Indefinitely Oscillating Martingales

We construct a class of nonnegative martingale processes that oscillate indefinitely with high probability. For these processes, we state a uniform rate of the number of oscillations and show that this rate is asymptotically close to the theoretical upper bound. These bounds on probability and expectation of the number of upcrossings are compared to classical bounds from the martingale literature. We discuss two applications. First, our results imply that the limit of the minimum description length operator may not exist. Second, we give bounds on how often one can change one's belief in a given hypothesis when observing a stream of data.Comment: ALT 2014, extended technical repor

Compression and intelligence: social environments and communication

Compression has been advocated as one of the principles which pervades inductive inference and prediction - and, from there, it has also been recurrent in definitions and tests of intelligence. However, this connection is less explicit in new approaches to intelligence. In this paper, we advocate that the notion of compression can appear again in definitions and tests of intelligence through the concepts of `mind-reading¿ and `communication¿ in the context of multi-agent systems and social environments. Our main position is that two-part Minimum Message Length (MML) compression is not only more natural and effective for agents with limited resources, but it is also much more appropriate for agents in (co-operative) social environments than one-part compression schemes - particularly those using a posterior-weighted mixture of all available models following Solomonoff¿s theory of prediction. We think that the realisation of these differences is important to avoid a naive view of `intelligence as compression¿ in favour of a better understanding of how, why and where (one-part or two-part, lossless or lossy) compression is needed.We thank the anonymous reviewers for their helpful comments, and we thank Kurt Kleiner for some challenging and ultimately very helpful questions in the broad area of this work. We also acknowledge the funding from the Spanish MEC and MICINN for projects TIN2009-06078-E/TIN, Consolider-Ingenio CSD2007-00022 and TIN2010-21062-C02, and Generalitat Valenciana for Prometeo/2008/051.Dowe, DL.; Hernández Orallo, J.; Das, PK. (2011). Compression and intelligence: social environments and communication. En Artificial General Intelligence. Springer Verlag (Germany). 6830:204-211. https://doi.org/10.1007/978-3-642-22887-2_21S2042116830Chaitin, G.J.: Godel’s theorem and information. International Journal of Theoretical Physics 21(12), 941–954 (1982)Dowe, D.L.: Foreword re C. S. Wallace. Computer Journal 51(5), 523–560 (2008); Christopher Stewart WALLACE (1933-2004) memorial special issueDowe, D.L.: Minimum Message Length and statistically consistent invariant (objective?) Bayesian probabilistic inference - from (medical) “evidence”. Social Epistemology 22(4), 433–460 (2008)Dowe, D.L.: MML, hybrid Bayesian network graphical models, statistical consistency, invariance and uniqueness. In: Bandyopadhyay, P.S., Forster, M.R. (eds.) Handbook of the Philosophy of Science. Philosophy of Statistics, vol. 7, pp. 901–982. Elsevier, Amsterdam (2011)Dowe, D.L., Hajek, A.R.: A computational extension to the Turing Test. Technical Report #97/322, Dept Computer Science, Monash University, Melbourne, Australia, 9 pp (1997)Dowe, D.L., Hajek, A.R.: A non-behavioural, computational extension to the Turing Test. In: Intl. Conf. on Computational Intelligence & multimedia applications (ICCIMA 1998), Gippsland, Australia, pp. 101–106 (February 1998)Hernández-Orallo, J.: Beyond the Turing Test. J. Logic, Language & Information 9(4), 447–466 (2000)Hernández-Orallo, J.: Constructive reinforcement learning. International Journal of Intelligent Systems 15(3), 241–264 (2000)Hernández-Orallo, J.: On the computational measurement of intelligence factors. In: Meystel, A. (ed.) Performance metrics for intelligent systems workshop, pp. 1–8. National Institute of Standards and Technology, Gaithersburg, MD, U.S.A (2000)Hernández-Orallo, J., Dowe, D.L.: Measuring universal intelligence: Towards an anytime intelligence test. Artificial Intelligence 174(18), 1508–1539 (2010)Hernández-Orallo, J., Minaya-Collado, N.: A formal definition of intelligence based on an intensional variant of Kolmogorov complexity. In: Proc. Intl Symposium of Engineering of Intelligent Systems (EIS 1998), pp. 146–163. ICSC Press (1998)Legg, S., Hutter, M.: Universal intelligence: A definition of machine intelligence. Minds and Machines 17(4), 391–444 (2007)Lewis, D.K., Shelby-Richardson, J.: Scriven on human unpredictability. Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition 17(5), 69–74 (1966)Oppy, G., Dowe, D.L.: The Turing Test. In: Zalta, E.N. (ed.) Stanford Encyclopedia of Philosophy, Stanford University, Stanford (2011), http://plato.stanford.edu/entries/turing-test/Salomon, D., Motta, G., Bryant, D.C.O.N.: Handbook of data compression. Springer-Verlag New York Inc., Heidelberg (2009)Sanghi, P., Dowe, D.L.: A computer program capable of passing I.Q. tests. In: 4th International Conference on Cognitive Science (and 7th Australasian Society for Cognitive Science Conference), vol. 2, pp. 570–575. Univ. of NSW, Sydney, Australia (July 2003)Sayood, K.: Introduction to data compression. Morgan Kaufmann, San Francisco (2006)Scriven, M.: An essential unpredictability in human behavior. In: Wolman, B.B., Nagel, E. (eds.) Scientific Psychology: Principles and Approaches, pp. 411–425. Basic Books (Perseus Books), New York (1965)Searle, J.R.: Minds, brains and programs. Behavioural and Brain Sciences 3, 417–457 (1980)Solomonoff, R.J.: A formal theory of inductive inference. Part I. Information and control 7(1), 1–22 (1964)Sutton, R.S.: Generalization in reinforcement learning: Successful examples using sparse coarse coding. Advances in neural information processing systems, 1038–1044 (1996)Sutton, R.S., Barto, A.G.: Reinforcement learning: An introduction. The MIT Press, Cambridge (1998)Turing, A.M.: Computing machinery and intelligence. Mind 59, 433–460 (1950)Veness, J., Ng, K.S., Hutter, M., Silver, D.: A Monte Carlo AIXI Approximation. Journal of Artificial Intelligence Research, JAIR 40, 95–142 (2011)Wallace, C.S.: Statistical and Inductive Inference by Minimum Message Length. Springer, Heidelberg (2005)Wallace, C.S., Boulton, D.M.: An information measure for classification. Computer Journal 11(2), 185–194 (1968)Wallace, C.S., Dowe, D.L.: Intrinsic classification by MML - the Snob program. In: Proc. 7th Australian Joint Conf. on Artificial Intelligence, pp. 37–44. World Scientific, Singapore (November 1994)Wallace, C.S., Dowe, D.L.: Minimum message length and Kolmogorov complexity. Computer Journal 42(4), 270–283 (1999); Special issue on Kolmogorov complexityWallace, C.S., Dowe, D.L.: MML clustering of multi-state, Poisson, von Mises circular and Gaussian distributions. Statistics and Computing 10, 73–83 (2000

Reconstruction of Causal Networks by Set Covering

We present a method for the reconstruction of networks, based on the order of nodes visited by a stochastic branching process. Our algorithm reconstructs a network of minimal size that ensures consistency with the data. Crucially, we show that global consistency with the data can be achieved through purely local considerations, inferring the neighbourhood of each node in turn. The optimisation problem solved for each individual node can be reduced to a Set Covering Problem, which is known to be NP-hard but can be approximated well in practice. We then extend our approach to account for noisy data, based on the Minimum Description Length principle. We demonstrate our algorithms on synthetic data, generated by an SIR-like epidemiological model.Comment: Under consideration for the ECML PKDD 2010 conferenc

mtDNA lineage analysis of mouse L-cell lines reveals the accumulation of multiple mtDNA mutants and intermolecular recombination

The role of mitochondrial DNA (mtDNA) mutations and mtDNA recombination in cancer cell proliferation and developmental biology remains controversial. While analyzing the mtDNAs of several mouse L cell lines, we discovered that every cell line harbored multiple mtDNA mutants. These included four missense mutations, two frameshift mutations, and one tRNA homopolymer expansion. The LA9 cell lines lacked wild-type mtDNAs but harbored a heteroplasmic mixture of mtDNAs, each with a different combination of these variants. We isolated each of the mtDNAs in a separate cybrid cell line. This permitted determination of the linkage phase of each mtDNA and its physiological characteristics. All of the polypeptide mutations inhibited their oxidative phosphorylation (OXPHOS) complexes. However, they also increased mitochondrial reactive oxygen species (ROS) production, and the level of ROS production was proportional to the cellular proliferation rate. By comparing the mtDNA haplotypes of the different cell lines, we were able to reconstruct the mtDNA mutational history of the L-L929 cell line. This revealed that every heteroplasmic L-cell line harbored a mtDNA that had been generated by intracellular mtDNA homologous recombination. Therefore, deleterious mtDNA mutations that increase ROS production can provide a proliferative advantage to cancer or stem cells, and optimal combinations of mutant loci can be generated through recombination

Entropy creation inside black holes points to observer complementarity

Heating processes inside large black holes can produce tremendous amounts of entropy. Locality requires that this entropy adds on space-like surfaces, but the resulting entropy (10^10 times the Bekenstein-Hawking entropy in an example presented in the companion paper) exceeds the maximum entropy that can be accommodated by the black hole's degrees of freedom. Observer complementarity, which proposes a proliferation of non-local identifications inside the black hole, allows the entropy to be accommodated as long as individual observers inside the black hole see less than the Bekenstein-Hawking entropy. In the specific model considered with huge entropy production, we show that individual observers do see less than the Bekenstein-Hawking entropy, offering strong support for observer complementarity.Comment: 13 pages. This is a companion paper to arXiv:0801.4415; Added reference

An almost sure limit theorem for super-Brownian motion

We establish an almost sure scaling limit theorem for super-Brownian motion on $\mathbb{R}^d$ associated with the semi-linear equation $u_t = {1/2}\Delta u +\beta u-\alpha u^2$, where $\alpha$ and $\beta$ are positive constants. In this case, the spectral theoretical assumptions that required in Chen et al (2008) are not satisfied. An example is given to show that the main results also hold for some sub-domains in $\mathbb{R}^d$.Comment: 14 page

Unsupervised Classification of SAR Images using Hierarchical Agglomeration and EM

We implement an unsupervised classification algorithm for high resolution Synthetic Aperture Radar (SAR) images. The foundation of algorithm is based on Classification Expectation-Maximization (CEM). To get rid of two drawbacks of EM type algorithms, namely the initialization and the model order selection, we combine the CEM algorithm with the hierarchical agglomeration strategy and a model order selection criterion called Integrated Completed Likelihood (ICL). We exploit amplitude statistics in a Finite Mixture Model (FMM), and a Multinomial Logistic (MnL) latent class label model for a mixture density to obtain spatially smooth class segments. We test our algorithm on TerraSAR-X data

Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks

Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data. Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the fields of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere's three-dimensional geopotential height field uncovers known as well as interesting novel features of the atmosphere's vertical stratification and general circulation. Specifically, the new measure "cross-betweenness" identifies regions which are particularly important for mediating vertical wind field interactions. The promising results obtained by following the coupled climate subnetwork approach present a first step towards an improved understanding of the Earth system and its complex interacting components from a network perspective

Diverse consequences of algorithmic probability

We reminisce and discuss applications of algorithmic probability to a wide range of problems in artificial intelligence, philosophy and technological society. We propose that Solomonoff has effectively axiomatized the field of artificial intelligence, therefore establishing it as a rigorous scientific discipline. We also relate to our own work in incremental machine learning and philosophy of complexity. © 2013 Springer-Verlag Berlin Heidelberg

Adaptive cluster expansion for the inverse Ising problem: convergence, algorithm and tests

We present a procedure to solve the inverse Ising problem, that is to find the interactions between a set of binary variables from the measure of their equilibrium correlations. The method consists in constructing and selecting specific clusters of variables, based on their contributions to the cross-entropy of the Ising model. Small contributions are discarded to avoid overfitting and to make the computation tractable. The properties of the cluster expansion and its performances on synthetic data are studied. To make the implementation easier we give the pseudo-code of the algorithm.Comment: Paper submitted to Journal of Statistical Physic