MaxEnt 2017 July, 09-14, 2017 – Paradies Resort Hotel – Jarinu/SP – Brazil

Talks:


Survival Analysis based on the cumulative hazard function
Anaya-Izquierdo, Karim
University of Bath, UK

In this talk we introduce a new methodology for inference in survival analysis where the key building block is the cumulative hazard function. We exploit novel analytical properties that allow the cumulative hazard function (rather than the hazard rate) to serve as a swift modelling tool to construct new and flexible parametric families of distributions. We will show that the new constructions recover and generalise classical survival models such as the Proportional Hazards and Accelerated Failure Time models and apply the new methodology to English transplant data.


A Bayesian hidden Markov mixture model to detect over-expressed chromosome regions
Bambirra, Flávio
Federal University of Minas Gerais, Brazil

In this study, we propose a hidden Markov mixture model for the analysis of gene expression measurements mapped to chromosome locations. These expression values represent preprocessed light intensities observed in each probe of Affymetrix oligonucleotide arrays. Here, the algorithm BLAT is used to align thousands of probe sequences to each chromosome. The main goal is to identify genome regions associated with high expression values which define clusters composed by consecutive observations. The proposed model assumes a mixture distribution in which one of the components (the one with the highest expected value) is supposed to accommodate the over-expressed clusters. The model takes advantage of the serial structure of the data and uses the distance information between neighbours to infer about the existence of a Markov dependence. This dependence is crucially important in the detection of over-expressed regions. We propose and discuss a Markov chain Monte Carlo algorithm to fit the model. Finally, the proposed methodology is used to analyse five data sets representing three types of cancer (breast, ovarian and brain). This is joint work with Vinícius Mayrink.


Entropic Dynamics: from Entropy and Information Geometry to Quantum Mechanics
Caticha, Ariel
University at Albany USA

There is considerable evidence suggesting a deep connection between the fundamental laws of physics and information. Our goal here is to discuss the derivation of dynamical laws, and in particular, of quantum theory as an application of entropic methods of inference. In such an “Entropic Dynamics” there is no need to postulate an underlying action principle. Instead, the dynamics is driven by entropy subject to the constraints appropriate to the physical problem at hand. In this talk we review three examples of entropic dynamics. First we tackle the simpler case of a standard diffusion process which allows us to address the central issue of the nature of time. Then we show that imposing the additional constraint that the dynamics be non-dissipative leads to Hamiltonian dynamics. Finally, considerations from information geometry naturally lead to the type of Hamiltonian that describes quantum theory.


Modelling the kurtosis of spatio-temporal processes
Fonseca, Thais
Federal University of Rio de Janeiro – Brazil

This talk presents a new class of robust models for phenomena that vary continuously in space and time. In particular, the variance function, and therefore the covariance function, of the process is allowed to depend on spatial covariates. Thus, it is expected that the covariates help to explain spatial heterogeneity which is not accommodated by the mean function. The resulting model is non-stationary as the covariance function depends on spatial locations. The idea is to improve the explanation of variability of the process by allowing the kurtosis to vary spatially. This means that the marginal distributions for each location may have different tail behaviour changing according to covariates. The inference procedure is performed under the Bayesian framework. Two simulated examples illustrates how this proposal is able to model tranformed fields throught covariates and how it is able to capture the effect of heterogeneity in space caused by covariates. An illustration in the analysis of temperature data is presented. The temperature variance process is allowed to depend on altitude, which improves model fitting and prediction of new observations.


Never-Ending Learning to Populate and Extend an Ontology by reading the web
Hruschka Jr, Estevam R.
Federal University of São Carlos – Brazil

NELL (Never-Ending Language Learner) is a computer system that runs 24/7, forever, learning to read the web and, as a result, populating and extending its own ontology. NELL has two main tasks to be performed each day: i) extract (read) more facts from the web, and integrate these into its growing ontology; and ii) learn to read better than yesterday, enabling it to go back to the text it read yesterday, and today extract more facts, more accurately. This system has been running 24 hours/day for over seven years now. The result so far is an ontology having +100 million interconnected instances (e.g., servedWith(coffee, applePie), isA(applePie, bakedGood)), that NELL is considering at different levels of confidence, along with hundreds of thousands of learned phrasings, morphological features, and web page structures that NELL uses to extract beliefs from the web. The main motivation for building NELL is based on the belief that we will never really understand machine learning until we can build machines that learn many different things, over years, and become better learners over time.


EXONEST: The Bayesian Exoplanetary Explorer
Knuth, Kevin
University at Albany (SUNY), USA

The fields of astronomy and astrophysics are currently engaged in an unprecedented era of discovery as recent missions have revealed thousands of exoplanets orbiting other stars. While, the successful Kepler mission has enabled most of these exoplanets to be detected by identifying transiting events, exoplanets often exhibit additional photometric effects that can be used to improve characterization of transiting exoplanets as well as detect and characterize non-transiting exoplanets. The EXONEST Exoplanetary Explorer is a Bayesian exoplanet inference engine based on nested sampling, and designed to analyze archived Kepler and CoRoT data. EXONEST accommodates plug-and-play models of exoplanet-associated photometric effects for the purpose of exoplanet detection, characterization, and scientific hypothesis testing. The currently suite of models allows for both circular and eccentric orbits in conjunction with photometric effects, such as primary and secondary transits, reflected light, thermal emissions, ellipsoidal variations, Doppler beaming, and super-rotation. I will describe our discoveries to date, as well as our careful re-analysis of several known exoplanets, such as Kepler 13b, and the intriguing Kepler 91b, which has been suspected of having a Trojan partner. I will discuss the EXONEST inference engine design, and introduce our plans to make the EXONEST Exoplanetary Explorer into an open source project with the capability to employ third party plug-and-play models of exoplanet-related photometric effects.


Dynamics of a base-driven stick-slip oscillator
Sampaio, Rubens
Pontifical Catholic University of Rio de Janeiro, Brazil

In this paper the dynamics of a dry-friction oscillator driven by a stochastic base motion has been analyzed. The system consists of a simple oscillator (mass-spring) moving on a base with a rough surface. This roughness induces a dry-frictional force between the mass and the base which is modeled as a Coulomb friction. It is considered that the base has an imposed stochastic bang-bang motion which excites the system in a stochastic way. The non-smooth behavior of the dry-frictional force associated with the non-smooth stochastic base motion induces in the system stochastic stick-slip oscillations. A statistical model is constructed for the stick-slip dynamics of the system. The objective is to characterize, from a statistical view point, the response of the dry-friction oscillator composed by a sequence of stick and slip-modes. Defined a time interval for analysis, some of the variables which appear in this statistical model are the number of time intervals in which stick and slip occur, the instants at which they begin and their duration. These variables are modeled as stochastic objects. Statistics of them, as mean, variance and entropy, and histograms, are computed by the integration of the dynamics equations of the system using independent samples of the base movement generated with the Monte Carlo method.

Quantum Theory is not weird
Skilling, John
Maximum Entropy Data Consultants, Ireland

The domain of science is finite. Questionable assumptions about infinity or the continuum cannot possibly relate to practical observation. Big, yes. Infinite, no (we would have been instantly destroyed and would not be writing this account). Small, yes. Infinitesimal, no. Infinitesimals are unobservable, so can be excluded from science. If our results did depend on some infinitesimal, then it would become observable through that comparison between acceptance and denial, which it wasn’t. An unobservable assumption should not be and should never have been a required part of scientific theory.
Consequently, and following Cox (1946), we build our theories from small num- bers of objects and the relationships between them. From 1,2,3 objects, we build out to any finite number by induction. Going further “to infinity” would require extra assumptions to enable return from the limit, but there is no need to do that for science, and we keep our development finite and simple.
Mathematicians can and do develop careful theories about what we could do if we had the infinitely powerful technology to store and manipulate infinities. However, we finite beings neither possess nor need such powers.
It is known that elementary symmetries such as associativity, commutativity and order underlie and define the standard sum and product rules for classical scalar quantities like measure and probability. However, the same assumptions applied to binary interactions lead directly to the standard complex (two-dimensional) calculus of quantum theory. Investigation of objects that are so small that they are perturbed by observation requires a calculus of interaction between two components, typically treated as object and observer. And that calculus is quantum theory, intimately connected with probability through a shared and simple foundation.
Thought of as a theory of objects alone, quantum theory is weird. But the derivation shows quantum theory to be a theory of interactions in which objects leave traces on whatever they interact with in a finite world. Viewed this way in accordance with the derivation, the weirdness should disappear.


Uncertainty quantification for complex computer models
Toussaint, Udo
Max-Planck-Institut fuer Plasmaphysik, DE

The quantification of uncertainty for computer simulations is of increasing importance in science due to the increasing use of complex models but presents also a significant challenge. Bayesian and non-Bayesian probabilistic uncertainty quantification methods like polynomial chaos (PC) expansion methods or Gaussian processes have found increasing use over the recent years. The present contribution describes the use of Gaussian processes and recently developed (parallelizable) batch processing approaches for the propagation of uncertainty in computational models. The new approach will be demonstrated using an illustrative example and then applied to a real-world problem in plasma-wall interaction.


Tutorials:


Approximate Bayesian Computation tools for hierarchical models for Big Data
Mohammad-Djafari, Ali
Centre National de la Recherche Scientifique, France

Usually, methods evaluating system reliability require engineers to quantify the reliability of each of the system components. For series and parallel systems, there are some options to handle the estimation of each component’s reliability. We will treat the reliability estimation of complex problems of two classes of coherent systems: series-parallel, and parallel-series. In both of the cases, the component reliabilities may be unknown. We will present estimators for reliability functions at all levels of the system (component and system reliabilities). Nonparametric Bayesian estimators of all sub-distribution and distribution functions are derived, and a Dirichlet multivariate process as a prior distribution is presented. Parametric estimator of the component's reliability based on Weibull model is presented for any kind of system. Also, some ideas in systems with masked data are discussed.
In many applications, we can model the observations via a hierarchical models where the hidden variables play an essential role. This is the case in inverse problems in general, where the observed data g are linked to some hidden variables f which itself is modeled via another hidden variable z. we also have all the parameters theta of these variables which has to be infered from the data.
In general, the expression of the joint posterior law p(f,z,theta | g) is intractable, in particular when f and z are great dimentional. To be able to propose tractable Bayesian computation, there are different methods. We may mention: efficient sampling methods such as Nested sampling, but still for Big Data handeling, this method as well as all the MCMC methods cost too much to be used.
In this tutorial talk, I propose to give a synthetic view of Approximate Bayesian Computation (ABC) methods such as: Variational Bayesian Approximation (VBA), Expectation Propagation (EP) and Approximate Message Passing (AMP).
I will show some application in Computed Tomography and in biological data, signal and image classification and clustering.


Reliability Estimation in Coherent Systems
Rodrigues, Agatha S. (Univeristy of São Paulo, Brazil)
Pereira, Carlos (Univeristy of São Paulo, Brazil)
Polpo, Adriano (Federal Univeristy of São Carlos, Brazil)

Usually, methods evaluating system reliability require engineers to quantify the reliability of each of the system components. For series and parallel systems, there are some options to handle the estimation of each component’s reliability. We will treat the reliability estimation of complex problems of two classes of coherent systems: series-parallel, and parallel-series. In both of the cases, the component reliabilities may be unknown. We will present estimators for reliability functions at all levels of the system (component and system reliabilities). Nonparametric Bayesian estimators of all sub-distribution and distribution functions are derived, and a Dirichlet multivariate process as a prior distribution is presented. Parametric estimator of the component's reliability based on Weibull model is presented for any kind of system. Also, some ideas in systems with masked data are discussed.


A model of evolution for languages
Stern, Rafael Bassi
Federal Univeristy of São Carlos, Brazil

Historical Linguistics studies language change over time. If a group of languages derives from changes to a common ancestor language (proto-language) then they are said to be related. Whenever there exists a lack of written records for an ancestor language, a relevant question in Historical Linguistics is to determine whether two languages are related.
The gold standard for finding these relationships is the Comparative Method. Despite the success of the Comparative Method in finding language relationships, it suffers from at least two limitations. First, the Comparative Method involves the manual comparison of various features from a group of languages. Second, the Comparative Method doesn’t provide a numerical measure of evidence for how much the database under consideration corroborates an hypothesis.
Given the above limitations, the field of Computational Historical Linguistics is presented as a complement to the Comparative Method. This field has experienced a recent expansion with the adaptation of methods from biological phylogenetics. Nevertheless, there is debate whether the evolutionary models used in phylogenetics also incorporate valid linguistical assumptions.
In this tutorial, I'll present a model for infering the evolution of the phonology of languages. A relevant innovation of this model is that it captures the regularity of sound changes. In order to compute the probability of linguistic hypotheses regarding language relationships new algorithms were developed. The main problem that this algorithm overcomes is that it efficiently explores the possible regular sound changes, mutations in languages that simultaneously affect several words The algorithm is based on a new variant of Nested Sequential Monte Carlo that is used to explore the large space of language relationships and regular sound changes.


Methods for portfolio allocation
Takada, Hellinton
Itaú, Brazil

The Modern Portfolio Theory is introduced and the main portfolio allocation methodologies focused on computational optimization problems and statistical modeling. Specifically, it will highlight the aspects of maximum entropy and Bayesian inference are applied in this context. The tutorial will consider the following content: Modern theory of portfolios; Mean-Variance methodologies; Robust methodologies; Black-Litterman methodology; Risk Parity methodologies.