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Predicting Genetic Regulatory Response Using Classification Us v. Them (“Them” being Manuel Middendorf, Anshul Kundaje, Chris Wiggins, Yoav Freund, and Christina Leslie, in “Predicting Genetic Regulatory Response Using Classification” (2004) The Problem • Current studies of gene transcription tend to be descriptive • Need for a predictive system – the ability to predict gene regulation for new experiments • Rather than determining patterns in sets of genes and conditions, look at underyling causes of those patterns The Important Parts of Genes & Experiments • Regulation is determined by binding sites (motifs) and regulators (parents) • The significance of experiments, then, is how they affect regulators • The significance of genes is what motifs they contain Binding Sites and Regulation • Discretize gene response into only up-regulated (1), down-regulated(-1), or unchanged (0) • A motif is either present (1) or absent (0) • A parent is either up-regulated (1), downregulated (-1), or unchanged (0) • Assume (and we need to check with someone who actually knows something about biology on this) that things only happen if motif is present and parent is either up- or down-regulated What our matrix really looks like • • • • • • g = # of genes e = # of experiments p = # of parents m = # of motifs Then we have g*e response values For each response, we have p*m parent/motif combinations • For each parent/motif combination, there are three possibilities – present and up-regulated, present and down-regulated, or all those other possibilities where nothing happens • Represent these possibilities as a pair of binary variables, one for up and one for down M1, P1 + M1, P1 - M1, P2 + M1, P2 - … M1, Pp + … Mm, Pp - G1, E1 M1, P1 + M1, P1 - M1, P2 + M1, P2 - … M1, Pp + … Mm, Pp - G1, E2 M1, P1 + M1, P1 - M1, P2 + M1, P2 - … M1, Pp + … Mm, Pp - … M1, P1 + M1, P1 - M1, P2 + M1, P2 - … M1, Pp + … Mm, Pp - G1, Ee M1, P1 + M1, P1 - M1, P2 + M1, P2 - … M1, Pp + … Mm, Pp - … M1, P1 + M1, P1 - M1, P2 + M1, P2 - … M1, Pp + … Mm, Pp - Gg, Ee Some Numbers • In the paper, the initial dataset had 6110 genes and 173 experiments • 354 motifs are considered • 475 regulators are considered • Set of genes to consider is reduced to only 1411 genes of interest Some More Numbers • Only train on genes that are up- or downregulated • Approx. 8% of gene/experiment pairs from the overall sample appear to be, so, assuming this holds true in the reduced sample, we have 19,632 gene / experiment pairs to train on • For each of these values we have 2*354*475 = 336,300 predictor variables Some Problems • 19,632 by 336,300 is an awfully large matrix to want to do any calculations with • We have far more variables than observations Possible Solutions • Random Projection: – Pro: we can reduce our dimensionality – Con: it seems like a somewhat silly approach – Con: there’ll still be a lot of calculations just to make the projection Possible Solutions • Variable Selection or PCA – Pro: we could reduce our dimensionality in a more informed way – Con: computationally painful Possible Solutions • Random Forest • From Breiman and Cutler: • Grow a number of classification trees, and take the vote of the classifications of all trees • For each tree, if we have n cases, sample, with replacement, n cases, using some number of randomly chosen variables much smaller than the full number of variables – Pro: allows for flexibility in reduction of dimensions being considered – Pro: dimension is reduced without computation problems – Con: ? Their Solution • Alternating decision tree: • A tree with alternating levels of prediction nodes and splitter nodes • Combines a set of weak prediction rules (the splitter nodes) to make one strong rule Alternating Decision Trees v. Random Forests • Both the same rough concept – take a vote from many weak rules to get a strong rule • In ADTs, rules are based on single variables, and may be conditioned on values of other variables • In random forests, rules can be based on multiple variables, and are only marginal over all values of other variables • ADTs are fairly straightforward to read and interpret Alternating Decision Trees • Pro: computationally kind • Pro: works better than Random Forests (Creamer & Freund, 2004) • Con: we didn’t come up with it Other Ideas?