Showing papers on "Generalization published in 1986"

Explanation-based generalization: a unifying view

Abstract: The problem of formulating general concepts from specific training examples has long been a major focus of machine learning research. While most previous research has focused on empirical methods for generalizing from a large number of training examples using no domain-specific knowledge, in the past few years new methods have been developed for applying domain-specific knowledge to formulate valid generalizations from single training examples. The characteristic common to these methods is that their ability to generalize from a single example follows from their ability to explain why the training example is a member of the concept being learned. This paper proposes a general, domain-independent mechanism, called EBG, that unifies previous approaches to explanation-based generalization. The EBG method is illustrated in the context of several example problems, and used to contrast several existing systems for explanation-based generalization. The perspective on explanation-based generalization afforded by this general method is also used to identify open research problems in this area.

Optimal stopping times for detecting changes in distributions

Abstract: It is shown that Page's stopping time is optimal for the detection of changes in distributions, in a well defined sense This work is a generalization of an existing result where it was shown that Page's stopping time is optimal asymptotically

Network design problem with congestion effects: A case of bilevel programming

Abstract: Recently much attention has been focused on multilevel programming, a branch of mathematical programming that can be viewed either as a generalization of min-max problems or as a particular class of Stackelberg games with continuous variables The network design problem with continuous decision variables representing link capacities can be cast into such a framework We first give a formal description of the problem and then develop various suboptimal procedures to solve it Worst-case behaviour results concerning the heuristics, as well as numerical results on a small network, are presented

Complexity of strings in the class of Markov sources

Abstract: Shannon's self-information of a string is generalized to its complexity relative to the class of finite-state-machine (FSM) defined sources. Unlike an earlier generalization, the new one is valid for both short and long strings. The definition is justified in part by a theorem stating that, asymptotically, the mean complexity provides a tight lower bound for the mean length of all so-called regular codes. This also generalizes Shannon's noiseless coding theorem. For a large subclass of FSM sources a simple algorithm is described for computing the complexity.

The logic of persistence

Abstract: A recent paper [Hanks 1985] examines temporal reasoning as an example of default reasoning. They conclude that all current systems of default reasoning, including non-monotonic logic, default logic, and circumscription, are inadequate for reasoning about persistence. I present a way of representing persistence in a framework based on a generalization of circumscription, which captures Hanks and McDermott's procedural representation.

Tense And Modality

Abstract: Conditionals may be viewed as relations between propositions, as we have seen, in striking analogy with the extensional treatment of determiners and quantifiers. But the more traditional intensional constructions are rather operators on propositions, such as modality or tense. Still, given the generalization made in Chapter 3 to arbitrary extensional categories, a similar move is possible for intensional notions. Instead of pursuing this topic in its full generality, we present two concrete cases.

Filtering by repeated integration

Abstract: Many applications of digital filtering require a space variant filter - one whose shape or size varies with position. The usual algorithm for such filters, direct convolution, is very costly for wide kernels. Image prefiltering provides an efficient alternative. We explore one prefiltering technique, repeated integration, which is a generalization of Crow's summed area table.We find that convolution of a signal with any piecewise polynomial kernel of degree n--1 can be computed by integrating the signal n times and point sampling it several times for each output sample. The use of second or higher order integration permits relatively high quality filtering. The advantage over direct convolution is that the cost of repeated integration filtering does not increase with filter width. Generalization to two-dimensional image filtering is straightforward. Implementations of the simple technique are presented in both preprocessing and stream processing styles.

The analytic network process in energy policy planning

Abstract: This paper describes the application of the so-called supermatrix technique of the analytic hierarchy process to a complex energy decision problem. Practical problems related to the method are discussed and a generalization, where elements of the network are allowed to have multiple levels, is suggested. The model considered describes a nuclear power plant licensing problem in Finland.

A domain independent explanation-based generalizer

Abstract: A domain independent technique for generalizing a broad class of explanations is described. This method is compared and contrasted with other approaches to generalizing explanations, including an abstract version of the algorithm used in the STRIPS system and the EBG technique recently developed by Mitchell, Keller, and Kedar-Cabelli. We have tested this generalization technique on a number examples in different domains, and present detailed descriptions of several of these.

Use of general potentials in multiple-scattering theory.

Abstract: A mathematically transparent derivation of the multiple-scattering equations valid for a general non-muffin-tin potential, as applied to clusters of atoms with and without a surrounding outer sphere, is presented. These equations are shown to be a natural generalization of the analogous equations valid for muffin-tin potentials. An expression for the photoabsorption and electron scattering cross section in the framework of the multiple-scattering theory valid for a general potential is derived for what may be the first time, providing the necessary generalization for the similar expression valid in the muffin-tin case. A connection with the Green-function approach to the problem is also established via a generalized optical theorem.

Measurement: The Theory of Numerical Assignments

Abstract: In this article we review some generalizations of classical theories of measurement for concatenation (e.g., mass or length) and conjoint structures (e.g., momentum of mass-velocity pairs or loudness of intensity-frequency pairs). The earlier results on additive representations are briefly surveyed. Generalizations to nonadditive structures are outlined, and their more complex uniqueness results are described. The latter leads to a definition of scale type in terms of the symmetries (automorphisms) of the underlying qualitative structure. The major result is that for any measurement onto the real numbers, only three possible scale types exist that are both rich in symmetries but not too redundant: ratio, interval, and another lying between them. The possible numerical representations for concatenation structures corresponding to these scale types are completely described. The interval scale case leads to a generalization of subjective expected-utility theory that copes with some empirical violations of the classical theory. Partial attempts to axiomatize concatenation structures of these three scale types are described. Such structures are of interest because they make clear that there is a rich class of nonadditive concatenation and conjoint structures with representations of the same scale types as those used in physics. Many scientists and philosophers are well aware of what the physicist E. P. Wigner in 1960 called "the unreasonable effectiveness of mathematics in the natural sciences." Some, like Wigner, have remarked on it; a few, like the ancient philosopher Pythagoras (c. 582-500 B.C.) have tried to explain it. Today as throughout much of history, it is still considered a mystery. There is, however, a part of applied mathematical science that is slowly chipping away at a portion of the mystery. This subfield, usually

A Note on Validity Generalization Procedures.

Abstract: : Validity generalization procedures are reviewed and found to be subject to the logical fallacy of affirming the consequent. Alternative models may explain variation in validity coefficients as well as the cross-situational consistency model espoused by proponents of validity generalization. Moreover, many of the assumptions that form the statistical foundation for validity generalization are false. It is recommended that (a) the conditionality of inferences based on validity generalization analyses be explicitly stated, (b) the decision rule for the validity generalization ratio be changed from .75 to .90, and (c) validity generalization analyses employ Fisher z coefficients rather than (Pearson) correlation coefficients. (Author).

A Generalization of the Conjugate-Gradient Method to Solve Complex Systems

Abstract: Generalisation aux systemes complexes de la methode des gradients conjugues pour la resolution d'un systeme d'equations algebriques lineaires

NON-STATIONARY q-DEPENDENT PROCESSES AND TIME-VARYING MOVING-AVERAGE MODELS: INVERTIBILITY PROPERTIES AND THE FORECASTING PROBLEM

Abstract: The spectral factorization problem was solved in Hallin (1984) for the class of (non-stationary) m-variate MA(q) stochastic processes, i.e. the class of second-order q-dependent processes. It was shown that such a process generally admits an infinite (mq(mq + 1)/2-dimensional) family of possible MA(q) representations. The present paper deals with the invertibility properties and asymptotic behaviour of these MA(q) models, in connection with the problem of producing asymptotically efficient forecasts. Invertible and borderline non-invertible models are characterized (Theorems 3.1 and 3.2). A criterion is provided (Theorem 4.1) by which it can be checked whether a given MA model is a Wold-Cramir decomposition or not; and it is shown (Theorem 4.2) that, under mild conditions, almost every MA model is asymptotically identical with some Wold-Cram6r decomposition. The forecasting problem is investigated in detail, and it is established that the relevant invertibility concept, with respect to asymptotic forecasting efficiency, is what we define as Granger-Andersen invertibility rather than the classical invertibility concept (Theorem 5.3). The properties of this new invertibility concept are studied and contrasted with those of its classical counterpart (Theorems 5.2 and 5.4). Numerical examples are also treated (Section 6), illustrating the fact that non-invertible models may provide asymptotically efficient forecasts, whereas invertible models, in some cases, may not. The mathematical tools throughout the paper are linear difference equations (Green's matrices, adjoint operators, dominated solutions, etc.), and a matrix generalization of continued fractions.

Mapping explanation-based generalization onto soar

Abstract: Explanation-based generalization (EBG) is a powerful approach to concept formation in which a justifiable concept definition is acquired from a single training example and an underlying theory of how the example is an instance of the concept. Soar is an attempt to build a general cognitive architecture combining general learning, problem solving, and memory capabilities. It includes an independently developed learning mechanism, called chunking, that is similar to but not the same as explanation-based generalization. In this article we clarify the relationship between the explanation-based generalization framework and the Soar/chunking combination by showing how the EBG framework maps onto Soar, how several EBG concept-formation tasks are implemented in Soar, and how the Soar approach suggests answers to some of the outstanding issues in explanation-based generalization.

Arabic root and pattern morphology without tiers

Abstract: This paper is an argument for the constraint on grammars known as the 'true generalization condition' (Hooper, 1976: I3): all rules express generalizations true for all surface forms. I make this condition fully explicit by interpreting it to mean the prohibition of the three transformational rule-types: deletion, movement and feature-changing. The argument takes the form of a comparison of a recent autosegmental analysis of the intricate facts of Arabic root and pattern verb stem morphology with an alternative which observes the condition. I hope to show how the latter analysis in every empirical aspect is equivalent to the former in its claims about Arabic, and significantly differs, as the result of observing the true generalization condition, in its lack of numerous un-empirical claims made in the autosegmental analysis. In so far as both have descriptive adequacy, the analysis governed by the true generalization condition, termed 'non-transformational', has also explanatory adequacy in the sense of Chomsky, I964: 28-9, since it is closely determined, or selected, by the true generalization condition. The form of the present paper is as follows: first, a quick look at the facts of Arabic at issue (Section 2), then a presentation of the autosegmental analysis of these by John McCarthy (I98 I) (Section 3), some criticisms of the autosegmental analysis (Section 4), presentation of an alternative analysis which has none of the faults of the autosegmental analysis and which is governed by the true generalization condition (Section 5), and concluding discussion which summarizes the essential criticisms of the autosegmentaltransformational analysis of Arabic root and pattern morphology and presents the main argument of the explanatory adequacy of the nontransformational alternative (Section 6).

Not the path to perdition: the utility of similarity-based learning

Abstract: A large portion of the research in machine learning has involved a paradigm of comparing many examples and analyzing them in terms of similarities and differences, assuming that the resulting generalizations will have applicability to new examples. While such research has been very successful, it is by no means obvious why similarity-based generalizations should be useful, since they may simply reflect coincidences. Proponents of explanation-based learning, a new, knowledge-intensive method of examining single examples to derive generalizations based on underlying causal models, could contend that their methods are more fundamentally grounded, and that there is no need to look for similarities across examples. In this paper, we present the issues, and then show why similarity-based methods are important. We present four reasons why robust machine learning must involve the integration of similarity-based and explanation-based methods. We argue that: 1) it may not always be practical or even possible to determine a causal explanation; 2) similarity usually implies causality; 3) similarity-based generalizations can be refined over time; 4) similarity-based and explanation-based methods complement each other in important ways.

A generalization of Smith's determinant

Abstract: We shall evaluate the determinants of n x n matrices of the form [f(i,j)], where f (w, r) is an even function of m (mod r). Among the examples of determinants of this kind are H. J. S. Smith's determinant det [(i,j)], where (m, r) is the greatest common divisor of m and r, and a generalization of Smith's determinant due to T. M. Apostol.

Programming Rapid Generalization of Correct Articulation through Self-Monitoring Procedures

Abstract: The purpose of this study was to investigate the use of a self-monitoring activity in the clinical and natural environment as a method of promoting rapid generalization of a target speech sound to ...

The role of prior causal theories in generalization

Abstract: OCCAM is a program which organizes memories of events and learns by creating generalizations describing the reasons for the outcomes of the events. OCCAM integrates two sources of information when forming a generalization: • Correlational information which reveals perceived regularities in events. • Prior causal theories which explain regularities in events The former has been extensively studied in machine learning. Recently, there has been interest in explanation-based learning in which the latter source of information is utilized. In OCCAM, prior causal theories are preferred to correlational information when forming generalizations. This strategy is supported by a number of empirical investigations. Generalization rules are used to suggest causal and intentional relational relationships. In familiar domains, these relationships are confirmed or denied by prior causal theories which differentiate the relevant and irrelevant features. In unfamiliar domains, the postulated causal and intentional relationships serve as a basis for the construction of causal theories.

Integer flows in network with fuzzy capacity constraints

Abstract: A generalization of the maximum flow problem in a network with one-sided (upper) and two sided constraints on arc capacities is presented. It allows for violating the capacity constraints in some ranges of tolerance. To solve the generalized problem the apparatus of the fuzzy set theory is used. The efficient algorithms are developed for integer flows.

Variational Estimates for the Overall Response of an Inhomogeneous Nonlinear Dielectric

Abstract: For any problem that can be formulated as a “minimum energy” principle, a procedure is given for generating sets of upper and lower bounds for the energy It makes use of “comparison bodies” whose energy functions may be easier to handle than those in the given problem No structure for the energy functions is assumed in the formal development but useful results are most likely to follow when they are convex When applied to linear field equations, the procedure yields the Hashin-Shtrikman variational principle, and so can be regarded as its generalization to nonlinear problems

Envelopes, Conjugate Points, and Optimal Bang-Bang Extremals

Abstract: The theory of envelopes and conjugate points constitutes an important chapter of the classical Calculus of Variations. In Optimal Control theory, it is often desirable to get better information about optimal trajectories than that provided by the Pontryagin Maximum Principle. To do this, it is useful to have necessary conditions for optimality that exclude, for instance, bang-bang trajectories that have too many switchings, even if those trajectories satisfy the Maximum Principle. It turns out that, in a number of cases, this can be done by means of a suitable generalization of envelope theory. The purpose of this note is to outline one such generalization and to illustrate its use by proving theorems on the structure of optimal bang-bang trajectories for certain problems in two and three dimensions.

Rank tests in 2x2 designs

Abstract: . In literature numerous attempts can be found for the evaluation of two factor designs with fixed effects by means of rank tests. The aim of the present article is to show the limits of these methods and to give some new procedures for 2X2 designs. First, functionals of distribution functions shall be defined whose relations to the usual parameters of the linear model are analysed. These functionals are free of nuissance parameters under the respective hypothesis; they are estimated by special ranks of the data. The asymptotic distribution of these statistics is derived by a generalization of the Chemoff–Savage theorem for correlated random variables. The asymptotic variance depends on the parent distribution function but it can be estimated by using special rank methods. Thus, one obtains asymptotically distribution–free tests for two–factor designs with fixed effects. Some counter examples show why it is not possible to construct suitable rank tests for greater designs than the 2X2 design. The paper closes with a discussion of the drawbacks of the well known rank transform.