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A Fully Bayesian Inference Approach for Multivariate McDonald's Beta Mixture Model with Feature Selection 9

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A Fully Bayesian Inference Approach for Multivariate McDonal...

9th International Conference on Control, Decision and Information Technologies, CoDIT 2023

作者： Forouzanfar, Darya Manouchehri, Narges Bouguila, Nizar Karolinska Institute Algorithmic Dynamics Lab Unit of Computational Medicine Stockholm171 77 Sweden Concordia University Concordia Institute for Information Systems Engineering Montreal Canada

ISBN: (纸本)9798350311402

Mixture models are widely used in unsupervised machine learning applications where annotating a large amount of data is not feasible. They have succeeded in various real-world problems, including medical applications, human activity recognition, and anomaly detection. This paper proposes a fully Bayesian analysis of the multivariate McDonald's Beta mixture model (McDBMM) using Gibbs sampling method and Metropolis-Hastings to estimate parameters. In addition, we integrated a feature selection technique which simultaneously determines the most relevant features for our mixture model. This allows for the simultaneous selection of the most relevant features, improving the accuracy and efficiency of the unsupervised learning process. Our approach is evaluated on challenging applications, including lung cancer image analysis and human activity recognition. Experimental results indicate that our proposed method is an effective solution compared to the Gaussian mixture model (GMM). © 2023 IEEE.

关键词： Medical applications

A Nonparametric Bayesian Framework for Multivariate Libby-Novick Beta Mixture Models

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A Nonparametric Bayesian Framework for Multivariate Libby-No...

International Conference on Control, Decision and Information Technologies (CoDIT)

作者： Niloufar Samiee Narges Manouchehri Nizar Bouguila Concordia Institute for Information Systems Engineering (CIISE) Concordia University Montreal Canada Algorithmic Dynamics Lab Unit of Computational Medicine Karolinska Institute Stockholm Sweden

ISBN: (数字)9798350373974

ISBN: (纸本)9798350373981

This work presents a nonparametric Bayesian approach that utilizes a mixture of multivariate Libby-Novick Beta distributions to address clustering challenges. When using mixtures, model selection is a significant obstacle. As a solution to this problem, we extend the finite Libby-Novick Beta mixture model (FLNBMM)to the infinite case. This enables us to accurately represent the data distribution by accommodating an unspecified number of mixture components. We develop a Bayesian inference strategy based on Markov Chain Monte Carlo to estimate the posterior distribution, which provides strong power and flexibility for modeling and analyzing complicated data. Our suggested method’s effectiveness is assessed on three applications and contrasted with that of FLNBMM, the infinite Gaussian mixture model (IGMM), and the finite Gaussian mixture model (FGMM) to show the efficacy of our methodology. It is evident from the results that our proposed model is a good alternative.

关键词： Analytical models Monte Carlo methods Process control Mixture models Data models Bayes methods Information technology Gaussian mixture model

A Fully Bayesian Inference Approach for Multivariate McDonald's Beta Mixture Model with Feature Selection

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A Fully Bayesian Inference Approach for Multivariate McDonal...

International Conference on Control, Decision and Information Technologies (CoDIT)

作者： Darya Forouzanfar Narges Manouchehri Nizar Bouguila Concordia University Concordia Institute for Information Systems Engineering Montreal Canada Algorithmic Dynamics Lab Unit of Computational Medicine Karolinska Institute Stockholm Sweden

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Maximum Likelihood-Based Estimation of Finite Multivariate Libby-Novick Beta Mixture Models in Medical Applications

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Maximum Likelihood-Based Estimation of Finite Multivariate L...

IEEE International Conference on Industrial Technology (ICIT)

作者： Niloufar Samiee Narges Manouchehri Nizar Bouguila Concordia Institute for Information Systems Engineering (CIISE) Concordia University Montreal QC Canada Algorithmic Dynamics Lab Unit of Computational Medicine Karolinska Institute Stockholm Sweden

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A computable piece of uncomputable art whose expansion may explain the universe in software space

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arXiv 2021年

作者： Zenil, Hector Oxford Immune Algorithmics Reading United Kingdom The Alan Turing Institute British Library London United Kingdom Algorithmic Dynamics Lab Unit of Computational Medicine Center for Molecular Medicine Karolinska Institute Stockholm Sweden Algorithmic Nature Group LABORES for the Natural and Digital Sciences Paris France

At the intersection of what I call uncomputable art and computational epistemology, a form of experimental philosophy, we find a most exciting and promising areas of science related to causation with an alternative, possibly best possible, solution to the challenge of the inverse problem. That is, the problem of finding the possible causes, mechanistic origins, first principles, and generative models of a piece of data from a physical phenomenon. Here we explain how generating and exploring software space following the framework of algorithmic Information dynamics, it is possible to find small models and learn to navigate a sci-fi-looking space that can advance the field of scientific discovery with complementary tools to offer an opportunity to advance science itself. Copyright © 2021, The Authors. All rights reserved.

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A SIMPLICITY BUBBLE PROBLEM IN FORMAL-THEORETIC LEARNING SYSTEMS

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arXiv 2021年

作者： Abrahão, Felipe S. Zenil, Hector Porto, Fabio Winter, Michael Wehmuth, Klaus D'Ottaviano, Itala M.L. Brazil RJ Petropolis Brazil for the Natural and Digital Sciences Paris France Machine Learning Group Department of Chemical Engineering and Biotechnology The University of Cambridge United Kingdom Oxford Immune Algorithmics England United Kingdom Algorithmic Dynamics Lab Unit of Computational Medicine Department of Medicine Solna Center for Molecular Medicine Karolinska Institute Stockholm Sweden

When mining large datasets in order to predict new data, limitations of the principles behind statistical machine learning pose a serious challenge not only to the Big Data deluge, but also to the traditional assumptions that data generating processes are biased toward low algorithmic complexity. Even when one assumes an underlying algorithmic-informational bias toward simplicity in finite dataset generators, we show that current approaches to machine learning (including deep learning, or any formal-theoretic hybrid mix of top-down AI and statistical machine learning approaches), can always be deceived, naturally or artificially, by sufficiently large datasets. In particular, we demonstrate that, for every learning algorithm (with or without access to a formal theory), there is a sufficiently large dataset size above which the algorithmic probability of an unpredictable deceiver is an upper bound (up to a multiplicative constant that only depends on the learning algorithm) for the algorithmic probability of any other larger dataset. In other words, very large and complex datasets can deceive learning algorithms into a "simplicity bubble" as likely as any other particular non-deceiving dataset. These deceiving datasets guarantee that any prediction effected by the learning algorithm will unpredictably diverge from the high-algorithmic-complexity globally optimal solution while converging toward the low-algorithmic-complexity locally optimal solution, although the latter is deemed a global one by the learning algorithm. We discuss the framework and additional empirical conditions to be met in order to circumvent this deceptive phenomenon, moving away from statistical machine learning towards a stronger type of machine learning based on, and motivated by, the intrinsic power of algorithmic information theory and computability theory. Copyright © 2021, The Authors. All rights reserved.

关键词： Large dataset

IHCV: Discovery of Hidden Time-Dependent Control Variables in NonLinear Dynamical Systems

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arXiv 2023年

作者： Munoz, Juan Balsamy, Subash Bernal-Tamayo, Juan P. Balubaid, Ali Ruiz de Infante, Alberto Maillo Lagani, Vincenzo Gomez-Cabrero, David Kiani, Narsis A. Tegner, Jesper Thuwal23955-6900 Saudi Arabia Thuwal23955-6900 Saudi Arabia IdiSNA Pamplona Spain SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence Thuwal23952 Saudi Arabia Institute of Chemical Biology Ilia State University Tbilisi0162 Georgia Algorithmic Dynamic Lab Department of Oncology and pathology Karolinska Institute Stockholm Sweden Unit of Computational Medicine Department of Medicine Center for Molecular Medicine Karolinska Institutet Karolinska University Hospital L8:05 StockholmSE-171 76 Sweden Science for Life Laboratory Tomtebodavagen 23A SolnaSE-17165 Sweden

Discovering non-linear dynamical models from data is at the core of science. Recent progress hinges upon sparse regression of observables using extensive libraries of candidate functions. However, it remains challenging to model hidden non-observable control variables governing switching between different dynamical *** Codes 37M20 © 2023, CC BY.

关键词： Nonlinear dynamical systems

Emergence and algorithmic information dynamics of systems and observers

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arXiv 2021年

作者： Abrahão, Felipe S. Zenil, Hector RJ Petropolis25651-075 Brazil the Natural and Digital Sciences Paris75005 France Oxford Immune Algorithmics ReadingRG1 3EU United Kingdom Alan Turing Institute British Library 2QR 96 Euston Rd LondonNW1 2DB United Kingdom Algorithmic Dynamics Lab Unit of Computational Medicine Department of Medicine Solna Center for Molecular Medicine Karolinska Institute StockholmSE-171 77 Sweden

Previous work has shown that perturbation analysis in software space can produce candidate computable generative models and uncover possible causal properties from the finite description of an object or system quantifying the algorithmic contribution of each of its elements relative to the whole. One of the challenges for defining emergence is that one observer's prior knowledge may cause a phenomenon to present itself to such observer as emergent while for another as reducible. By formalising the act of observing as mutual perturbations between dynamical systems, we demonstrate that emergence of algorithmic information do depend on the observer's formal knowledge, while robust to other subjective factors, particularly: the choice of the programming language and the measurement method;errors or distortions during the information acquisition;and the informational cost of processing. This is called observer-dependent emergence (ODE). In addition, we demonstrate that the unbounded and fast increase of emergent algorithmic information implies asymptotically observer-independent emergence (AOIE). Unlike ODE, AOIE is a type of emergence for which emergent phenomena will remain considered to be emergent for every formal theory that any observer might devise. We demonstrate the existence of an evolutionary model that displays the diachronic variant of AOIE and a network model that displays the holistic variant of AOIE. Our results show that, restricted to the context of finite discrete deterministic dynamical systems, computable systems, and irreducible information content measures, AOIE is the strongest form of emergence that formal theories can attain. Copyright © 2021, The Authors. All rights reserved.

关键词： Dynamical systems

An algorithmic information distortion in multidimensional networks

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arXiv 2020年

作者： Abrahão, Felipe S. Wehmuth, Klaus Zenil, Hector Ziviani, Artur Petropolis RJ25651-075 Brazil Oxford Immune Algorithmics RG1 3EU Reading U.K. Algorithmic Dynamics Lab Unit of Computational Medicine Department of Medicine Solna Center for Molecular Medicine Karolinska Institute StockholmSE-171 77 Sweden for the Natural and Digital Sciences Paris75005 France

Network complexity, network information content analysis, and lossless compressibility of graph representations have been played an important role in network analysis and network modeling. As multidimensional networks, such as time-varying, multilayer, or dynamic multilayer networks, gain more relevancy in network science, it becomes crucial to investigate in which situations universal algorithmic methods based on algorithmic information theory applied to graphs cannot be straightforwardly imported into the multidimensional case. In this direction, as a worst-case scenario of lossless compressibility distortion that increases linearly with the number of distinct dimensions, this article presents a counter-intuitive phenomenon that occurs when dealing with networks within non-uniform and sufficiently large multidimensional spaces. In particular, we demonstrate that the algorithmic information necessary to encode multidimensional networks that are isomorphic to logarithmically compressible monoplex networks may display exponentially larger distortions in the general case. Copyright © 2020, The Authors. All rights reserved.

关键词： Compressibility