https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5226236/#R71
In the 65 years since its formal specification, information theory has become an established statistical paradigm, providing powerful tools for quantifying probabilistic relationships. Behavior analysis has begun to adopt these tools as a novel means of measuring the interrelations between behavior, stimuli, and contingent outcomes. This approach holds great promise for making more precise determinations about the causes of behavior and the forms in which conditioning may be encoded by organisms. In addition to providing an introduction to the basics of information theory, we review some of the ways that information theory has informed the studies of Pavlovian conditioning, operant conditioning, and behavioral neuroscience. In addition to enriching each of these empirical domains, information theory has the potential to act as a common statistical framework by which results from different domains may be integrated, compared, and ultimately unified.
Keywords: information theory, entropy, probability, behavior analysis
The brain's business is computation, and the task it faces is monumental. It must take sensory inputs from the external world, translate this information into a computationally accessible form, and then use the results to make decisions about which course of action is appropriate given the most probable state of the world. It must then communicate this state of affairs to appropriate efferent channels so that the selected action can take place.
Even this description is a gross oversimplification. At any given moment, the brain continuously processes imperfect signals from a noisy world and initiates and channels activity given the available information, doing so in a distributed fashion. Our knowledge of this computation is incomplete. We know details about the transduction of sensory stimulation as well as some aspects of how that signal is transformed as it travels through various stages of processing. How then, does the brain use seemingly binary all-or-nothing action potentials, or “spikes,” to manage the information needed for the extremely complicated computations it must carry out? Moreover, how can this information be extracted and these computations be made “on the fly,” as they so often must be? Because it is impossible a priori to exactly represent all of the possible states of the real world (or to even know what states need to be represented), and even harder to accurately extrapolate the future, the brain must rely on an imperfect, plausible-seeming approximation of the world given the available evidence and prior assumptions.
One of the central challenges in behavioral neuroscience is to frame general statements like those above in adequately specific terms. What is meant by “an imperfect approximation of the world?” How does one quantify “available evidence?” Without operationalizing these concepts, a quantitative approach to the neurobiological analysis of behavior is impossible. In this regard, we believe that behavior analysis has much to contribute to creating a successful neuroscience (Ward, Simpson, Kandel, & Balsam, 2011). In particular, the precise specification of behavioral processes is necessary for a successful mapping between neurobiology and behavior. In this review, we suggest that an information-theoretic approach benefits behavioral analysis greatly, as well as providing the foundation for a deeper understanding of the neural mechanisms of behavior.
In practice, behavior analysts (and psychologists in general) have developed frameworks specific to domains of interest. For example, there have been few attempts to unite the approaches used in the study of Pavlovian and operant conditioning into a common paradigm. The analyses of operant choice and stimulus control not only emphasize different parameters of behavior but also employ different technical language; the relation between the two is thus uncertain. While this by no means invalidates the analyses, it has complicated attempts to relate and unify different branches of the literature. Historically, such reconciliation was attempted in rhetorical terms by attempting to translate one form of conditioning into the other (e.g. Colwill, 1994; Smith, 1954), or to translate both paradigms into a hybrid framework (e.g. Guilhardi, Keen, MacInnis, & Church, 2005; Maia, 2010). Throughout, these projects have sought to evaluate observable events (i.e. “evidence”) and relate these to behavior. The need for common terminology is readily apparent in these projects, which devote considerable space to translating between technical terminologies.
We propose that information theory has the potential to both integrate and unify a broad range of phenomena into a single framework, while also facilitating specific hypothesis testing in all areas of behavior analysis. As a branch of mathematics arising from probability theory, information theory already underlies statistical inference taken for granted throughout psychology. It can readily be applied to behavior analysis, as was observed almost from its inception (Miller, 1953), and it has achieved considerable traction in neurobiology (Rieke, Warland, de Ruyter van Steveninck, & Bialek, 1997). Furthermore, because its most fundamental operations involve the objective definition and measurement of information itself, it provides behavior analysts with metrics for assessing not only how information is processed in the brain, but also how much information is objectively available in the environment.
Before we outline some of the benefits of information theory, we first address two common misunderstandings.
Behavior analysts routinely take strident positions against so-called “cognitive” or “mentalistic” theories of behavior. This backlash was originally driven by the intractable subjectivity of “experimental introspection” in the 1910s and ‘20s (Leahey, 1992), and was rekindled by the vague metaphors of the cognitive revolution (Skinner, 1985). Fundamentally, this is a rejection of speculation about internal, unseen causes of behavior, in favor of measuring environmental and contextual features that control behavior. Mentalistic theories are also accused of relying on intervening variables, many of which are psychological constructs with no known physical realization in the brain.
Thus, at first glance, information-theoretic approaches might seem inconsistent with behavior analysis. However, there are two ways in which we think information-theoretic accounts have much to add to the understanding of behavioral processes. The first relates to their description of environmental contingencies. “Information” is not, in this framework, a rhetorical metaphor that changes form to suit the author, but is instead a technical term involved in measures of probabilistic relationships. It is in this very precise sense that a CS conveys information about a US or that a reinforcer conveys information about the response that precedes it.
The second benefit offered by information theory is the way in which it allows one to analyze the neurobiological bases of behavior. Skinner (1985) accused cognitive theories of being “premature neurology,” but information metrics instead provide formally rigorous characterizations of observed brain activity. Invoking a “computation” in information-theoretic terms refers not to conscious manipulation of symbols, but instead to distributed processing carried out by networks of neurons. Thus, any and all computations we refer to are made at the neuronal level. If a computational operation like averaging is performed, no mentalistic homunculus is implied. This fundamental difference puts information theory accounts on solid biological footing already appreciated by anatomists and physiologists (Quiroga & Panzeri, 2009).
Another approach that behavior analysts routinely oppose is that of “optimality theories.” The common feature of optimality theories is to assert what an organism should do, as opposed to characterizing how organisms actually behave. A wide range of disciplines favor the “normative” approach, most notably classical economics (Herrnstein, 1990), but normative theories have also recently seen flashes of popularity among psychologists, behavioral ecologists, and evolutionary theorists (Staddon, 2007). A common criticism of information theory is to assert that it requires that organisms respond in an optimal fashion (e.g. Miller, 2012).