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137
Selective sampling using the Query by Committee algorithm
 Machine Learning
, 1997
"... We analyze the "query by committee" algorithm, a method for filtering informative queries from a random stream of inputs. We show that if the twomember committee algorithm achieves information gain with positive lower bound, then the prediction error decreases exponentially with the numbe ..."
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Cited by 346 (7 self)
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We analyze the "query by committee" algorithm, a method for filtering informative queries from a random stream of inputs. We show that if the twomember committee algorithm achieves information gain with positive lower bound, then the prediction error decreases exponentially with the number of queries. We show that, in particular, this exponential decrease holds for query learning of perceptrons.
InformationBased Objective Functions for Active Data Selection
 Neural Computation
"... Learning can be made more efficient if we can actively select particularly salient data points. Within a Bayesian learning framework, objective functions are discussed which measure the expected informativeness of candidate measurements. Three alternative specifications of what we want to gain infor ..."
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Cited by 331 (5 self)
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Learning can be made more efficient if we can actively select particularly salient data points. Within a Bayesian learning framework, objective functions are discussed which measure the expected informativeness of candidate measurements. Three alternative specifications of what we want to gain information about lead to three different criteria for data selection. All these criteria depend on the assumption that the hypothesis space is correct, which may prove to be their main weakness. 1 Introduction Theories for data modelling often assume that the data is provided by a source that we do not control. However, there are two scenarios in which we are able to actively select training data. In the first, data measurements are relatively expensive or slow, and we want to know where to look next so as to learn as much as possible. According to Jaynes (1986), Bayesian reasoning was first applied to this problem two centuries ago by Laplace, who in consequence made more important discoveries...
Bayesian Experimental Design: A Review
 Statistical Science
, 1995
"... This paper reviews the literature on Bayesian experimental design, both for linear and nonlinear models. A unified view of the topic is presented by putting experimental design in a decision theoretic framework. This framework justifies many optimality criteria, and opens new possibilities. Various ..."
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Cited by 179 (1 self)
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This paper reviews the literature on Bayesian experimental design, both for linear and nonlinear models. A unified view of the topic is presented by putting experimental design in a decision theoretic framework. This framework justifies many optimality criteria, and opens new possibilities. Various design criteria become part of a single, coherent approach.
A rational analysis of the selection task as optimal data selection
 67 – 215535 Deliverable 4.1
, 1994
"... Human reasoning in hypothesistesting tasks like Wason's (1966, 1968) selection task has been depicted as prone to systematic biases. However, performance on this task has been assessed against a now outmoded falsificationist philosophy of science. Therefore, the experimental data is reassessed ..."
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Cited by 166 (9 self)
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Human reasoning in hypothesistesting tasks like Wason's (1966, 1968) selection task has been depicted as prone to systematic biases. However, performance on this task has been assessed against a now outmoded falsificationist philosophy of science. Therefore, the experimental data is reassessed in the light of a Bayesian model of optimal data selection in inductive hypothesis testing. The model provides a rational analysis (Anderson, 1990) of the selection task that fits well with people's performance on both abstract and thematic versions of the task. The model suggests that reasoning in these tasks may be rational rather than subject to systematic bias. Over the past 30 years, results in the psychology of reasoning have raised doubts about human rationality. The assumption of human rationality has a long history. Aristotle took the capacity for rational thought to be the defining characteristic of human beings, the capacity that separated us from the animals. Descartes regarded the ability to use language and to reason as the hallmarks of the mental that separated it from the merely physical. Many contemporary philosophers of mind also appeal to a basic principle of rationality in accounting for everyday, folk psychological explanation whereby we explain each other's behavior in terms of our beliefs and desires (Cherniak, 1986; Cohen, 1981; Davidson, 1984; Dennett, 1987; but see Stich, 1990). These philosophers, both ancient and modern, share a common view of rationality: To be rational is to reason according to rules (Brown, 1989). Logic and mathematics provide the normative rules that tell us how we should reason. Rationality therefore seems to demand that the human cognitive system embodies the rules of logic and mathematics. However, results in the psychology of reasoning appear to show that people do not reason according to these rules. In both deductive (Evans, 1982, 1989;
Model Selection and the Principle of Minimum Description Length
 Journal of the American Statistical Association
, 1998
"... This paper reviews the principle of Minimum Description Length (MDL) for problems of model selection. By viewing statistical modeling as a means of generating descriptions of observed data, the MDL framework discriminates between competing models based on the complexity of each description. This ..."
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Cited by 149 (5 self)
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This paper reviews the principle of Minimum Description Length (MDL) for problems of model selection. By viewing statistical modeling as a means of generating descriptions of observed data, the MDL framework discriminates between competing models based on the complexity of each description. This approach began with Kolmogorov's theory of algorithmic complexity, matured in the literature on information theory, and has recently received renewed interest within the statistics community. In the pages that follow, we review both the practical as well as the theoretical aspects of MDL as a tool for model selection, emphasizing the rich connections between information theory and statistics. At the boundary between these two disciplines, we find many interesting interpretations of popular frequentist and Bayesian procedures. As we will see, MDL provides an objective umbrella under which rather disparate approaches to statistical modeling can coexist and be compared. We illustrate th...
Computer Experiments
, 1996
"... Introduction Deterministic computer simulations of physical phenomena are becoming widely used in science and engineering. Computers are used to describe the flow of air over an airplane wing, combustion of gasses in a flame, behavior of a metal structure under stress, safety of a nuclear reactor, a ..."
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Cited by 69 (5 self)
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Introduction Deterministic computer simulations of physical phenomena are becoming widely used in science and engineering. Computers are used to describe the flow of air over an airplane wing, combustion of gasses in a flame, behavior of a metal structure under stress, safety of a nuclear reactor, and so on. Some of the most widely used computer models, and the ones that lead us to work in this area, arise in the design of the semiconductors used in the computers themselves. A process simulator starts with a data structure representing an unprocessed piece of silicon and simulates the steps such as oxidation, etching and ion injection that produce a semiconductor device such as a transistor. A device simulator takes a description of such a device and simulates the flow of current through it under varying conditions to determine properties of the device such as its switching speed and the critical voltage at which it switches. A circuit simulator takes a list of devices and the
Finding the number of clusters in a data set: An information theoretic approach
 Journal of the American Statistical Association
, 2003
"... One of the most difficult problems in cluster analysis is the identification of the number of groups in a data set. Most previously suggested approaches to this problem are either somewhat ad hoc or require parametric assumptions and complicated calculations. In this paper we develop a simple yet po ..."
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Cited by 54 (1 self)
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One of the most difficult problems in cluster analysis is the identification of the number of groups in a data set. Most previously suggested approaches to this problem are either somewhat ad hoc or require parametric assumptions and complicated calculations. In this paper we develop a simple yet powerful nonparametric method for choosing the number of clusters based on distortion, a quantity that measures the average distance, per dimension, between each observation and its closest cluster center. Our technique is computationally efficient and straightforward to implement. We demonstrate empirically its effectiveness, not only for choosing the number of clusters but also for identifying underlying structure, on a wide range of simulated and real world data sets. In addition, we give a rigorous theoretical justification for the method based on information theoretic ideas. Specifically, results from the subfield of electrical engineering known as rate distortion theory allow us to describe the behavior of the distortion in both the presence and absence of clustering. Finally, we note that these ideas potentially can be extended to a wide range of other statistical model selection problems. 1
Rational explanation of the selection task
 Psychological Review
, 1996
"... M. Oaksford and N. Chater (O&C; 1994) presented the first quantitative model of P. C. Wason's ( 1966, 1968) selection task in.which performance is rational. J. St B T Evans and D. E. Over (1996) reply that O&C's account is normatively incorrect and cannot model K. N. Kirby's ( ..."
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Cited by 49 (4 self)
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M. Oaksford and N. Chater (O&C; 1994) presented the first quantitative model of P. C. Wason's ( 1966, 1968) selection task in.which performance is rational. J. St B T Evans and D. E. Over (1996) reply that O&C's account is normatively incorrect and cannot model K. N. Kirby's (1994b) or P. Pollard and J. St B T Evans's (1983) data. It is argued that an equivalent measure satisfies their normative concerns and that a modification of O&C's model accounts for their empirical concerns. D. Laming (1996) argues that O&C made unjustifiable psychological assumptions and that a "correct" Bayesian analysis agrees with logic. It is argued that O&C's model makes normative and psychological sense and that Laming's analysis is not Bayesian. A. Almor and S. A. Sloman (1996) argue that O&C cannot explain their data. It is argued that Almor and Sloman's data do not bear on O&C's model because they alter the nature of the task. It is concluded that O&C's model remains the most compelling and comprehensive account of the selection task. Research on Wason's (1966, 1968) selection task questions human rationality because performance is not "logically correct?' Recently, Oaksford and Chater (O&C; 1994) provided a rational analysis (Anderson, 1990, 1991) of the selection task that appeared to vindicate human rationality. O&C argued that the selection task is an inductive, rather than a deductive, reasoning task: Participants must assess the truth or falsity of a general rule from specific instances. In particular, participants face a problem of optimal data selection (Lindley, 1956): They must decide which of four cards (p, notp, q, or notq) is likely to provide the most useful data to test a conditional rule,/fp then q. The "logical " solution is to select the p and the notq cards. O&C argued that this solution presupposes falsificationism (Popper, 1959), which argues that only data that can disconfirm, not confirm, hypotheses are of interest. In contrast, O&C's rational analysis uses a Bayesian approach to inductive
Stochastic Plans for Robotic Manipulation
, 1990
"... Geometric uncertainty is unavoidable when programming robots for physical applications. We propose a stochastic framework for manipulation planning where plans are ranked on the basis of expected cost. That is, we express the desirability of states and actions with a cost function and describe uncer ..."
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Cited by 34 (7 self)
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Geometric uncertainty is unavoidable when programming robots for physical applications. We propose a stochastic framework for manipulation planning where plans are ranked on the basis of expected cost. That is, we express the desirability of states and actions with a cost function and describe uncertainty with probability distributions. We illustrate the approach with a new design for a programmable parts feeder, a mechanism that orients twodimensional parts using a sequence of openloop mechanical motions. We present a planning algorithm that accepts an nsided polygonal part as input and, in time O(n²), generates a stochastically optimal plan for orienting the part.
Fast, frugal, and rational: How rational norms explain behavior
 ORGANIZATIONAL BEHAVIOR AND HUMAN DECISION PROCESSES
, 2003
"... Much research on judgment and decision making has focussed on the adequacy of classical rationality as a description of human reasoning. But more recently it has been argued that classical rationality should also be rejected even as normative standards for human reasoning. For example, Gigerenzer an ..."
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Cited by 23 (0 self)
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Much research on judgment and decision making has focussed on the adequacy of classical rationality as a description of human reasoning. But more recently it has been argued that classical rationality should also be rejected even as normative standards for human reasoning. For example, Gigerenzer and Goldstein (1996) and Gigerenzer and Todd (1999a) argue that reasoning involves ‘‘fast and frugal’ ’ algorithms which are not justified by rational norms, but which succeed in the environment. They provide three lines of argument for this view, based on: (A) the importance of the environment; (B) the existence of cognitive limitations; and (C) the fact that an algorithm with no apparent rational basis, TaketheBest, succeeds in an judgment task (judging which of two cities is the larger, based on lists of features of each city). We reconsider (A)–(C), arguing that standard patterns of explanation in psychology and the social and biological sciences, use rational norms to explain why simple cognitive algorithms can succeed. We also present new computer simulations that compare TaketheBest with other cognitive models (which use connectionist, exemplarbased, and decisiontree algorithms). Although TaketheBest still performs well, it does not perform noticeably better than the other models. We conclude that these results provide no strong reason to prefer TaketheBest over alternative cognitive models.