Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Using Random Forests to explore a complex Metabolomic data set Susan Simmons Department of Mathematics and Statistics University of North Carolina Wilmington 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) Large data sets • Examples – Walmart • 20 million transactions daily – AT&T • 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 Dimensionality 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 Today’s talk • Focus on classification (supervised learning…use 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) 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 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 n<p problem Random Forests • Developed by Leo Breiman (Berkeley) and Adele Cutler (Utah State) • Can handle the n<p problem • Random forests are comparable in accuracy to support vector machines • Random forests are a combination of tree predictors Constructing a tree Observation 1 2 3 4 5 6 7 8 Gender F F M F F M F M Height (inches) 60 66 68 70 66 72 64 67 Tree for previous data set All observations N=8 Height < 66 Height > 66 N=4 N=4 Male Female Male Female N=0 N=4 N=3 N=1 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. Random Forest 2. The node is split using the best split among the selected variables. 3. 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” Example: Cereal Data N=70 (40 G, 30K) Calories <100 Calories <100 (2 G, 15 K) (38 G, 15 K) Fat <1 Fat >1 Carbo<12 Carbo>12 15 K 2G 15 K 38G 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 N=70 (40 G, 30K) Calories <100 Calories <100 (2 G, 15 K) (38 G, 15 K) Fat <1 Fat >1 Carbo<12 Carbo>12 15 K 2G 15 K 38G Observation withheld from creating this tree Calories Fat Carbo Mfr 98 2 10 K 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 The era of the “omics” sciences Just a few of the “omics” sciences • • • • • • • • Genomics Transcriptomics Proteomics Metabolomics Phenomics Toxicogenomics Phylomics Foldomics • • • • • Kinomics Interactomics Behavioromics Variomics Pharmacogenomics Functional Genomics Genomics Transciptomics Proteomics Metabolomics 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 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”) Confusion matrix 1 2 3 1 40 1 8 2 0 5 1 3 2 0 1 Oob error = 20.69% Outlier Variable Importance Visual Data • Dostat 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. Thank you