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Design of Experiments Questions Network Inference Working Group October 8, 2008

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Questions: Model Classification How do we classify models? –Linear –Dynamic Bayesian networks –Log transformed –Differential equations –Polynomial dynamical systems –Hybrid: discrete-continuous (for example, Glass networks) What kinds of restrictions do we put on a model space in order to identify models from a given data set? Distinguish between correlation and causation (direct vs. indirect; with and without strengths).

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Questions: Model Identification What kinds of data sets identify a fixed model class? –Linear, i.e. sums of variables –Products of variables, perhaps over a fixed field, such as ZZ/2 –How many random data points (perhaps independent samples) will identify a monomial dynamical system with fixed degree? –How many correlated data points (i.e., time course) will identify…? What kinds of models are identifiable by a fixed class of data set? –Orthogonal arrays –Factorial designs –Symmetric designs What kinds of data identify a given nested canalyzing function?

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Questions: Model Validation How do we test the effect of a variable/term (sum of terms) on a function? –Sensitivity analysis (e.g., for computer programs) –Information-theoretic measures ANOVA (or some other measure of variance) for discrete data? –Discrete noise? –Look to coding theory literature

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8.1 ADDING AND SUBTRACTING POLYNOMIALS To classify, add, and subtract polynomials.

8.1 ADDING AND SUBTRACTING POLYNOMIALS To classify, add, and subtract polynomials.

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