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Complexity Approximation Principle
 Computer Journal
, 1999
"... INTRODUCTION The subject of this note is another inductive principle, which can be regarded as a direct generalization of the minimum description length (MDL) and minimum message length (MML) principles. We will describe the work started at the Computer Learning Research Centre (Royal Holloway, Uni ..."
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INTRODUCTION The subject of this note is another inductive principle, which can be regarded as a direct generalization of the minimum description length (MDL) and minimum message length (MML) principles. We will describe the work started at the Computer Learning Research Centre (Royal Holloway, University of London) related to this new principle, which we call the complexity approximation principle (CAP). Both MDL and MML principles can be interpreted as Kolmogorov complexity approximation principles (as explained in Rissanen [1, 2] and Wallace and Freeman [3]; see also [4]). It is shown in [5] and [6] that it is possible to generalize Kolmogorov complexity to describe the optimal performance in different `games of prediction'. Using this general notion, called predictive complexity,itis straightforward to extend the MDL and MML principles to our more general CAP. In Section 2 we define predictive complexity, in Section 3 several examples are given and in Section 4
Best Empirical Models when the Parameter Space is Infinite Dimensional, Paper Presented at EC 2
, 2002
"... ..."
Artificial Neural Networks
, 2006
"... Artificial neural networks (ANNs) constitute a class of flexible nonlinear models designed to mimic biological neural systems. In this entry, we introduce ANN using familiar econometric terminology and provide an overview of ANN modeling approach and its implementation methods. ..."
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Artificial neural networks (ANNs) constitute a class of flexible nonlinear models designed to mimic biological neural systems. In this entry, we introduce ANN using familiar econometric terminology and provide an overview of ANN modeling approach and its implementation methods.
A Statistical Perspective on Data Mining
"... Technological advances have led to new and automated data collection methods. Datasets once at a premium are often plentiful nowadays and sometimes indeed massive. A new breed of challenges are thus presented – primary among them is the need for methodology to analyze such masses of data with a view ..."
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Technological advances have led to new and automated data collection methods. Datasets once at a premium are often plentiful nowadays and sometimes indeed massive. A new breed of challenges are thus presented – primary among them is the need for methodology to analyze such masses of data with a view to understanding complex phenomena and relationships. Such capability is provided by data mining which combines core statistical techniques with those from machine intelligence. This article reviews the current state of the discipline from a statistician’s perspective, illustrates issues with reallife examples, discusses the connections with statistics, the differences, the failings and the challenges ahead. 1
Aspects of the Interface between STatistics and . . .
, 1999
"... In recent years the crossfertilisation of ideas between the statistics and machine learning communities has become increasingly important. This exchange of ideas resulted from a recognition that the two communities often have to tackle similar problems and has resulted in an exchange which has enri ..."
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In recent years the crossfertilisation of ideas between the statistics and machine learning communities has become increasingly important. This exchange of ideas resulted from a recognition that the two communities often have to tackle similar problems and has resulted in an exchange which has enriched both disciplines. There is much to be gained in considering the two literatures in tandem, and the aim of this thesis is to build on some of the research currently taking place at the interface between these two disciplines. Specifically we will be considering a class of models called Bayesian belief networks. These are models which are closely related to neural networks, a type of model often used in machine learning but largely eschewed by statisticians due to their `black box' approach. Neural networks, while useful tools, lack transparency; by their nature it is difficult to interpret the method in which neural network
UC405 (Ml INTERPRETABLE PROJECTION PURSUIT*
, 1989
"... The goal of this thesis is to modify projection pursuit by trading accuracy for interpretability. The modification produces a more parsimonious and understandable model without sacrificing the structure which projection pursuit seeks. The method retains the nonlinear versatility of projection pursui ..."
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The goal of this thesis is to modify projection pursuit by trading accuracy for interpretability. The modification produces a more parsimonious and understandable model without sacrificing the structure which projection pursuit seeks. The method retains the nonlinear versatility of projection pursuit while clarifying the results. Following an introduction which outlines the dissertation, the first and second chapters contain the technique as applied to exploratory projection pursuit and projection pursuit regression respectively. The interpretability of a description is measured as the simplicity of the coefficients which define its linear projections. Several interpretability indices for a set of vectors are defined based on the ideas of rotation in factor analysis and entropy. The two methods require slightly different indices due to their contrary goals. A roughness penalty weighting approach is used to search for a more parsimonious
STATISTICAL APPLICATIONS OF NEURAL NETWORKS
, 1995
"... An elementary introduction to the theory of neutral networks is made from a statistical perspective. The networks are estimated by two different methods one derivative based and the other derivative free. The theory is illustrated by three different examples and where possible results are compared ..."
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An elementary introduction to the theory of neutral networks is made from a statistical perspective. The networks are estimated by two different methods one derivative based and the other derivative free. The theory is illustrated by three different examples and where possible results are compared to those obtained from a classical statistical model. The methodology is seen as a new paradigm for data analysis where models are not explicitly stated but rather implicitly defined by the network. KEYWORDS Backpropagation, data analysis, feed forward, genetic algorithm.
An Algorithm to Handle Structural Uncertainties in Learning Bayesian Network
"... Abstract. Bayesian network is a graphical model appropriated to represent and to analyze uncertainty, knowledge and beliefs contained implicitly in the data. In this paper we propose the XPC algorithm for structural learning in Bayesian networks using decomposable metrics in families (a variable and ..."
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Abstract. Bayesian network is a graphical model appropriated to represent and to analyze uncertainty, knowledge and beliefs contained implicitly in the data. In this paper we propose the XPC algorithm for structural learning in Bayesian networks using decomposable metrics in families (a variable and its parents) in order to obtain the maximumscore network. The concept of conditional independence, based on Pearl’s dseparation, is used to identify conflicting regions, where the existence of some edges depends on the nonexistence of others. Hence, the user is required to choose which edges are relevant in the structure. The comparative experiments using wellknow benchmarks show XPC produces better results than other algorithms mainly when the amount of data is small. A heuristic for optimizes the independence
estimation of (dynamical
, 2004
"... application of probabilistic techniques for the state/parameter ..."