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Boosting and Microarray Data
 MACHINE LEARNING
, 2003
"... We have found one reason why AdaBoost tends not to perform well on gene expression data, and identified simple modifications that improve its ability to find accurate class prediction rules. These modifications appear especially to be needed when there is a strong association between expression prof ..."
Abstract

Cited by 16 (1 self)
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We have found one reason why AdaBoost tends not to perform well on gene expression data, and identified simple modifications that improve its ability to find accurate class prediction rules. These modifications appear especially to be needed when there is a strong association between expression profiles and class designations. Crossvalidation analysis of six microarray datasets with different characteristics suggests that, suitably modified, boosting provides competitive classification accuracy in general. Sometimes the goal
Generalization errors of the simple perceptron
 Journal of Physics A
, 1998
"... Abstract. To find an exact form for the generalization error of a learning machine is an open ..."
Abstract

Cited by 3 (3 self)
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Abstract. To find an exact form for the generalization error of a learning machine is an open
Aesthetics of Newspaper Layout  and a Survey on Architecture Determining Algorithms
, 1995
"... Contents I Theoretical Foundation 1 1 Basic Notation 3 2 Learning & Generalisation 5 2.1 A Model of a Learning System . . . . . . . . . . . . . . . . . . . . 5 2.2 Generalising From Examples . . . . . . . . . . . . . . . . . . . . . 6 2.3 Theory on the VC dimension . . . . . . . . . . . . . . . . ..."
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Contents I Theoretical Foundation 1 1 Basic Notation 3 2 Learning & Generalisation 5 2.1 A Model of a Learning System . . . . . . . . . . . . . . . . . . . . 5 2.2 Generalising From Examples . . . . . . . . . . . . . . . . . . . . . 6 2.3 Theory on the VC dimension . . . . . . . . . . . . . . . . . . . . . 8 2.3.1 Growth Function and VC Dimension . . . . . . . . . . . . 9 2.3.2 Bounds on Generalisation Error . . . . . . . . . . . . . . . 10 2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3 Decremental Algorithms 13 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.1.1 The Principle of Pruning . . . . . . . . . . . . . . . . . . . 14 3.2 Trail & Error Pruning . . . . . . . . . . . . . . . . . . . . . . . . 15 3.3 Estimating Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3.1 Magnitude Based Pruning . . . . . . . . . . . . . . . . . . 18 3.3.2 A Local Model Of Error F
On the VapnikChervonenkis dimension of the Ising perceptron
, 1996
"... . The VapnikChervonenkis (VC) dimension of the Ising perceptron with binary patterns is calculated by numerical enumerations for system sizes N # 31. It is significantly larger than 1 2 N . ..."
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.<F3.733e+05> The VapnikChervonenkis<F3.733e+05><F3.733e+05> (VC) dimension of the Ising perceptron with binary patterns is calculated by numerical enumerations for system sizes<F3.184e+05> N<F4.078e+05> #<F3.733e+05> 31. It is significantly larger than<F3.733e+05> 1 2<F3.184e+05> N<F3.733e+05> . The data suggest that there is probably no welldefined asymptotic behaviour for<F3.184e+05> N<F4.401e+05><F3.733e+05> ##.<F3.733e+05> The VapnikChervonenkis<F3.733e+05><F3.733e+05> (VC) dimension is one of the central quantities used in both mathematical statistics and computer science to characterize the performance of classifier systems [1, 2]. In the case of feedforward neural networks it establishes connections between the storage and generalization abilities of these systems [35]. In this letter we will discuss the<F3.733e+05> VC<F3.733e+05> dimension of the Ising perceptron with binary patterns. The<F3.733e+05> VC<F3.733e+05> dimension<F3.184e+05> d<F3.733e+05> VC<F3.733e+05> i...
LEARNING THROUGH THEORIES
"... This paper builds a decisiontheoretic framework to examine the relationship between language and knowledge. A decision maker describes the world through theories. A theory consists of universal propositions called patterns, and it is formulated in some language. I look at two characteristics of a s ..."
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This paper builds a decisiontheoretic framework to examine the relationship between language and knowledge. A decision maker describes the world through theories. A theory consists of universal propositions called patterns, and it is formulated in some language. I look at two characteristics of a successful theory. A theory is informative if it allows agents to precisely predict outcomes of some process. A theory is brief if it consists of finitely many patterns. The main result of the paper identifies languages for which there is no tradeoff between both characteristics: Any informative theory logically implies a theory that is informative as well as brief. I illustrate the main result on specific problems of reasoning under uncertainty: recommendation problems, binary preferences of a customer, or a stylized example of a chemical research.
LETTER TO THE EDITOR On the Vapnik–Chervonenkis dimension of the Ising perceptron
, 1996
"... Abstract. The Vapnik–Chervonenkis (VC) dimension of the Ising perceptron with binary patterns is calculated by numerical enumerations for system sizes N � 31. It is significantly larger than 1 2 N. The data suggest that there is probably no welldefined asymptotic behaviour for N →∞. The Vapnik–Cher ..."
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Abstract. The Vapnik–Chervonenkis (VC) dimension of the Ising perceptron with binary patterns is calculated by numerical enumerations for system sizes N � 31. It is significantly larger than 1 2 N. The data suggest that there is probably no welldefined asymptotic behaviour for N →∞. The Vapnik–Chervonenkis (VC) dimension is one of the central quantities used in both mathematical statistics and computer science to characterize the performance of classifier systems [1, 2]. In the case of feedforward neural networks it establishes connections between the storage and generalization abilities of these systems [3–5]. In this letter we will discuss the VC dimension of the Ising perceptron with binary patterns. The VC dimension dVC is defined via the growth function �(p). Consider a set of instances x and a system C of binary classifiers c: x ↦ → {−1, 1} that group all x ∈ X into two classes labelled by 1 and −1, respectively. For any set {xµ} of p different instances x1,...,xp we determine the number �(x1,...,xp) of different classifications c(x1),...,c(xp) that can be induced by running through all classifiers c ∈ C. A set of instances is called shattered by the system C if �(x1,...,xp) equals 2p, the maximum possible number of different binary classifications of p instances. Large values of �(x1,...,xp) roughly correspond to a large diversity of mappings contained in C. The growth function �(p) is now defined by �(p) = max x µ �(x1,...,x p). (1) It is obvious that �(p) cannot decrease with p. Moreover, for small p one expects that there will be at least one shattered set of size p and hence �(p) = 2p. On the other hand, this exponential increase in the growth function is unlikely to continue for all p. The value of p where it starts to slow down gives a hint as to the complexity of the system C. In fact the Sauer lemma [1, 6] states that for all systems C of binary classifiers there exists a natural number dVC (which may be infinite) such that
Let (Xn)
, 810
"... In this paper we obtain some uniform laws of large numbers and functional central limit theorems for sequential empirical measure processes indexed by classes of product functions satisfying appropriate VapnikČervonenkis properties. ..."
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In this paper we obtain some uniform laws of large numbers and functional central limit theorems for sequential empirical measure processes indexed by classes of product functions satisfying appropriate VapnikČervonenkis properties.
Coarse Decision Making
, 2009
"... We study decision makers who willingly forgo acts that finely vary with states, even though these acts are informationally and technologically feasible. They opt instead for coarse rules that are less sensitive to state by state variations. We model this coarse decision making as a consequence of in ..."
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We study decision makers who willingly forgo acts that finely vary with states, even though these acts are informationally and technologically feasible. They opt instead for coarse rules that are less sensitive to state by state variations. We model this coarse decision making as a consequence of individuals using classical, frequentist methods to draw robust inferences from scarce data. Our central theme is that coarse decision making arises to mitigate the problem of overfitting the data. The main implication of this framework is behavior that is biased towards simplicity: decision makers choose models, or decision frames that are statistically simple, in a sense we make precise. We are also able to give a unified interpretation of many seemingly anomalous cognitive and decision making procedures, such as categorization,