instantaneous information gain
• Select examples with high information gain.

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Monte Carlo approach

• Choose k2 concepts (committee) at random from
  the version space. If the two concepts agree on
  an example x, we estimate the entropy of c(x) to
  be low, if they disagree, high .
• Apply this to a stream of examples, selecting
  those with high entropy.

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Likelihood for the forest

• P(yx)y(1-P(yx))(1-y)
• (x,y) is a sample point.
• For certain sample
• High likelihood means good forest.
• For fixed forest
• Low likelihood means informative sample.

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Our approach

• Use weighted random forest as committee,
• Use the likelihood for each tree as weights for
  the corresponding tree.
• use the likelihood for the forest as an
  information measure,
• Select those examples with low forest
  likelihood (high information gain)
• Update the forest.

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Procedures

• Generate random multidimensional Gaussian
  distribution data.
• Revise random Forest packages in R to weighted
  random forest.
• Compute the likelihood for each tree in the
  forest.
• Compute the likelihood for the forest.
• Developing some forest updating functions

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Generating data

• Very flexible, could simulating almost all kinds
  of data.
• The data in reality is limited.
• The generated data already have labels.
• Easy for use in doing research work.
• Easy to control Bayesians error, decision
  boundary.

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Random forest

• Each tree is a classifier.
• Random forest is a bunch of such kind trees.
• Using randomly selected features to split each
  node in the tree.
• The overall error for forest converges as the
  number of trees becomes large.

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Why weighted random forest?

• Some trees in the forest are more important than
  other trees.
• When the number of trees in the random forest
  becomes larger, Its efficiency goes slow.
• When using weighted random forest, need only
  relatively a small number of trees.
• Theoretically want the forest to approximate the
  posterior distribution, need weights.
• When adding new training data, we could just
  update the weights of the forest.

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Simple example

• Suppose we have a two classes problem
• Class 0 N((-1,2), I) p1/2
• N((-1,-2),I) p1/2
• Class 1 N((1,4),I) p1/3
• N((1,0),I) p1/3
• N((1,-4),I) p1/3
• Where I is the 2 dimensional identity matrix,
  here we use it as the covariance matrix of random
  data.

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Simple example cont,

• Generating data and plot.
• How to find a good classifier?

6000 data points, 500 trees
3000 data points, 500 trees
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Acknowledgement

• Reid
• Ansu
• Scott
• Irene
• Nancy
• ACSM interns
• ACSM family