606 research outputs found

    The GIST of Concepts

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    A unified general theory of human concept learning based on the idea that humans detect invariance patterns in categorical stimuli as a necessary precursor to concept formation is proposed and tested. In GIST (generalized invariance structure theory) invariants are detected via a perturbation mechanism of dimension suppression referred to as dimensional binding. Structural information acquired by this process is stored as a compound memory trace termed an ideotype. Ideotypes inform the subsystems that are responsible for learnability judgments, rule formation, and other types of concept representations. We show that GIST is more general (e.g., it works on continuous, semi-continuous, and binary stimuli) and makes much more accurate predictions than the leading models of concept learning difficulty,such as those based on a complexity reduction principle (e.g., number of mental models,structural invariance, algebraic complexity, and minimal description length) and those based on selective attention and similarity (GCM, ALCOVE, and SUSTAIN). GIST unifies these two key aspects of concept learning and categorization. Empirical evidence from three\ud experiments corroborates the predictions made by the theory and its core model which we propose as a candidate law of human conceptual behavior

    CP-nets: From Theory to Practice

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    Conditional preference networks (CP-nets) exploit the power of ceteris paribus rules to represent preferences over combinatorial decision domains compactly. CP-nets have much appeal. However, their study has not yet advanced sufficiently for their widespread use in real-world applications. Known algorithms for deciding dominance---whether one outcome is better than another with respect to a CP-net---require exponential time. Data for CP-nets are difficult to obtain: human subjects data over combinatorial domains are not readily available, and earlier work on random generation is also problematic. Also, much of the research on CP-nets makes strong, often unrealistic assumptions, such as that decision variables must be binary or that only strict preferences are permitted. In this thesis, I address such limitations to make CP-nets more useful. I show how: to generate CP-nets uniformly randomly; to limit search depth in dominance testing given expectations about sets of CP-nets; and to use local search for learning restricted classes of CP-nets from choice data

    Categorical invariance and structural complexity in human concept learning

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    An alternative account of human concept learning based on an invariance measure of the categorical\ud stimulus is proposed. The categorical invariance model (CIM) characterizes the degree of structural\ud complexity of a Boolean category as a function of its inherent degree of invariance and its cardinality or\ud size. To do this we introduce a mathematical framework based on the notion of a Boolean differential\ud operator on Boolean categories that generates the degrees of invariance (i.e., logical manifold) of the\ud category in respect to its dimensions. Using this framework, we propose that the structural complexity\ud of a Boolean category is indirectly proportional to its degree of categorical invariance and directly\ud proportional to its cardinality or size. Consequently, complexity and invariance notions are formally\ud unified to account for concept learning difficulty. Beyond developing the above unifying mathematical\ud framework, the CIM is significant in that: (1) it precisely predicts the key learning difficulty ordering of\ud the SHJ [Shepard, R. N., Hovland, C. L.,&Jenkins, H. M. (1961). Learning and memorization of classifications.\ud Psychological Monographs: General and Applied, 75(13), 1-42] Boolean category types consisting of three\ud binary dimensions and four positive examples; (2) it is, in general, a good quantitative predictor of the\ud degree of learning difficulty of a large class of categories (in particular, the 41 category types studied\ud by Feldman [Feldman, J. (2000). Minimization of Boolean complexity in human concept learning. Nature,\ud 407, 630-633]); (3) it is, in general, a good quantitative predictor of parity effects for this large class of\ud categories; (4) it does all of the above without free parameters; and (5) it is cognitively plausible (e.g.,\ud cognitively tractable)

    Representational information: a new general notion and measure\ud of information

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    In what follows, we introduce the notion of representational information (information conveyed by sets of dimensionally deļ¬ned objects about their superset of origin) as well as an\ud original deterministic mathematical framework for its analysis and measurement. The framework, based in part on categorical invariance theory [Vigo, 2009], uniļ¬es three key constructsof universal science ā€“ invariance, complexity, and information. From this uniļ¬cation we deļ¬ne the amount of information that a well-deļ¬ned set of objects R carries about its ļ¬nite superset of origin S, as the rate of change in the structural complexity of S (as determined by its degree of categorical invariance), whenever the objects in R are removed from the set S. The measure captures deterministically the signiļ¬cant role that context and category structure play in determining the relative quantity and quality of subjective information conveyed by particular objects in multi-object stimuli

    A Dempster-Shafer theory inspired logic.

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    Issues of formalising and interpreting epistemic uncertainty have always played a prominent role in Artificial Intelligence. The Dempster-Shafer (DS) theory of partial beliefs is one of the most-well known formalisms to address the partial knowledge. Similarly to the DS theory, which is a generalisation of the classical probability theory, fuzzy logic provides an alternative reasoning apparatus as compared to Boolean logic. Both theories are featured prominently within the Artificial Intelligence domain, but the unified framework accounting for all the aspects of imprecise knowledge is yet to be developed. Fuzzy logic apparatus is often used for reasoning based on vague information, and the beliefs are often processed with the aid of Boolean logic. The situation clearly calls for the development of a logic formalism targeted specifically for the needs of the theory of beliefs. Several frameworks exist based on interpreting epistemic uncertainty through an appropriately defined modal operator. There is an epistemic problem with this kind of frameworks: while addressing uncertain information, they also allow for non-constructive proofs, and in this sense the number of true statements within these frameworks is too large. In this work, it is argued that an inferential apparatus for the theory of beliefs should follow premises of Brouwer's intuitionism. A logic refuting tertium non daturƬs constructed by defining a correspondence between the support functions representing beliefs in the DS theory and semantic models based on intuitionistic Kripke models with weighted nodes. Without addional constraints on the semantic models and without modal operators, the constructed logic is equivalent to the minimal intuitionistic logic. A number of possible constraints is considered resulting in additional axioms and making the proposed logic intermediate. Further analysis of the properties of the created framework shows that the approach preserves the Dempster-Shafer belief assignments and thus expresses modality through the belief assignments of the formulae within the developed logic

    Application of Decision Diagrams for Information Storage and Retrieval

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    Technology is improving at an amazing pace and one reason for this advancement is because of unprecedented growth in the field of Information Technology and also in Digital Integrated Circuit technology over the past few decades. The size of a typical modern database is in the order of high ends of gigabytes and even terabytes. Researchers were successful in designing complex databases but there is still lot of activity on effectively making use of this stored information. There have been significant advancements in the field of Logic optimization and also in Information storage and retrieval but there has been very little transfer of these methods. The purpose of this study is to investigate the use of powerful Computer Aided Design (CAD) techniques for efficient information storage and retrieval. In the work presented in this thesis, it is shown that Decision Diagrams can be used for efficient data storage and information retrieval. An efficient technique is proposed for each of the two key areas of research in Database systems known as Query Optimization and Datamining . Encouraging results are obtained indicating that using hardware techniques for information processing can be a new approach for solving these problems. An SQL query is represented using a hardware data structure known as an AND/OR graph and an SQL parser is interfaced with AND/OR package to achieve query optimization. Optimization using AND/OR graphs works only in the Boolean domain and to make the process of query optimization more complete it has to be investigated in Multivalued domain. The possibility of using MDD as a data structure to represent the query in the multi valued domain is discussed and a synthesis technique is developed to synthesize Multi Valued Logic Networks using MDD. Another useful data structure known as BDD can be used to store the large transaction files used in datamining applications very effectively

    A method of classification for multisource data in remote sensing based on interval-valued probabilities

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    An axiomatic approach to intervalued (IV) probabilities is presented, where the IV probability is defined by a pair of set-theoretic functions which satisfy some pre-specified axioms. On the basis of this approach representation of statistical evidence and combination of multiple bodies of evidence are emphasized. Although IV probabilities provide an innovative means for the representation and combination of evidential information, they make the decision process rather complicated. It entails more intelligent strategies for making decisions. The development of decision rules over IV probabilities is discussed from the viewpoint of statistical pattern recognition. The proposed method, so called evidential reasoning method, is applied to the ground-cover classification of a multisource data set consisting of Multispectral Scanner (MSS) data, Synthetic Aperture Radar (SAR) data, and digital terrain data such as elevation, slope, and aspect. By treating the data sources separately, the method is able to capture both parametric and nonparametric information and to combine them. Then the method is applied to two separate cases of classifying multiband data obtained by a single sensor. In each case a set of multiple sources is obtained by dividing the dimensionally huge data into smaller and more manageable pieces based on the global statistical correlation information. By a divide-and-combine process, the method is able to utilize more features than the conventional maximum likelihood method
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