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Concept learning, also known as category learning, concept attainment, and concept formation, is largely based on the works of the cognitive psychologist Jerome Bruner. Bruner, Goodnow, & Austin (1967) defined concept attainment (or concept learning) as "the search for and listing of attributes that can be used to distinguish exemplars from non exemplars of various categories". More simply put, concepts are the mental categories that help us classify objects, events, or ideas, building on the understanding that each object, event, or idea has a set of common relevant features. Thus, concept learning is a strategy which requires a learner to compare and contrast groups or categories that contain concept-relevant features with groups or categories that do not contain concept-relevant features.
Concept learning also refers to a learning task in which a human or machine learner is trained to classify objects by being shown a set of example objects along with their class labels. The learner simplifies what has been observed by condensing it in the form of an example. This simplified version of what has been learned is then applied to future examples. Concept learning may be simple or complex because learning takes place over many areas. When a concept is difficult, it is less likely that the learner will be able to simplify, and therefore will be less likely to learn. Colloquially, the task is known as learning from examples. Most theories of concept learning are based on the storage of exemplars and avoid summarization or overt abstraction of any kind.
- Concept Learning: Inferring a Boolean-valued function from training examples of its input and output.
- A concept is an idea of something formed by combining all its features or attributes which construct the given concept. Every concept has two components:
- Attributes: features that one must look for to decide whether a data instance is a positive one of the concept.
- A rule: denotes what conjunction of constraints on the attributes will qualify as a positive instance of the concept.
Types of concepts
Concept learning must be distinguished from learning by reciting something from memory (recall) or discriminating between two things that differ (discrimination). However, these issues are closely related, since memory recall of facts could be considered a "trivial" conceptual process where prior exemplars representing the concept are invariant. Similarly, while discrimination is not the same as initial concept learning, discrimination processes are involved in refining concepts by means of the repeated presentation of exemplars.
Concrete or Perceptual Concepts vs Abstract Concepts
Defined (or Relational) and Associated Concepts
Complex Concepts. Constructs such as a schema and a script are examples of complex concepts. A schema is an organization of smaller concepts (or features) and is revised by situational information to assist in comprehension. A script on the other hand is a list of actions that a person follows in order to complete a desired goal. An example of a script would be the process of buying a CD. There are several actions that must occur before the actual act of purchasing the CD and a script provides a sequence of the necessary actions and proper order of these actions in order to be successful in purchasing the CD.
Methods of learning a concept
Discovery – Every baby discovers concepts for itself, such as discovering that each of its fingers can be individually controlled or that care givers are individuals. Although this is perception driven, formation of the concept is more than memorizing perceptions.
Examples – Supervised or unsupervised generalizing from examples may lead to learning a new concept, but concept formation is more than generalizing from examples.
Words – Hearing or reading new words leads to learning new concepts, but forming a new concept is more than learning a dictionary definition. A person may have previously formed a new concept before encountering the word or phrase for it.
Exemplars comparison and contrast – An efficient way to learn new categories and to induce new categorization rules is by comparing a few example objects while being informed about their categorical relation. Comparing two exemplars while being informed that the two are from the same category allows identifying the attributes shared by the category members, as it exemplifies variability within this category. On the other hand, contrasting two exemplars while being informed that the two are from different categories may allow identifying attributes with diagnostic value. Within category comparison and between categories contrast are not similarly useful for category learning (Hammer et al., 2008), and the capacity to use these two forms of comparison-based learning changes at childhood (Hammer et al., 2009).
Invention – When prehistoric people who lacked tools used their fingernails to scrape food from killed animals or smashed melons, they noticed that a broken stone sometimes had a sharp edge like a fingernail and was therefore suitable for scraping food. Inventing a stone tool to avoid broken fingernails was a new concept.
In general, the theoretical issues underlying concept learning are those underlying induction. These issues are addressed in many diverse publications, including literature on subjects like Version Spaces, Statistical Learning Theory, PAC Learning, Information Theory, and Algorithmic Information Theory. Some of the broad theoretical ideas are also discussed by Watanabe (1969,1985), Solomonoff (1964a,1964b), and Rendell (1986); see the reference list below.
Modern psychological theories
It is difficult to make any general statements about human (or animal) concept learning without already assuming a particular psychological theory of concept learning. Although the classical views of concepts and concept learning in philosophy speak of a process of abstraction, data compression, simplification, and summarization, currently popular psychological theories of concept learning diverge on all these basic points. The history of psychology has seen the rise and fall of many theories about concept learning. Classical conditioning (as defined by Pavlov) created the earliest experimental technique. Reinforcement learning as described by Watson and elaborated by Clark Hull created a lasting paradigm in behavioral psychology. Cognitive psychology emphasized a computer and information flow metaphor for concept formation. Neural network models of concept formation and the structure of knowledge have opened powerful hierarchical models of knowledge organization such as George Miller's Wordnet. Neural networks are based on computational models of learning using factor analysis or convolution. Neural networks also are open to neuroscience and psychophysiological models of learning following Karl Lashley and Donald Hebb.
Rule-based theories of concept learning began with cognitive psychology and early computer models of learning that might be implemented in a high level computer language with computational statements such as if:then production rules. They take classification data and a rule-based theory as input which are the result of a rule-based learner with the hopes of producing a more accurate model of the data (Hekenaho 1997). The majority of rule-based models that have been developed are heuristic, meaning that rational analyses have not been provided and the models are not related to statistical approaches to induction. A rational analysis for rule-based models could presume that concepts are represented as rules, and would then ask to what degree of belief a rational agent should be in agreement with each rule, with some observed examples provided (Goodman, Griffiths, Feldman, and Tenenbaum). Rule-based theories of concept learning are focused more so on perceptual learning and less on definition learning. Rules can be used in learning when the stimuli are confusable, as opposed to simple. When rules are used in learning, decisions are made based on properties alone and rely on simple criteria that do not require a lot of memory ( Rouder and Ratcliff, 2006).
Example of rule-based theory:
"A radiologist using rule-based categorization would observe whether specific properties of an X-ray image meet certain criteria; for example, is there an extreme difference in brightness in a suspicious region relative to other regions? A decision is then based on this property alone." (see Rouder and Ratcliff 2006)
The prototype view of concept learning holds that people abstract out the central tendency (or prototype) of the examples experienced and use this as a basis for their categorization decisions.
The prototype view of concept learning holds that people categorize based on one or more central examples of a given category followed by a penumbra of decreasingly typical examples. This implies that people do not categorize based on a list of things that all correspond to a definition, but rather on a hierarchical inventory based on semantic similarity to the central example(s).
To illustrate, imagine the following mental representations of the category: Sports
The first illustration demonstrates a mental representation if we were to categorize by definition:
Definition of Sports: an athletic activity requiring skill or physical prowess and often of a competitive nature.
Basketball Football Bowling Baseball Skiing Track and field Snowboarding Lacrosse rugby Soccer Sports Skateboarding Golf Bike-Racing Hockey Surfing Weightlifting Tennis
The second illustration demonstrates a mental representation that prototype theory would predict:
It is evident that prototype theory hypothesizes a more continuous (less discrete) way of categorization in which the list of things that match the category's definition is not limited.
Exemplar theory is the storage of specific instances (exemplars), with new objects evaluated only with respect to how closely they resemble specific known members (and nonmembers) of the category. This theory hypothesizes that learners store examples verbatim. This theory views concept learning as highly simplistic. Only individual properties are represented. These individual properties are not abstract and they do not create rules. An example of what exemplar theory might look like is, "water is wet". It is simply known that some (or one, or all) stored examples of water have the property wet. Exemplar based theories have become more empirically popular over the years with some evidence suggesting that human learners use exemplar based strategies only in early learning, forming prototypes and generalizations later in life. An important result of exemplar models in psychology literature has been a de-emphasis of complexity in concept learning. One of the best known exemplar theories of concept learning is the Generalized Context Model (GCM).
A problem with exemplar theory is that exemplar models critically depend on two measures: similarity between exemplars, and having a rule to determine group membership. Sometimes it is difficult to attain or distinguish these measures.
More recently, cognitive psychologists have begun to explore the idea that the prototype and exemplar models form two extremes. It has been suggested that people are able to form a multiple prototype representation, besides the two extreme representations. For example, consider the category 'spoon'. There are two distinct subgroups or conceptual clusters: spoons tend to be either large and wooden, or small and made of metal. The prototypical spoon would then be a medium-size object made of a mixture of metal and wood, which is clearly an unrealistic proposal. A more natural representation of the category 'spoon' would instead consist of multiple (at least two) prototypes, one for each cluster. A number of different proposals have been made in this regard (Anderson, 1991; Griffiths, Canini, Sanborn & Navarro, 2007; Love, Medin & Gureckis, 2004; Vanpaemel & Storms, 2008). These models can be regarded as providing a compromise between exemplar and prototype models.
The basic idea of explanation-based learning suggests that a new concept is acquired by experiencing examples of it and forming a basic outline.1 Put simply, by observing or receiving the qualities of a thing the mind forms a concept which possesses and is identified by those qualities.
The original theory, proposed by Mitchell, Keller, and Kedar-Cabelli in 1986 and called explanation-based generalization, is that learning occurs through progressive generalizing.2 This theory was first developed to program machines to learn. When applied to human cognition, it translates as follows: the mind actively separates information that applies to more than one thing and enters it into a broader description of a category of things. This is done by identifying sufficient conditions for something to fit in a category, similar to schematizing.
The revised model revolves around the integration of four mental processes – generalization, chunking, operationalization, and analogy3.
- Generalization is the process by which the characteristics of a concept which are fundamental to it are recognized and labeled. For example, birds have feathers and wings. Anything with feathers and wings will be identified as ‘bird’.
- When information is grouped mentally, whether by similarity or relatedness, the group is called a chunk. Chunks can vary in size from a single item with parts or many items with many parts.4
- A concept is operationalized when the mind is able to actively recognize examples of it by characteristics and label it appropriately.5
- Analogy is the recognition of similarities among potential examples.6
This particular theory of concept learning is relatively new and more research is being conducted to test it.
Bayes' theorem is important because it provides a powerful tool for understanding, manipulating and controlling data5 that takes a larger view that is not limited to data analysis alone6. The approach is subjective, and this requires the assessment of prior probabilities6, making it also very complex. However, if Bayesians show that the accumulated evidence and the application of Bayes' law are sufficient, the work will overcome the subjectivity of the inputs involved7. Bayesian inference can be used for any honestly collected data and has a major advantage because of its scientific focus6.
One model that incorporates the Bayesian theory of concept learning is the ACT-R model, developed by John R. Anderson. The ACT-R model is a programming language that defines the basic cognitive and perceptual operations that enable the human mind by producing a step-by-step simulation of human behavior. This theory exploits the idea that each task humans perform consists of a series of discrete operations. The model has been applied to learning and memory, higher level cognition, natural language, perception and attention, human-computer interaction, education, and computer generated forces.
In addition to John R. Anderson, Joshua Tenenbaum has been a contributor to the field of concept learning; he studied the computational basis of human learning and inference using behavioral testing of adults, children, and machines from Bayesian statistics and probability theory, but also from geometry, graph theory, and linear algebra. Tenenbaum is working to achieve a better understanding of human learning in computational terms and trying to build computational systems that come closer to the capacities of human learners.
Component display theory
M. D. Merrill's component display theory (CDT) is a cognitive matrix that focuses on the interaction between two dimensions: the level of performance expected from the learner and the types of content of the material to be learned. Merrill classifies a learner's level of performance as: find, use, remember, and material content as: facts, concepts, procedures, and principles. The theory also calls upon four primary presentation forms and several other secondary presentation forms. The primary presentation forms include: rules, examples, recall, and practice. Secondary presentation forms include: prerequisites, objectives, helps, mnemonics, and feedback. A complete lesson includes a combination of primary and secondary presentation forms, but the most effective combination varies from learner to learner and also from concept to concept. Another significant aspect of the CDT model is that it allows for the learner to control the instructional strategies used and adapt them to meet his or her own learning style and preference. A major goal of this model was to reduce three common errors in concept formation: over-generalization, under-generalization and misconception.
[Sample exclusion dimension]
- Rouder, Jeffrey; Ratcliff, Roger (2006). "Comparing Exemplar and Rule-Based Theories of Categorization". Current Directions in Psychological Science. 15: 9–13. doi:10.1111/j.0963-7214.2006.00397.x.
- "A Rational Analysis of Rule-based Concept Learning" (PDF). Retrieved 2007-12-04.
- "GA-based Rule Enhancement in Concept Learning". Retrieved 2007-12-04.
- Bruner, J., Goodnow, J. J., & Austin, G. A. (1967). A study of thinking. New York: Science Editions.
- Feldman, Jacob (2003). "The Simplicity Principle in Human Concept Learning". Current Directions in Psychological Science. 12: 227–232. doi:10.1046/j.0963-7214.2003.01267.x.
- Rendell, Larry (1986). "A general framework for induction and a study of selective induction". Machine Learning. 1 (2): 177–226. doi:10.1007/BF00114117.
- Hammer, Rubi (2008). "Comparison processes in category learning: From theory to behavior". Brain Research. 1225 (15): 102–118. PMID 18614160. doi:10.1016/j.brainres.2008.04.079.
- Hammer, Rubi (2009). "The development of category learning strategies: What makes the difference?". Cognition. 112 (1): 105–119. PMID 19426967. doi:10.1016/j.cognition.2009.03.012.
- Watanabe, Satosi (1969). Knowing and Guessing: A Quantitative Study of Inference and Information. New York: Wiley.
- Watanabe, Satosi (1985). Pattern Recognition: Human and Mechanical. New York: Wiley.
- Solomonoff, R. J. (1964). "A formal theory of inductive inference. Part I". Information and Control. 7 (1): 1–22. doi:10.1016/S0019-9958(64)90223-2.
- Solomonoff, R. J. (1964). "A formal theory of inductive inference. Part II". Information and Control. 7 (2): 224–254. doi:10.1016/S0019-9958(64)90131-7.
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- 7Brown, Harold I. (1994). "Reason, Judgment and Bayes's Law". Philosophy of Science. 61 (3): 351–369. doi:10.1086/289808.
- 5Lindley, Dennis V. (1983). "Theory and Practice of Bayesian Statistics". The Statistician. Journal of the Royal Statistical Society. Series D (The Statistician), Vol. 32, No. 1. 32 (1/2): 1–11. JSTOR 2987587. doi:10.2307/2987587.