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Unsupervised Satellite Image Segmentation using a Bivariate Beta type-II Mixture Model

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Unsupervised Satellite Image Segmentation using a Bivariate ...

IEEE International Conference on Computational Cybernetics

作者： Taher Ben Arab Mourad Zribi Afif Masmoudi Laboratoire d'Informatique Signal et Image de la Cote d'Opale (LISIC-EA 4491) ULCO 50 Rue Ferdinand Buisson BP 719 62228 Calais Cedex France. Laboratoire de Probabilités et Statistique Faculté des Sciences de Sfax Université de Sfax. B. P. 1171 Sfax Laboratoire d'Informatique Signal et Image de la C?te d'Opale (LISIC-EA 4491) ULCO 50 Rue Ferdinand Buisson BP 719 62228 Calais Cedex France. Laboratoire de Probabilités et Statistique Faculté des Sciences de Sfax Université de Sfax. B. P. 1171 Sfax Tunisie.

ISBN: (纸本)9781479900626

This paper presents an unsupervised satellite color image segmentation approach based on Bivariate Beta type-II. Such a method could be considered as original since it uses a K-Means clustering algorithm in order to initialize the image class number. Moreover, it exploits a Bivariate Beta type-II for statistical distributions applying it for each class. Satellite image exploitation requires the use of different approaches, especially those based on the unsupervised statistical segmentation principle. Such approaches necessitate the definition of several parameters such as image class number, class variables estimation and mixture distributions. The use of statistical image attributes has allowed us to get convincing results, provided that we ensure under the condition of having an initialization step with appropriate statistical distributions. Bivariate Beta type-II associated with a K-means clustering algorithm and expectation-maximization (EM) algorithm could be adapted to such a problem. For each image class, Bivariate Beta type-II attributes a specific distribution type according to different parameters. Different adapted algorithms (namely K-Means clustering algorithm, EM algorithm and Bivariate Beta type-II algorithm) are then applied to the satellite image segmentation problem. The efficiency of those combined algorithms is validated with the Mean Squared Errors (MSE), Signal to Noise Ratio (SNR) and Maximum Distance (MD).

关键词： Bivariate Beta type-II expectation maximization algorithm K-means clustering algorithm Mean Squared Errors Unsupervised color image segmentation

The Generalization Error of Machine Learning algorithms

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arXiv 2024年

作者： Perlaza, Samir M. Zou, Xinying INRIA Centre Inria d’Université Côte d’Azur Sophia Antipolis06902 France The Department of Electrical and Computer Engineering Princeton University PrincetonNJ08544 United States The GAATI Mathematics Laboratory University of French Polynesia Faaa98702 French Polynesia

In this paper, the method of gaps, a technique for deriving closed-form expressions in terms of information measures for the generalization error of machine learning algorithms is introduced. The method relies on two central observations: (a) The generalization error is an average of the variation of the expected empirical risk with respect to changes on the probability measure (used for expectation);and (b) these variations, also referred to as gaps, exhibit closed-form expressions in terms of information measures. The expectation of the empirical risk can be either with respect to a measure on the models (with a fixed dataset) or with respect to a measure on the datasets (with a fixed model), which results in two variants of the method of gaps. The first variant, which focuses on the gaps of the expected empirical risk with respect to a measure on the models, appears to be the most general, as no assumptions are made on the distribution of the datasets. The second variant develops under the assumption that datasets are made of independent and identically distributed data points. All existing exact expressions for the generalization error of machine learning algorithms can be obtained with the proposed method. Also, this method allows obtaining numerous new exact expressions, which improves the understanding of the generalization error;establish connections with other areas in statistics, e.g., hypothesis testing;and potentially, might guide algorithm designs. © 2024, CC BY.

关键词： expectation maximization algorithm

Fitting Multilevel Factor Models

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arXiv 2024年

作者： Parshakova, Tetiana Hastie, Trevor Boyd, Stephen

We examine a special case of the multilevel factor model, with covariance given by multilevel low rank (MLR) matrix [PHDB24]. We develop a novel, fast implementation of the expectation-maximization (EM) algorithm, tailored for multilevel factor models, to maximize the likelihood of the observed data. This method accommodates any hierarchical structure and maintains linear time and storage complexities per iteration. This is achieved through a new efficient technique for computing the inverse of the positive definite MLR matrix. We show that the inverse of an invertible PSD MLR matrix is also an MLR matrix with the same sparsity in factors, and we use the recursive Sherman-Morrison-Woodbury matrix identity to obtain the factors of the inverse. Additionally, we present an algorithm that computes the Cholesky factorization of an expanded matrix with linear time and space complexities, yielding the covariance matrix as its Schur complement. This paper is accompanied by an open-source package that implements the proposed *** Codes 62H12 Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Quasi-likelihood-based EM algorithm for regime-switching SDE

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arXiv 2024年

作者： Cheng, Yuzhong Masuda, Hiroki Graduate School of Mathematics Kyushu University 744 Motooka Nishi-ku Fukuoka819-0395 Japan Graduate School of Mathematical Sciences University of Tokyo 3-8-1 Komaba Meguro-ku Tokyo153-8914 Japan

This paper considers estimating the parameters in a regime-switching stochastic differential equation(SDE) driven by Normal Inverse Gaussian(NIG) noise. The model under consideration incorporates a continuous-time finite state Markov chain to capture regime changes, enabling a more realistic representation of evolving market conditions or environmental factors. Although the continuous dynamics are typically observable, the hidden nature of the Markov chain introduces significant complexity, rendering standard likelihood-based methods less effective. To address these challenges, we propose an estimation algorithm designed for discrete, high-frequency observations, even when the Markov chain is not directly observed. Our approach integrates the expectation-maximization (EM) algorithm, which iteratively refines parameter estimates in the presence of latent variables, with a quasi-likelihood method adapted to NIG noise. Notably, this method can simultaneously estimate parameters within both the SDE coefficients and the driving noise. Simulation results are provided to evaluate the performance of the algorithm. These experiments demonstrate that the proposed method provides reasonable estimation under challenging conditions. © 2024, CC BY.

关键词： expectation maximization algorithm

In-context Learning for Mixture of Linear Regressions: Existence, Generalization and Training Dynamics

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arXiv 2024年

作者： Jin, Yanhao Balasubramanian, Krishnakumar Lai, Lifeng Department of Statistics University of California Davis United States Department of Electrical and Computer Engineering University of California Davis United States

We investigate the in-context learning capabilities of transformers for the d-dimensional mixture of linear regression model, providing theoretical insights into their existence, generalization bounds, and training dynamics. Specifically, we prove that there exists a transformer capable of achieving a prediction error of order O(√d/n) with high probability, where n represents the training prompt size in the high signal-to-noise ratio (SNR) regime. Moreover, we derive in-context excess risk bounds of order O(L/√B) for the case of two mixtures, where B denotes the number of training prompts, and L represents the number of attention layers. The dependence of L on the SNR is explicitly characterized, differing between low and high SNR settings. We further analyze the training dynamics of transformers with single linear self-attention layers, demonstrating that, with appropriately initialized parameters, gradient flow optimization over the population mean square loss converges to a global optimum. Extensive simulations suggest that transformers perform well on this task, potentially outperforming other baselines, such as the expectation-maximization algorithm. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

A Large Confirmatory Dynamic Factor Model for Stock Market Returns in Different Time Zones

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arXiv 2022年

作者： Linton, Oliver B. Tang, Haihan Wu, Jianbin Faculty of Economics University of Cambridge Austin Robinson Building Sidgwick Avenue CambridgeCB3 9DD United Kingdom International School of Finance Fudan University 220 Handan Road Yangpu District Shanghai200433 China School of Business Nanjing University 22 Hankou Road Gulou District Nanjing210093 China

We propose a confirmatory dynamic factor model for a large number of stocks whose returns are observed daily across multiple time zones. The model has a global factor and a continental factor that both drive the individual stock return series. We propose two estimators of the model: a quasi-maximum likelihood estimator (QML-just-identified), and an improved estimator based on an expectation maximization (EM) algorithm (QML-all-res). Our estimators are consistent and asymptotically normal under the large approximate factor model setting. In particular, the asymptotic distributions of QML-all-res are the same as those of the infeasible OLS estimators that treat factors as known and utilize all the restrictions on the parameters of the model. We apply the model to MSCI equity indices of 42 developed and emerging markets, and find that most markets are more integrated when the CBOE Volatility Index (VIX) is high. © 2022, CC BY-NC-ND.

关键词： expectation maximization algorithm

A Thorough Comparison Between Independent Cascade and Susceptible-Infected-Recovered Models

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arXiv 2024年

作者： Liu, Panfeng Qiu, Guoliang Tao, Biaoshuai Yang, Kuan Shanghai Jiao Tong University China

We study cascades in social networks with the independent cascade (IC) model and the Susceptible-Infected-recovered (SIR) model. The well-studied IC model fails to capture the feature of node recovery, and the SIR model is a variant of the IC model with the node recovery feature. In the SIR model, by computing the probability that a node successfully infects another before its recovery and viewing this probability as the corresponding IC parameter, the SIR model becomes an "out-going-edge-correlated" version of the IC model: the events of the infections along different out-going edges of a node become dependent in the SIR model, whereas these events are independent in the IC model. In this paper, we thoroughly compare the two models and examine the effect of this extra dependency in the SIR model. By a carefully designed coupling argument, we show that the seeds in the IC model have a stronger influence spread than their counterparts in the SIR model, and sometimes it can be significantly stronger. Specifically, we prove that, given the same network, the same seed sets, and the parameters of the two models being set based on the above-mentioned equivalence, the expected number of infected nodes at the end of the cascade for the IC model is weakly larger than that for the SIR model, and there are instances where this dominance is significant. We also study the influence maximization problem (the optimization problem of selecting a set of nodes as initial seeds in a social network to maximize their influence) with the SIR model. We show that the above-mentioned difference in the two models yields different seed-selection strategies, which motivates the design of influence maximization algorithms specifically for the SIR model. We design efficient approximation algorithms with theoretical guarantees by adapting the reverse-reachable-set-based algorithms, commonly used for the IC model, to the SIR model. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Learning Submodular Sequencing from Samples

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arXiv 2024年

作者： Yuan, Jing Tang, Shaojie Department of Computer Science and Engineering The University of North Texas United States Department of Management Science and Systems University at Buffalo United States

This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility function, we assume that we are given only a set of samples. Each sample includes a random sequence of items and its associated utility. We present an algorithm that, given polynomially many samples drawn from a two-stage uniform distribution, achieves an approximation ratio dependent on the curvature of individual submodular functions. Our results apply in a wide variety of real-world scenarios, such as ranking products in online retail platforms, where complete knowledge of the utility function is often impossible to obtain. Our algorithm gives an empirically useful solution in such contexts, thus proving that limited data can be of great use in sequencing tasks. From a technical perspective, our results extend prior work on "optimization from samples" by generalizing from optimizing a set function to a sequence-dependent function. © 2024, CC BY.

关键词： expectation maximization algorithm

Fitting Multiple Machine Learning Models with Performance Based Clustering

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arXiv 2024年

作者： Lorasdagi, Mehmet E. Koc, Ahmet B. Koc, Ali T. Kozat, Suleyman S. The Department of Electrical and Electronics Engineering Bilkent University Turkey

Traditional machine learning approaches assume that data comes from a single generating mechanism, which may not hold for most real life data. In these cases, the single mechanism assumption can result in suboptimal performance. We introduce a clustering framework that eliminates this assumption by grouping the data according to the relations between the features and the target values, and we obtain multiple separate models to learn different parts of the data. We further extend our framework to applications having streaming data where we produce outcomes using an ensemble of models. For this, the ensemble weights are updated based on the incoming data batches. We demonstrate the performance of our approach over the widely-studied real life datasets, showing significant improvements over the traditional single-model approaches. © 2024, CC BY-NC-ND.

关键词： expectation maximization algorithm