Frederick Eberhardt

Interventions and Causal Inference

The literature on causal discovery has focused on interventions that involve randomly assigning values to a single variable. But such a randomized intervention is not the only possibility, nor is it always optimal. In some cases it is impossible or it would be unethical to perform such an intervention. We provide an account of ‘hard’ and ‘soft’ interventions and discuss what they can contribute to causal discovery. We also describe how the choice of the optimal intervention(s) depends heavily on the particular experimental setup and the assumptions that can be made.

Actual causation: a stone soup essay

AbstractWe argue that current discussions of criteria for actual causation are ill-posed in several respects. (1) The methodology of current discussions is by induction from intuitions about an infinitesimal fraction of the possible examples and counterexamples; (2) cases with larger numbers of causes generate novel puzzles; (3) “neuron” and causal Bayes net diagrams are, as deployed in discussions of actual causation, almost always ambiguous; (4) actual causation is (intuitively) relative to an initial system state since state changes are relevant, but most current accounts ignore state changes through time; (5) more generally, there is no reason to think that philosophical judgements about these sorts of cases are normative; but (6) there is a dearth of relevant psychological research that bears on whether various philosophical accounts are descriptive. Our skepticism is not directed towards the possibility of a correct account of actual causation; rather, we argue that standard methods will not lead to such an account. A different approach is required. Once upon a time a hungry wanderer came into a village. He filled an iron cauldron with water, built a fire under it, and dropped a stone into the water. “I do like a tasty stone soup” he announced. Soon a villager added a cabbage to the pot, another added some salt and others added potatoes, onions, carrots, mushrooms, and so on, until there was a meal for all.

N-1 Experiments Suffice to Determine the Causal Relations Among N Variables

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 approaches in active learning methods of causal discovery, which currently use less informative measures.

Confirmation in the Cognitive Sciences: The Problematic Case of Bayesian Models

Bayesian models of human learning are becoming increasingly popular in cognitive science. We argue that their purported confirmation largely relies on a methodology that depends on premises that are inconsistent with the claim that people are Bayesian about learning and inference. Bayesian models in cognitive science derive their appeal from their normative claim that the modeled inference is in some sense rational. Standard accounts of the rationality of Bayesian inference imply predictions that an agent selects the option that maximizes the posterior expected utility. Experimental confirmation of the models, however, has been claimed because of groups of agents that “probability match” the posterior. Probability matching only constitutes support for the Bayesian claim if additional unobvious and untested (but testable) assumptions are invoked. The alternative strategy of weakening the underlying notion of rationality no longer distinguishes the Bayesian model uniquely. A new account of rationality—either for inference or for decision-making—is required to successfully confirm Bayesian models in cognitive science.

Compact Similarity Joins

Similarity joins have attracted significant interest, with applications in geographical information systems, astronomy, marketing analyzes, and anomaly detection. However, all the past algorithms, although highly fine-tuned, suffer an output explosion if the query range is even moderately large relative to the local data density. Under such circumstances, the response time and the search effort are both almost quadratic in the database size, which is often prohibitive. We solve this problem by providing two algorithms that find a compact representation of the similarity join result, while retaining all the information in the standard join. Our algorithms have the following characteristics: (a) they are at least as fast as the standard similarity join algorithm, and typically much faster, (b) they generate significantly smaller output, (c) they provably lose no information, (d) they scale well to large data sets, and (e) they can be applied to any of the standard tree data structures. Experiments on real and realistic point-sets show that our algorithms are up to several orders of magnitude faster.

A sufficient condition for pooling data

We consider the problems arising from using sequences of experiments to discover the causal structure among a set of variables, none of whom are known ahead of time to be an “outcome”. In particular, we present various approaches to resolve conflicts in the experimental results arising from sampling variability in the experiments. We provide a sufficient condition that allows for pooling of data from experiments with different joint distributions over the variables. Satisfaction of the condition allows for an independence test with greater sample size that may resolve some of the conflicts in the experimental results. The pooling condition has its own problems, but should—due to its generality—be informative to techniques for meta-analysis.

Introduction to the foundations of causal discovery

This article presents an overview of several known approaches to causal discovery. It is organized by relating the different fundamental assumptions that the methods depend on. The goal is to indicate that for a large variety of different settings the assumptions necessary and sufficient for causal discovery are now well understood.

Reliability via synthetic a priori: Reichenbach’s doctoral thesis on probability

Hans Reichenbach is well known for his limiting frequency view of probability, with his most thorough account given in The Theory of Probability in 1935/1949. Perhaps less known are Reichenbach’s early views on probability and its epistemology. In his doctoral thesis from 1915, Reichenbach espouses a Kantian view of probability, where the convergence limit of an empirical frequency distribution is guaranteed to exist thanks to the synthetic a priori principle of lawful distribution. Reichenbach claims to have given a purely objective account of probability, while integrating the concept into a more general philosophical and epistemological framework. A brief synopsis of Reichenbach’s thesis and a critical analysis of the problematic steps of his argument will show that the roots of many of his most influential insights on probability and causality can be found in this early work.

HANS REICHENBACH'S PROBABILITY LOGIC

Publisher Summary Reichenbach states that an inductive logic cannot be built up entirely from logical principles independent of experience, but must develop out of the reasoning practiced and useful to the natural sciences. Inductive inference system needs to be built on some solid to guide scientific methodology. This chapter describes Reichenbachs reasons for stating the inverse approach for inductive logic. Instead of “a priori” foundation of inductive logic, Reichenbachs approach to induction is largely axiomatic. Reichenbach distinguishes deductive and mathematical logic from inductive logic. The former deals with the relations among tautologies, whereas the latter deals with truth in the sense of truth in reality. Deductive and mathematical logic are built on an axiomatic system. In contrast to the formal relations that are of interest in deductive logic, inductive logic is concerned with the determination of whether various relations among quantities are true in the world.

Experimental Indistinguishability of Causal Structures

Using a variety of different results from the literature, I show how causal discovery with experiments is limited unless substantive assumptions about the underlying causal structure are made. These results undermine the view that experiments, such as randomized controlled trials, can independently provide a gold standard for causal discovery. Moreover, I present a concrete example in which causal underdetermination persists despite exhaustive experimentation and argue that such cases undermine the appeal of an interventionist account of causation as its dependence on other assumptions is not spelled out.