If we assume that components of human cognitive processing approximately follow the principles of probability theory, we can computationally reason backwards from observed human behavioral data to the engagement of particular cognitive functions as an inverse problem. In this way, the computational framework for probabilistic inference provides a general approach to understanding the deeper cognitive processing that is not directly observable to us based on sparse, noisy and ambiguous behavioral data.
To understand the computational basis of the knowledge-based diagnosis processes, there are several principles that must be addressed.
Persons may have different prior experience of what the world would be. This leads to their use of unique prior knowledge to guide a learning process. Bayesian methods of the probability theory allow us to incorporate various forms of prior knowledge into learning, inference and decision-making in a principled manner. The basic notion called ``prior'' can be formulated as the probabilistic representation of human abstract knowledge regarding how they expect the world to be.
To uncover what are the forms and contents of persons' knowledge of the world and make comparison between them, there are two schools of approaches available. One typically represents the knowledge relevancy with simple probabilistic models based on numbers or parametric probability distributions without considering more structural representation. The other approaches the problem with structured logical and symbolic knowledge representation. The tools they normally use are graphs, grammars and system of logic. We realize that the integration of the two is absolutely essential to our particular study on perception-based diagnostic-reasoning. To combine these two knowledge representation strategies, we need to use structures and symbols as a way of representing the structure of human knowledge and then define probabilistic models over those structure representations. As Glenn Shafer and Judea Pearl pointed out, probability is not really about numbers, it is about the structure of reasoning. Graphical models as a general class of probabilistic models are used to define probabilities over structured knowledge representations. This modeling technique allows us to model not only how systems of knowledge can be applied to guide perceptual processing but also how they can be learned by various kinds of statistical inferences. The key characters of diagnostic reasoning processes can be depicted using several properties of the probabilistic graphical models:
- Levels of abstraction: Hierarchical probabilistic models allow us to use multiple levels of abstraction to represent human cognitive processing. We assume there are multiple levels of representation which are all linked by probability distribution, for example physicians' prior at the lowest level (a set of specific diagnostic cues) itself is generated by a distribution over distribution, some sort of prior on priors. And by doing this inference on multiple levels models, we can understand how physicians acquire the conceptual knowledge of the world as well as how they use it to guide their perceptual reasoning process.
- Infinity of learning: medical training is not just accumulation of more and more bits of knowledge, but qualitatively transformation as real cognitive growth. This requires us to have ways of building probabilistic models which in some sense are not constrained by initial structure but where the structure itself can do qualitative transformation as data come in and may grow in qualitative ways. We propose to use non-parametric probabilistic graphical models whose structures can keep evolving as more data are observed via assimilation-accommodation mechanism.
- Dynamics of learning: If the diagnostic-reasoning process can be characterized as dynamic systems, we can reinterpret these dynamic systems as stochastic processes that can be represented as non-parametric probabilistic graphical models.
According to these analysis, we review the statistical theories and methodologies upon which our contributions are based.