Using Random Forests to explore a complex Metabolomic data set

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Using Random Forests to explore a complex
Metabolomic data set

• Susan Simmons
• Department of Mathematics and Statistics
• University of North Carolina Wilmington

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Collaborators

• Dr. David Banks (Duke)
• Dr. Jacqueline Hughes-Oliver (NC State)
• Dr. Stan Young (NISS)
• Dr. Young Truoung (UNC)
• Dr. Chris Beecher (Metabolon)
• Dr. Xiaodong Lin (SAMSI)

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(No Transcript)
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Large data sets

• Examples
• Walmart
• 20 million transactions daily
• ATT
• 100 million customers and carries 200 million
  calls a day on its long-distance network
• Mobil Oil
• over 100 terabytes of data with oil exploration
• Human genome
• Gigabytes of data
• IRA

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Dimensionality
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Dimensionality

• 3,000 metabolites
• 40,000 genes
• 100,000 chemicals
• Try to find the signal in these data sets (and
  not the noise)..Data mining
• Examples of data mining techniques pattern
  recognition, expert systems, genetic algorithms,
  neural networks, random forests

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Todays talk

• Focus on classification (supervised learninguse
  a response to guide the learning process)
• Response is categorical (Each observation belongs
  to a class)
• Interested in relationship between variables and
  the response
• Short, fat data (instead of long, skinny data)

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Long, skinny data
X Y Z
2 8 9
3 4 4
7 5 46
8 7 3
4 56 35
6 58 63
12 9 3
14 2 35
24 1 45
2 7 4
13 78 25
14 56 34
18 6 89
35 8 56
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Short, fat data
X Y Z S T V M N R Q L H G K B C W
4 36 5 8 30 4 35 7 3 78 9 3 1 40 2 5 34
6 7 34 6 7 67 8 89 8 4 2 6 5 9 8 67 3
7 46 2 4 5 6 7 58 9 7 9 50 4 45 7 8 45
8 4 5 65 57 57 42 2 7 23 4 6 76 8 0 56 90
nltp problem
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Random Forests

• Developed by Leo Breiman (Berkeley) and Adele
  Cutler (Utah State)
• Can handle the nltp problem
• Random forests are comparable in accuracy to
  support vector machines
• Random forests are a combination of tree
  predictors

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Constructing a tree
Observation Gender Height (inches)
1 F 60
2 F 66
3 M 68
4 F 70
5 F 66
6 M 72
7 F 64
8 M 67
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Tree for previous data set
All observations N8
Height lt 66 N4
Height gt 66 N4
Male N0
Female N4
Male N3
Female N1
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Random Forest

• First, the number of trees to be grown must be
  specified.
• Also, the number of variables randomly selected
  at each node must be specified (m).
• Each tree is constructed in the following manner
• 1. At each node, randomly select m variables to
  split on.

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Random Forest

• The node is split using the best split among the
  selected variables.
• This process is continued until each node has
  only one observation, or all the observations
  belong to the same class.
• Do this for each tree in the forest

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Example Cereal Data
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N70 (40 G, 30K)
Calories lt100 (2 G, 15 K)
Calories lt100 (38 G, 15 K)
Fat lt1 15 K
Fat gt1 2 G
Carbolt12 15 K
Carbogt12 38G
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Random Forest

• Another important feature is that each tree is
  created using a bootstrap sample of the learning
  set.
• Each bootstrap sample contains approximately 2/3
  of the data (thus approximately 1/3 is left)
• Now, we can use the trees built not containing
  observations to get an idea of the error rate
  (each tree will vote on which class the
  observation belongs to).
• Example

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N70 (40 G, 30K)
Calories lt100 (2 G, 15 K)
Calories lt100 (38 G, 15 K)
Fat lt1 15 K
Fat gt1 2 G
Carbolt12 15 K
Carbogt12 38G
Observation withheld from creating this
tree Calories Fat Carbo Mfr 98 2
10 K
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Random Forest

• This gives us an out of bag error rate
• Random forests also give us an idea of which
  variables are important for classifying
  individuals.
• Also gives information about outliers

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The era of the omics sciences
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Just a few of the omics sciences

• Genomics
• Transcriptomics
• Proteomics
• Metabolomics
• Phenomics
• Toxicogenomics
• Phylomics
• Foldomics

• Kinomics
• Interactomics
• Behavioromics
• Variomics
• Pharmacogenomics

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Functional Genomics
Genomics
Transciptomics
Proteomics
Metabolomics
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Metabolomics

• Metabolites are all the small molecules in a cell
  (i.e. ATP, sugar, pyruvate, urea)
• 3,000 metabolites in the human body (compared to
  35,000 genes and approximately 100,000 proteins)
• Most direct measure of cell physiology
• Uses GC/MS and LC/MS to obtain measurements

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Data

• Currently only have GC/MS information
• Missing values are very informative (below
  detection limits)
• Imputed data using uniform random variables from
  0 to minimum value
• 105 metabolites
• 58 individuals (42 disease 1, 6 disease 2,
  and 10 controls)

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Confusion matrix
1 2 3
1 40 1 8
2 0 5 1
3 2 0 1
Oob error 20.69
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Outlier
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Variable Importance
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Visual Data

• Dostat

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Conclusions

• Random forests, support vector machines, and
  neural networks are some of the newest algorithms
  for understanding large datasets.
• There is still much more to be done.

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Thank you