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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

关键词：

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 REVIEW OF MATHEMATICAL AND COMPUTATIONAL METHODS IN CANCER dynamics

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arXiv 2022年

作者： Uthamacumaran, Abicumaran Zenil, Hector MontrealQC Canada The Alan Turing Institute British Library LondonNW1 2DB United Kingdom Oxford Immune Algorithmics ReadingRG30 1EU United Kingdom Algorithmic Dynamics Lab Karolinska Institute Stockholm171 77 Sweden Algorithmic Nature Group LABORES Paris76006 France

Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multicellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems medicine. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems, and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored. © 2022, CC BY-SA.

关键词： Complex networks

SuperARC: An Agnostic Test for Narrow, General, and Super Intelligence Based On the Principles of Causal Recursive Compression and algorithmic Probability

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arXiv 2025年

作者： Hernández-Espinosa, Alberto Ozelim, Luan Abrahão, Felipe S. Zenil, Hector Oxford Immune Algorithmics Oxford University Innovation London Institute for Healthcare Engineering United Kingdom Algorithmic Dynamics Lab Center of Molecular Medicine Karolinska Institute & King’s College London United Kingdom Brazil Brazil Department of Biomedical Computing Department of Digital Twins School of Biomedical Engineering and Imaging Sciences United Kingdom King’s Institute for Artificial Intelligence King’s College London United Kingdom

We introduce an open-ended test grounded in algorithmic probability that can avoid benchmark contamination in the quantitative evaluation of frontier models in the context of their Artificial General Intelligence (AGI) and Superintelligence (ASI) claims. Unlike other tests, this test does not rely on statistical compression methods (such as GZIP or LZW), which are more closely related to Shannon entropy than to Kolmogorov complexity and are not able to test beyond simple pattern matching. The test challenges aspects of AI, in particular LLMs, related to features of intelligence of fundamental nature such as synthesis and model creation in the context of inverse problems (generating new knowledge from observation). We argue that metrics based on model abstraction and abduction (optimal Bayesian ‘inference’) for predictive ‘planning’ can provide a robust framework for testing intelligence, including natural intelligence (human and animal), narrow AI, AGI, and ASI. We found that LLM model versions tend to be fragile and incremental as a result of memorisation only with progress likely driven by the size of training data. The results were compared with a hybrid neurosymbolic approach that theoretically guarantees universal intelligence based on the principles of algorithmic probability and Kolmogorov complexity. The method outperforms LLMs in a proof-of-concept on short binary sequences. We prove that compression is equivalent and directly proportional to a system’s predictive power and vice versa. That is, if a system can better predict it can better compress, and if it can better compress, then it can better predict. Our findings strengthen the suspicion regarding the fundamental limitations of LLMs, exposing them as systems optimised for the perception of mastery over human language. Copyright © 2025, The Authors. All rights reserved.

关键词： Inverse problems

Non-Random Data Encodes Its Geometric and Topological Dimensions

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arXiv 2024年

作者： Zenil, Hector Abrahão, Felipe S. Ozelim, Luan School of Biomedical Engineering and Imaging Sciences King’s College London United Kingdom The Alan Turing Institute British Library United Kingdom King’s Institute for Artificial Intelligence King’s College London United Kingdom The Arrival Institute United Kingdom Oxford Immune Algorithmics Oxford University Innovation United Kingdom Algorithmic Dynamics Lab Center for Molecular Medicine Karolinska Institutet Sweden Brazil Brazil

Based on the principles of information theory, measure theory, and theoretical computer science, we introduce a signal deconvolution method with a wide range of applications to coding theory, particularly in zero-knowledge one-way communication channels, such as in deciphering messages (i.e., objects embedded into multidimensional spaces) from unknown generating sources about which no prior knowledge is available and to which no return message can be sent. Our multidimensional space reconstruction method from an arbitrary received signal is proven to be agnostic vis-à-vis the encoding-decoding scheme, computation model, programming language, formal theory, the computable (or semi-computable) method of approximation to algorithmic complexity, and any arbitrarily chosen (computable) probability measure. The method derives from the principles of an approach to Artificial General Intelligence (AGI) capable of building a general-purpose model of models independent of any arbitrarily assumed prior probability distribution. We argue that this optimal and universal method of decoding non-random data has applications to signal processing, causal deconvolution, topological and geometric properties encoding, cryptography, and bio- and technosignature detection. Copyright © 2024, The Authors. All rights reserved.

关键词： Topology

Assembly Theory is an approximation to algorithmic complexity based on LZ compression that does not explain selection or evolution

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arXiv 2024年

作者： Abrahão, Felipe S. Hernández-Orozco, Santiago Kiani, Narsis A. Tegnér, Jesper Zenil, Hector Oxford Immune Algorithmics Reading United Kingdom Center for Logic Epistemology and the History of Science University of Campinas Brazil DEXL National Laboratory for Scientific Computing Brazil Department of Oncology-Pathology Center for Molecular Medicine Karolinska Institutet Sweden Algorithmic Dynamics Lab Center for Molecular Medicine Karolinska Institutet Sweden Living Systems Lab KAUST Thuwal Saudi Arabia The Alan Turing Institute British Library London United Kingdom School of Biomedical Engineering and Imaging Sciences King’s College London Saudi Arabia

We prove the full equivalence between Assembly Theory (AT) and Shannon Entropy via a method based upon the principles of statistical compression renamed ‘assembly index’ that belongs to the LZ family of popular compression algorithms (ZIP, GZIP, JPEG). Such popular algorithms have been shown to empirically reproduce the results of AT, results that have also been reported before in successful applications to separating organic from non-organic molecules and in the context of the study of selection and evolution. We show that the assembly index value is equivalent to the size of a minimal context-free grammar. The statistical compressibility of such a method is bounded by Shannon Entropy and other equivalent traditional LZ compression schemes, such as LZ77, LZ78, or LZW. In addition, we demonstrate that AT, and the algorithms supporting its pathway complexity, assembly index, and assembly number, define compression schemes and methods that are subsumed into the theory of algorithmic (Kolmogorov-Solomonoff-Chaitin) complexity. Due to AT’s current lack of logical consistency in defining causality for non-stochastic processes and the lack of empirical evidence that it outperforms other complexity measures found in the literature capable of explaining the same phenomena, we conclude that the assembly index and the assembly number do not lead to an explanation or quantification of biases in generative (physical or biological) processes, including those brought about by (abiotic or Darwinian) selection and evolution, that could not have been arrived at using Shannon Entropy or that have not been reported before using classical information theory or algorithmic complexity. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

A review of methods for estimating algorithmic complexity: Options, challenges, and new directions

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arXiv 2020年

作者： Zenil, Hector Algorithmic Dynamics Lab Karolinska Institute Stockholm Sweden Oxford Immune Algorithmics Reading United Kingdom Algorithmic Nature Group LABORES Paris France

Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression to newer approaches that advance, complement and also pose new challenges and may exhibit their own limitations. Evidence suggesting that these different methods complement each other for different regimes is presented and despite their many challenges, some of these methods can be better motivated by and better grounded in the principles of algorithmic information theory. It will be explained how different approaches to algorithmic complexity can explore the relaxation of different necessary and sufficient conditions in their pursuit of numerical applicability, with some of these approaches entailing greater risks than others in exchange for greater relevance. We conclude with a discussion of possible directions that may or should be taken into consideration to advance the field and encourage methodological innovation, but more importantly, to contribute to scientific discovery. This paper also serves as a rebuttal of claims made in a previously published minireview by another author, and offers an alternative account. Copyright © 2020, The Authors. All rights reserved.

关键词： Computational complexity