Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made 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 least-squares fitting are known to produce systematically biased estimates of parameters for power-law distributions and should not be used in most circumstances. Here we describe statistical techniques for making accurate parameter estimates for power-law data, based on maximum likelihood methods and the Kolmogorov-Smirnov statistic. We also show how to tell whether the data follow a power-law 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 real-world data sets from a range of different disciplines. Each of the data sets has been conjectured previously to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.

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 semi-structured 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 multi-phase 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.

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 bag-of-features image classification, and image segmentation.

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.

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:

General purpose intelligent learning agents cycle through (complex,non-MDP) sequences of observations, actions, and rewards. On the other hand, reinforcement learning is welldeveloped for small finite state Markov Decision Processes (MDPs). So far it is an art performed by human designers to extract the right state representation out of the bare observations, i.e. to reduce the agent setup to the MDP framework. 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 the companion article [Hut09].

Feature Markov Decision Processes (ΦMDPs) [Hut09] are well-suited for learning agents in general environments. Nevertheless, unstructured (Φ)MDPs are limited to relatively simple environments. Structured MDPs like Dynamic Bayesian Networks (DBNs) are used for large-scale realworld problems. In this article I extend ΦMDP to ΦDBN. The primary contribution is to derive a cost criterion that allows to automatically extract the most relevant features from the environment, leading to the “best ” DBN representation. I discuss all building blocks required for a complete general learning algorithm.

System logs come in a large and evolving variety of formats, many of which are semi-structured and/or non-standard. As a consequence, off-the-shelf tools for processing such logs often do not exist, forcing analysts to develop their own tools, which is costly and time-consuming. In this paper, we present an incremental algorithm that automatically infers the format of system log files. From the resulting format descriptions, we can generate a suite of data processing tools automatically. The system can handle large-scale data sources whose formats evolve over time. Furthermore, it allows analysts to modify inferred descriptions as desired and incorporates those changes in future revisions. 1

www.hutter1.net General-purpose, intelligent, learning agents cycle through sequences of observations, actions, and rewards that are complex, uncertain, unknown, and non-Markovian. On the other hand, reinforcement learning is well-developed 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

Increasingly encompassing models have been suggested for our world. Theories range from generally accepted to increasingly speculative to apparently bogus. The progression of theories from ego- to geo- to helio-centric models to universe and multiverse theories and beyond was accompanied by a dramatic increase in the sizes of the postulated worlds, with humans being expelled from their center to ever more remote and random locations. Rather than leading to a true theory of everything, this trend faces a turning point after which the predictive power of such theories decreases (actually to zero). Incorporating the location and other capacities of the observer into such theories avoids this problem and allows to distinguish meaningful from predictively meaningless theories. This also leads to a truly complete theory of everything consisting of a (conventional objective) theory of everything plus a (novel subjective) observer process. The observer localization is neither based on the controversial anthropic principle, nor has it anything to do with the quantum-mechanical