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131
Powerlaw distributions in empirical data
 ISSN 00361445. doi: 10.1137/ 070710111. URL http://dx.doi.org/10.1137/070710111
, 2009
"... Powerlaw distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and manmade phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the t ..."
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Cited by 198 (3 self)
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Powerlaw distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and manmade phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the tail of the distribution. In particular, standard methods such as leastsquares fitting are known to produce systematically biased estimates of parameters for powerlaw distributions and should not be used in most circumstances. Here we describe statistical techniques for making accurate parameter estimates for powerlaw data, based on maximum likelihood methods and the KolmogorovSmirnov statistic. We also show how to tell whether the data follow a powerlaw distribution at all, defining quantitative measures that indicate when the power law is a reasonable fit to the data and when it is not. We demonstrate these methods by applying them to twentyfour realworld data sets from a range of different disciplines. Each of the data sets has been conjectured previously to follow a powerlaw distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.
Supervised Learning of Quantizer Codebooks by Information Loss Minimization
, 2007
"... This paper proposes a technique for jointly quantizing continuous features and the posterior distributions of their class labels based on minimizing empirical information loss, such that the index K of the quantizer region to which a given feature X is assigned approximates a sufficient statistic fo ..."
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Cited by 33 (0 self)
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This paper proposes a technique for jointly quantizing continuous features and the posterior distributions of their class labels based on minimizing empirical information loss, such that the index K of the quantizer region to which a given feature X is assigned approximates a sufficient statistic for its class label Y. We derive an alternating minimization procedure for simultaneously learning codebooks in the Euclidean feature space and in the simplex of posterior class distributions. The resulting quantizer can be used to encode unlabeled points outside the training set and to predict their posterior class distributions, and has an elegant interpretation in terms of lossless source coding. The proposed method is extensively validated on synthetic and real datasets, and is applied to two diverse problems: learning discriminative visual vocabularies for bagoffeatures image classification, and image segmentation.
From dirt to shovels: Fully automatic tool generation from ad hoc data
 In POPL
, 2008
"... An ad hoc data source is any semistructured data source for which useful data analysis and transformation tools are not readily available. Such data must be queried, transformed and displayed by systems administrators, computational biologists, financial analysts and hosts of others on a regular bas ..."
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Cited by 30 (9 self)
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An ad hoc data source is any semistructured data source for which useful data analysis and transformation tools are not readily available. Such data must be queried, transformed and displayed by systems administrators, computational biologists, financial analysts and hosts of others on a regular basis. In this paper, we demonstrate that it is possible to generate a suite of useful data processing tools, including a semistructured query engine, several format converters, a statistical analyzer and data visualization routines directly from the ad hoc data itself, without any human intervention. The key technical contribution of the work is a multiphase algorithm that automatically infers the structure of an ad hoc data source and produces a format specification in the PADS data description language. Programmers wishing to implement custom data analysis tools can use such descriptions to generate printing and parsing libraries for the data. Alternatively, our software infrastructure will push these descriptions through the PADS compiler and automatically generate fully functional tools. We evaluate the performance of our inference algorithm, showing it scales linearly in the size of the training data — completing in seconds, as opposed to the hours or days it takes to write a description by hand. We also evaluate the correctness of the algorithm, demonstrating that generating accurate descriptions often requires less than 5 % of the available data. 1.
Information, Divergence and Risk for Binary Experiments
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2009
"... We unify fdivergences, Bregman divergences, surrogate regret bounds, proper scoring rules, cost curves, ROCcurves and statistical information. We do this by systematically studying integral and variational representations of these various objects and in so doing identify their primitives which all ..."
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Cited by 17 (6 self)
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We unify fdivergences, Bregman divergences, surrogate regret bounds, proper scoring rules, cost curves, ROCcurves and statistical information. We do this by systematically studying integral and variational representations of these various objects and in so doing identify their primitives which all are related to costsensitive binary classification. As well as developing relationships between generative and discriminative views of learning, the new machinery leads to tight and more general surrogate regret bounds and generalised Pinsker inequalities relating fdivergences to variational divergence. The new viewpoint also illuminates existing algorithms: it provides a new derivation of Support Vector Machines in terms of divergences and relates Maximum Mean Discrepancy to Fisher Linear Discriminants.
Feature reinforcement learning: Part I. Unstructured MDPs
 Journal of General Artificial Intelligence
, 2009
"... www.hutter1.net Generalpurpose, intelligent, learning agents cycle through sequences of observations, actions, and rewards that are complex, uncertain, unknown, and nonMarkovian. On the other hand, reinforcement learning is welldeveloped for small finite state Markov decision processes (MDPs). Up ..."
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Cited by 16 (7 self)
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www.hutter1.net Generalpurpose, intelligent, learning agents cycle through sequences of observations, actions, and rewards that are complex, uncertain, unknown, and nonMarkovian. On the other hand, reinforcement learning is welldeveloped for small finite state Markov decision processes (MDPs). Up to now, extracting the right state representations out of bare observations, that is, reducing the general agent setup to the MDP framework, is an art that involves significant effort by designers. The primary goal of this work is to automate the reduction process and thereby significantly expand the scope of many existing reinforcement learning algorithms and the agents that employ them. Before we can think of mechanizing this search for suitable MDPs, we need a formal objective criterion. The main contribution of this article is to develop such a criterion. I also integrate the various parts into one learning algorithm. Extensions to more realistic dynamic Bayesian networks are developed in Part
Suboptimal behavior of Bayes and MDL in classification under misspecification
 COLT
, 2004
"... We show that forms of Bayesian and MDL inference that are often applied to classification problems can be inconsistent. This means that there exists a learning problem such that for all amounts of data the generalization errors of the MDL classifier and the Bayes classifier relative to the Bayesian ..."
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Cited by 13 (3 self)
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We show that forms of Bayesian and MDL inference that are often applied to classification problems can be inconsistent. This means that there exists a learning problem such that for all amounts of data the generalization errors of the MDL classifier and the Bayes classifier relative to the Bayesian posterior both remain bounded away from the smallest achievable generalization error. From a Bayesian point of view, the result can be reinterpreted as saying that Bayesian inference can be inconsistent under misspecification, even for countably infinite models. We extensively discuss the result from both a Bayesian and an MDL perspective.
Make it home: automatic optimization of furniture arrangement
 ACM Trans. on Graph
, 2011
"... optimized to satisfy ergonomic criteria, such as unobstructed accessibility and visibility, required of a realistic furniture configuration. We present a system that automatically synthesizes indoor scenes realistically populated by a variety of furniture objects. Given examples of sensibly furnishe ..."
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Cited by 12 (2 self)
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optimized to satisfy ergonomic criteria, such as unobstructed accessibility and visibility, required of a realistic furniture configuration. We present a system that automatically synthesizes indoor scenes realistically populated by a variety of furniture objects. Given examples of sensibly furnished indoor scenes, our system extracts, in advance, hierarchical and spatial relationships for various furniture objects, encoding them into priors associated with ergonomic factors, such as visibility and accessibility, which are assembled into a cost function whose optimization yields realistic furniture arrangements. To deal with the prohibitively large search space, the cost function is optimized by simulated annealing using a MetropolisHastings state search step. We demonstrate that our system can synthesize multiple realistic furniture arrangements and, through a perceptual study, investigate whether there is a significant difference in the perceived functionality of the automatically synthesized results relative to furniture arrangements produced by human designers.
Causal inference using the algorithmic Markov condition
, 2008
"... Inferring the causal structure that links n observables is usually basedupon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only single observations are present. We develop a theory how to g ..."
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Cited by 11 (11 self)
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Inferring the causal structure that links n observables is usually basedupon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only single observations are present. We develop a theory how to generate causal graphs explaining similarities between single objects. To this end, we replace the notion of conditional stochastic independence in the causal Markov condition with the vanishing of conditional algorithmic mutual information anddescribe the corresponding causal inference rules. We explain why a consistent reformulation of causal inference in terms of algorithmic complexity implies a new inference principle that takes into account also the complexity of conditional probability densities, making it possible to select among Markov equivalent causal graphs. This insight provides a theoretical foundation of a heuristic principle proposed in earlier work. We also discuss how to replace Kolmogorov complexity with decidable complexity criteria. This can be seen as an algorithmic analog of replacing the empirically undecidable question of statistical independence with practical independence tests that are based on implicit or explicit assumptions on the underlying distribution. email:
A Philosophical Treatise of Universal Induction
 Entropy 2011
"... Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more ..."
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Cited by 11 (7 self)
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Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more recently computer scientists. In this article we argue the case for Solomonoff Induction, a formal inductive framework which combines algorithmic information theory with the Bayesian framework. Although it achieves excellent theoretical results and is based on solid philosophical foundations, the requisite technical knowledge necessary for understanding this framework has caused it to remain largely unknown and unappreciated in the wider scientific community. The main contribution of this article is to convey Solomonoff induction and its related concepts in a generally accessible form with the aim of bridging this current technical gap. In the process we examine the major historical contributions that have led to the formulation of Solomonoff Induction as well as criticisms of Solomonoff and induction in general. In particular we examine how Solomonoff induction addresses many issues that have plagued other inductive systems, such as the black ravens paradox and the confirmation problem, and compare this approach with other recent approaches.