Clark Glymour

Data mining is on the interface of Computer Science and Statistics, utilizing advances in both disciplines to make progress in extracting information from large databases. It is an emerging field that has attracted much attention in a very short period of time. This article highlights some statistical themes and lessons that are directly relevant to data mining and attempts to identify opportunities where close cooperation between the statistical and computational communities might reasonably provide synergy for further progress in data analysis.

We outline a cognitive and computational account of causal learning in children. We propose that children employ specialized cognitive systems that allow them to recover an accurate “causal map” of the world: an abstract, coherent representation of the causal relations among events. This kind of knowledge can be perspicuously represented by the formalism of directed graphical causal models, or “Bayes nets”. Human causal learning and inference may involve computations similar to those for learnig causal Bayes nets and for predicting with them. Preliminary experimental results suggest that 2- to 4-year-old children spontaneously construct new causal maps and that their learning is consistent with the Bayes-Net formalism.

Magnani, Lorenzo (2001), Abduction, Reason, and Science: Processes of Discovery and Explanation. New York: Kluwer Academic/ Plenum Publishers. Magnani. Lorenzo, and Nancy Nersessian (eds.) (2002), Model-Based Reasoning: Technology, Science, Values. New York: Kluwer Academic/ Plenum Publishers. Joseph E. Earley, Sr. (ed.), Chemical Explanation: Characteristics, Development, Autonomy, Annals of the New York Academy of Sciences, vol. 988. New York Academy of Sciences (2003), 370 pp., $130.00 (cloth).

A general principle for good pedagogic strategy is this: other things equal, make the essential principles of the subject explicit rather than tacit. We think that this principle is routinely violated in conventional instruction in statistics. Even though most of the early history of probability theory has been driven by causal considerations, the terms “cause” and “causation” have practically disappeared from statistics textbooks. Statistics curricula guide students away from the concept of causality, into remembering perhaps the cliche disclaimer “correlation does not mean causation,” but rarely thinking about what correlation does mean. The treatment of causality is a serious handicap to later studies of such topics as experimental design, where often the main goal is to establish (or disprove) causation. Much of the technical vocabulary of the language used in research design textbooks consists in euphemisms for specific causal relations, e.g, “latent variable,” “intervening variable,” “confounding factor,” etc. The multiplicity of terms used to refer to causation results in confusion and, in effect, may hinder understanding of the basic principles of research design.

Reflectance spectroscopy is a standard tool for studying the mineral composition of rock and soil samples and for remote sensing of terrestrial and extraterrestrial surfaces. We describe research on automated methods of mineral identification from reflectance spectra and give evidence that a simple algorithm, adapted from a well-known search procedure for Bayes nets, identifies the most frequently occurring classes of carbonates with reliability equal to or greater than that of human experts. We compare the reliability of the procedure to the reliability of several other automated methods adapted to the same purpose. Evidence is given that the procedure can be applied to some other mineral classes as well. Since the procedure is fast with low memory requirements, it is suitable for on-board scientific analysis by orbiters or surface rovers.

Simon Kochen and Ernst Specker's well-known argument against hidden variable theories for quantum mechanics is also an argument against the possibility of quantum systems having, simultaneously, precise values for all of the dynamical quantities associated with such systems. Devices for defeating the argument were in the literature even before its publication, but recently Arthur Fine has raised a new difficulty. Fine points out that Kochen and Specker's argument requires the following principles:Sum Rule: At all times, in all states, the value of the quantity with operator A + B is the sum of the values of the quantity with operator A and the quantity with operator B, provided A, B commute.Product Rule: At all times, in all states, the value of the quantity with operator AB is the product of the values of the quantities with operators A and B, provided A, B commute.

“It ain't nuthin' until I call it.”Bill Guthrie, UmpireNumerous criticisms of Adolf Grünbaum's account of conventions in physics have been published, and he has replied to most of them. Nonetheless, there seem to me to be good reasons for offering further criticism. In the first place Grünbaum's philosophy seems to me at least partly an extrapolation of one aspect of the views on conventions developed by Reichenbach and others. Since I think many of the issues which Reichenbach attempted to settle in his various discussions of conventions in physics are genuine and important, and I also think that those aspects of his views on which Grünbaum has focused are among the least satisfactory, it seems important to suggest questions and answers about conventions in physics which may develop more satisfactory Reichenbachian themes. Secondly, Grünbaum's philosophy centers on a distinction, that between extrinsic and intrinsic properties and relations, which has never been made satisfactorily clear either by Grünbaum or by his critics. Until it is clarified we will remain unsure of just what he is claiming and why we should think it true or think it false. Finally, Grünbaum's replies to his critics, especially his most recent reply, [9], involve unusually important claims which fail to be buttressed by the arguments he gives. I have in mind such claims as that we can learn something important about the ontological status of properties and relations by examining descriptions of them, that on the most straightforward and literal interpretation, the general theory of relativity is inconsistent, and that the foremost advocates of geometrodynamics, Clifford and Wheeler, were and are enmeshed in contradiction. My own view is that all of these claims are dubious or false, but I shall be less concerned with establishing their falsity than with discrediting the arguments offered for them.

The use of ceteris paribus clauses in philosophy and in the sciences has a long and fascinating history. Persky (1990) traces the use by economists of ceteris paribus clauses in qualifying generalizations as far back as William Petty’s Treatise of Taxes and Contributions (1662). John Cairnes’ The Character and Logical Method of Political Economy (1857) is credited with enunciating the idea that the conclusions of economic investigations hold “only in the absence of disturbing causes”.1 His Leading Principles (1874) contains the classic example of a ceteris paribus law: “The rate of wage, other things being equal, varies inversely with the supply of labour”. Carines’ ideas were popularized by Alfred Marshall in his Principles of Economics (1890) where he argued for a methodology that involved holding disturbing causes “in a pound called Caeteris Paribus”. It is unclear when the notion of ceteris paribus laws made its appearance in the philosophical literature; but in the nineteenth century it is to be found in Mill’s System of Logic (1843), and in the twentieth century it gained prominence in the Hempel-inspired debates of the 1950’s over the role of general laws in historical explanations, albeit under other labels such as quasi-laws (Rescher) or grounded generalizations (Scriven).

Through their transcript products genes regulate the rates at which an immense variety of transcripts and subsequent proteins occur. Understanding the mechanisms that determine which genes are expressed, and when they are expressed, is one of the keys to genetic manipulation for many purposes, including the development of new treatments for disease. Viewing each gene in a genome as a distinct variable that is either on or off, or more realistically as a continuous variable, the values of some of these variables influence the values of others through the regulatory proteins they express, including, of course, the possibility that the rate of expression of a gene at one time may, in various circumstances, influence the rate of expression of that same gene at a later time. If we imagine an arrow drawn from each gene expression variable at a given time to a gene variable whose expression it influences a short while after, the result is a network, technically a directed acyclic graph. For example, the DAG in Figure 1 is a representation of a system in which the expression level of gene G1 at time 1 ) causes the expression level of G2, which in turn causes the expression level of G3. The arrows in Figure 1 which do not have a variable at their tails are “error terms” which represent all of the causes of a variable other than the ones explicitly represented in the DAG. The DAG describes more than associations—it describes causal connections among gene expression rates. A shock to a cell—by mutation, heating, chemical treatment, etc. may alter the DAG describing the relations among gene expressions, for example by activating a gene that was otherwise not expressed, producing a cascade of new expression effects. Although “knockout” experiments can reveal some of the underlying causal network of gene expression levels, unless guided by information from other sources, such experiments are limited in how much of the network structure they can reveal, due to the sheer number of possible combinations of experimental manipulations of genes necessary to reveal the complete causal network. Recent developments have made it possible to compare quantitatively the expression of tens of thousands of genes in cells from different sources in a single experiment, and to trace gene expression over time in thousands of genes simultaneously. cDNA microarrays are already producing extensive data, much of it available on the web. Thus there are calls for analytic software that can be applied to microarray and other data to help infer regulatory networks. In this paper we will review current techniques that are available for searching for the causal relations between variables, describe algorithmic and data gathering obstacles to applying these techniques to gene expression levels, and describe the prospects for overcoming these obstacles

The notion of reduction in the natural sciences has been assimilated to the notion of inter-theoretical explanation. Many philosophers of science (following Nagel) have held that the apparently ontological issues involved in reduction should be replaced by analyses of the syntactic and semantic connections involved in explaining one theory on the basis of another. The replacement does not seem to have been especially successful, for we still lack a plausible account of inter-theoretical explanation. I attempt to provide one

Words, Thoughts and Theories argues that infants and children discover the physical and psychological features of the world by a process akin to scientific inquiry, more or less as conceived by philosophers of science in the 1960s (the theory theory). This essay discusses some of the philosophical background to an alternative, more popular, “modular” or “maturational” account of development, dismisses an array of philosophical objections to the theory theory, suggests that the theory theory offers an undeveloped project for artificial intelligence, and, relying on recent psychological work on causation, offers suggestions about how principles of causal inference may provide a developmental solution to the “frame problem”.