Clark Glymour

We study the identifiability and estimation of functional causal models under selection bias, with a focus on the situation where the selection depends solely on the effect variable, which is known as outcome-dependent selection. We address two questions of identifiability: the identifiability of the causal direction between two variables in the presence of selection bias, and, given the causal direction, the identifiability of the model with outcome-dependent selection. Regarding the first, we show that in the framework of post-nonlinear causal models, once outcome-dependent selection is properly modeled, the causal direction between two variables is generically identifiable; regarding the second, we identify some mild conditions under which an additive noise causal model with outcome-dependent selection is to a large extent identifiable. We also propose two methods for estimating an additive noise model from data that are generated with outcome-dependent selection.

This paper describes the application of eight statistical and machine-learning methods to derive computer models for predicting mortality of hospital patients with pneumonia from their findings at initial presentation. The eight models were each constructed based on 9847 patient cases and they were each evaluated on 4352 additional cases. The primary evaluation metric was the error in predicted survival as a function of the fraction of patients predicted to survive. This metric is useful in assessing a model’s potential to assist a clinician in deciding whether to treat a given patient in the hospital or at home. We examined the error rates of the models when predicting that a given fraction of patients will survive. We examined survival fractions between 0.1 and 0.6. Over this range, each model’s predictive error rate was within 1% of the error rate of every other model. When predicting that approximately 30°K of the patients will survive, all the models have an error rate of less than 1.5%. The models are distinguished more by the number of variables and parameters that they contain than by their error rates; these differences suggest which models may be the most amenable to future implementation as paper-based guidelines

DNA microarrays are perfectly suited for comparing gene expression in different populations of cells. An important application of microarray techniques is identifying genes which are activated by a particular drug of interest. This process will allow biologists to identify therapies targeted to particular diseases, and, eventually, to gain more knowledge about the biological processes in organisms. Such an application is described in this paper. It is focused on diabetes and obesity, which is a genetically heterogeneous disease, meaning that multiple defective genes are responsible for the diseases. The paper is divided in three parts, each dealing with a different problem addressed to our study. First we validate the data from our microarray experiment. We identified significant systematic sources of variability which are potentially issues for other microarray datasets. Second, we applied multiple hypothesis testing to identify differentially expressed genes. We found a set of genes which appear to change in expression level over time in response to a drug treatment. Third, we tried to address the problem of identification of co-expressed genes using cluster analysis. This last problem is still under discussion

The ability to identify the mineral composition of rocks and softs is an important tool for the exploration of geological sites. For instance, NASA intends to design robots that are sufficiently autonomous to perform this task on planetary missions. Spectrometer readings provide one important source of data for identifying sites with minerals of interest. Reflectance spectrometers measure intensities of light reflected from surfaces over a range of wavelengths. Spectral intensity patterns may in some cases be sufficiently distinctive for proper identification of minerals or classes of minerals. For some mineral classes, carbonates for example, specific short spectral intervals are known to carry a distinctive signature. Finding similar distinctive spectral ranges for other mineral classes is not an easy problem. We propose and evaluate data-driven techniques that automatically search for spectral ranges optimized for specific minerals. In one set of studies, we partition the whole interval of wavelengths available in our data into sub-intervals, or bins, and use a genetic algorithm to evaluate a candidate selection of subintervals. As alternatives to this computationally expensive search technique, we present an entropy-based heuristic that gives higher scores for wavelengths more likely to distinguish between classes, as well as other greedy search procedures. Results are presented for four different classes, showing reasonable improvements in identifying some, but not all, of the mineral classes tested.

Data analysis that merely fits an empirical covariance matrix or that finds the best least squares linear estimator of a variable is not of itself a reliable guide to judgements about policy, which inevitably involve causal conclusions. The policy implications of empirical data can be completely reversed by alternative hypotheses about the causal relations of variables, and the estimates of a particular causal influence can be radically altered by changes in the assumptions made about other dependencies.2 For these reasons, one of the common aims of empirical research in the..

Researchers routinely face the problem of inferring causal relationships from large amounts of data, sometimes involving hundreds of variables. Often, it is the causal relationships between "latent" (unmeasured) variables that are of primary interest. The problem is how causal relationships between unmeasured variables can be inferred from measured data. For example, naval manpower researchers have been asked to infer the causal relations among psychological traits such as job satisfaction and job challenge from a data base in which neither trait is measured directly, but in which answers to interview questions are plausibly associated with each trait. By combining background knowledge with an algorithm that searches for causal structure among the unobserved variables, we have created a tool that can reliably extract useful causal information about latent variables from large data bases. In what follows we describe the class of causal models to which our..

For most of the contributions to this volume, the project is this: Fill out “Event X is a cause of event Y if and only if……” where the dots on the right are to be filled in by a claims formulated in terms using any of (1) descriptions of possible worlds and their relations; (2) a special predicate, “is a law;” (3) “chances;” and (4) anything else one thinks one needs. The form of analysis is roughly the same as that sought in the Meno, and the methodology is likewise Socratic—proposals, examples, counterexamples, more proposals. The norms of the enterprise seem to be as follows (i) a proposal is defeated if someone can imagine a circumstance in which it would be false, or perhaps if one can imagine such a circumstance that is not obviously inconsistent with physical laws; (ii) approximately correct solutions, those which cover most but not all cases, are of no value unless they can be modified to cover all cases; (iii) no account is required of how the relations in the right hand side of a proposed analysis could be known or reliably..

It is “well known” that in linear models: (1) testable constraints on the marginal distribution of observed variables distinguish certain cases in which an unobserved cause jointly influences several observed variables; (2) the technique of “instrumental variables” sometimes permits an estimation of the influence of one variable on another even when the association between the variables may be confounded by unobserved common causes; (3) the association (or conditional probability distribution of one variable given another) of two variables connected by a path or pair of paths with a single common vertex (a trek) can be computed directly from the parameter values associated with each edge in the trek; (4) the association of two variables produced by multiple treks can be computed from the parameters associated with each trek; and (5) the independence of two variables conditional on a third implies the corresponding independence of the sums of the variables over all units conditional on the sums over all units of each of the original conditioning variables.

nature of modern data collection and storage techniques, and the increases in the speed and storage capacities of computers. Statistics books from 30 years ago often presented examples with fewer than 10 variables, in domains where some background knowledge was plausible. In contrast, in new domains, such as climate research where satellite data now provide daily quantities of data unthinkable a few decades ago, fMRI brain imaging, and microarray measurements of gene expression, the number of variables can range into the tens of thousands, and there is often limited background knowledge to reduce the space of alternative causal hypotheses. In such domains, non-automated causal discovery techniques appear to be hopeless, while the availability of faster computers with larger memories and disc space allow for the practical implementation of computationally intensive automated search algorithms over large search spaces. Contemporary science is not your grandfather’s science, or Karl Popper’s. Causal inference without experimental controls has long seemed as if it must somehow be capable of being cast as a kind of statistical inference involving estimators with some kind of convergence and accuracy properties under some kind of assumptions. Until recently, the statistical literature said not. While parameter estimation and experimental design for the effective use of data developed throughout the 20th century, as recently as 20 years ago the methodology of causal inference without experimental controls remained relatively primitive. Besides a cessation of hostilities from the majority of the statistical and philosophical communities (which has still only partially happened), several things were needed for theories of causal estimation to appear and to flower: well defined mathematical objects to represent causal relations; well defined connections between aspects of these objects and sample data; and a way to compute those connections. A sequence of studies beginning with Dempster’s work on the factorization of probability distributions [Dempster 1972] and culminating with Kiiveri and Speed’s [Kiiveri & Speed 1982] study of linear structural equation models, provided the first, in the form of directed acyclic graphs, and the second, in the form of the “local” Markov condition..

It has been shown in Spirtes(1995) that X and Y are d-separated given Z in a directed graph associated with a recursive or non-recursive linear model without correlated errors if and only if the model entails that ρXY.Z = 0. This result cannot be directly applied to a linear model with correlated errors, however, because the standard graphical representation of a linear model with correlated errors is not a directed graph. The main result of this paper is to show how to associate a directed graph with a linear model L with correlated errors, and then use d-separation in the associated directed graph to determine whether L entails that a particular partial correlation is zero.

Various algorithms have been proposed for learning (partial) genetic regulatory networks through systematic measurements of differential expression in wild type versus strains in which expression of specific genes has been suppressed or enhanced, as well as for determining the most informative next experiment in a sequence. While the behavior of these algorithms has been investigated for toy examples, the full computational complexity of the problem has not received sufficient attention. We show that finding the true regulatory network requires (in the worst-case) exponentially many experiments (in the number of genes). Perhaps more importantly, we provide an algorithm for determining the set of regulatory networks consistent with the observed data. We then show that this algorithm is infeasible for realistic data (specifically, nine genes and ten experiments). This infeasibility is not due to an algorithmic flaw, but rather to the fact that there are far too many networks consistent with the data (10 18 in the provided example). We conclude that gene perturbation experiments are useful in confirming regulatory network models discovered by other techniques, but not a feasible search strategy.

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.