Clark Glymour

Recent literature in philosophy of science has addressed purported notions of explanatory virtues—‘explanatory power’, ‘unification’, and ‘coherence’. In each case, a probabilistic relation between a theory and data is said to measure the power of an explanation, or degree of unification, or degree of coherence. This essay argues that the measures do not capture cases that are paradigms of scientific explanation, that the available psychological evidence indicates that the measures do not capture judgements of explanatory power, and, finally, that the measures do not provide useful methods for selecting hypotheses. 1. Introduction2. Some Proposed Measures of Explanatory Virtues3. Descriptive Inadequacy3.1 Excellent but false explanations3.2 Causal explanation4. Psychological Inadequacy5. Finding the Truth6. Conclusion

Of the many proposals for inferring genetic regulatory structure from microarray measurements of mRNA transcript hybridization, several aim to estimate regulatory structure from the associations of gene expression levels measured in repeated samples. The repeated samples may be from a single experimental condition, or from several distinct experimental conditions; they may be “equilibrium” measurements or time series; the associations may be estimated by correlation coefficients or by conditional frequencies (for discretized measurements) or by some other statistic. This paper describes two elementary statistical difficulties for all such procedures, no matter whether based on Bayesian updating, conditional independence testing, or other machine learning procedures such as simulated annealing or neural net pruning. One difficulty obtains if large numbers of cells are aggregated in a measurement of expression levels from a common population of cells; the other obtains if small numbers of cells are aggregated or if samples are separately aggregated over different populations of cells.

After reviewing theoretical reasons for doubting that machine learning methods can accurately infer gene regulatory networks from microarray data, we test 10 algorithms on simulated data from the sea urchin network, and on microarray data for yeast compared with recent experimental determinations of the regulatory network in the same yeast species. Our results agree with the theoretical arguments: most algorithms are at chance for determining the existence of a regulatory connection between gene pairs, and the algorithms that perform better than chance are nonetheless so errorprone as to be of little practical use in these applications.

By combining experimental interventions with search procedures for graphical causal models we show that under familiar assumptions, with perfect data, N - 1 experiments suffice to determine the causal relations among N > 2 variables when each experiment randomizes at most one variable. We show the same bound holds for adaptive learners, but does not hold for N > 4 when each experiment can simultaneously randomize more than one variable. This bound provides a type of ideal for the measure of success of heuristic approached in active learning methods of casual discovery, which currently use less informative measures