Relevant bibliographies by topics / Bernoulli-Gaussian

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  1. Journal articles
  2. Dissertations / Theses
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Academic literature on the topic 'Bernoulli-Gaussian'

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Published: 25 May 2024

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Journal articles on the topic "Bernoulli-Gaussian"

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Hrabovets, Anastasiia. "Feynman diagrams and their limits for Bernoulli noise." Theory of Stochastic Processes 27(43), no. 1 (November 16, 2023): 11–30. http://dx.doi.org/10.3842/tsp-4311781209-33.

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In this article, we will construct an approximation of Gaussian white noise based on the sequence of Bernoulli random variables and define Wick products and the stochastic exponent for the Bernoulli case. Here we will propose a method to calculate the expectations of Wick products for Bernoulli noise using diagrams, that converge to Feynman diagrams in the Gaussian case. We will prove that orthogonal polynomials for Bernoulli noise converge to Hermite polynomials, which form an orthogonal system in the Gaussian case.
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Törő, Olivér, Tamás Bécsi, Szilárd Aradi, and Péter Gáspár. "IMM Bernoulli Gaussian Particle Filter." IFAC-PapersOnLine 51, no. 22 (2018): 274–79. http://dx.doi.org/10.1016/j.ifacol.2018.11.554.

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Xie, Shaohao, Shaohua Zhuang, and Yusong Du. "Improved Bernoulli Sampling for Discrete Gaussian Distributions over the Integers." Mathematics 9, no. 4 (February 13, 2021): 378. http://dx.doi.org/10.3390/math9040378.

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Discrete Gaussian sampling is one of the fundamental mathematical tools for lattice-based cryptography. In this paper, we revisit the Bernoulli(-type) sampling for centered discrete Gaussian distributions over the integers, which was proposed by Ducas et al. in 2013. Combining the idea of Karney’s algorithm for sampling from the Bernoulli distribution Be−1/2, we present an improved Bernoulli sampling algorithm. It does not require the use of floating-point arithmetic to generate a precomputed table, as the original Bernoulli sampling algorithm did. It only needs a fixed look-up table of very small size (e.g., 128 bits) that stores the binary expansion of ln2. We also propose a noncentered version of Bernoulli sampling algorithm for discrete Gaussian distributions with varying centers over the integers. It requires no floating-point arithmetic and can support centers of precision up to 52 bits. The experimental results show that our proposed algorithms have a significant improvement in the sampling efficiency as compared to other rejection algorithms.
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Finamore, Weiler, Marcelo Pinho, Manish Sharma, and Moises Ribeiro. "Modeling Noise as a Bernoulli-Gaussian Process." Journal of Communication and Information Systems 38 (2023): 175–86. http://dx.doi.org/10.14209/jcis.2023.20.

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Transmission medium is always perturbed by noise with a random nature which can be characterized by taking a sequence of noise samples and, after analyzing the sequence, attributing a probabilistic model to represent the randomness of the noise. If thermal noise (receiver generated) is the only noise impairing the transmission (our only focus is digital transmission) the memoryless stationary discrete-time Gaussian process is the best model to probabilistically represent the noise. The mathematical representation of the transmission medium in such a situation yields the well known Gaussian Channel. As Information Theory points out, for a fixed noise power, the Gaussian channel is the worst channel to send information through. If thermal noise is not the only noise impairing the transmission (as in sonar communication and power line communication) finding the probabilistic model other than the single-parameter Gaussian process, which best match the noise can much improve the communication system design. The Bernoulli-Gaussian process, a three parameters model, is a common considered option. Finding the three parameters of the Bernoulli-Gaussian model (from known noise samples) is a formidable task that can be made simpler by considering the (original) results presented in the current paper. The Bernoulli-Gaussian model can be characterized, analytically, by using the noise power and two additional quantities: the expectation of the absolute value of the noise process plus the expected value of the third power of the absolute value. In practice the parameters would be calculated using estimates of the mentioned expected values. The communication system design can be much improved if a well fit Bernoulli-Gaussian stochastic process is selected to model the noise. This is an alternative to model the communication using power lines which is often modeled as Middleton Class-A. The rate harvested when modeling the medium as a Bernoulli-Gaussian channel, it is shown, is increased when compared to modeling the medium with the easily obtained Gaussian channel.
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Bobkov, Sergey G., Friedrich Gotze, and Christian Houdre. "On Gaussian and Bernoulli Covariance Representations." Bernoulli 7, no. 3 (June 2001): 439. http://dx.doi.org/10.2307/3318495.

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Lavielle, Marc. "Bayesian deconvolution of Bernoulli-Gaussian processes." Signal Processing 33, no. 1 (July 1993): 67–79. http://dx.doi.org/10.1016/0165-1684(93)90079-p.

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De La Rue, Thierry. "Systèmes dynamiques gaussiens d'entropie nulle, lâchement et non lâchement Bernoulli." Ergodic Theory and Dynamical Systems 16, no. 2 (April 1996): 379–404. http://dx.doi.org/10.1017/s0143385700008865.

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AbstractWe construct two real Gaussian dynamical systems of zero entropy; the first one is not loosely Bernoulli, and the second is a loosely Bernoulli Gaussian-Kronecker system. To get loose-Bernoullicity for the second system, we prove and use a property of planar Brownian motion on [0, 1]: we can recover the whole trajectory knowing only some angles formed by the motion.
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Al-Zuhairi, Dheyaa T., and Abbas Salman Hameed. "DOA estimation under Bernoulli-Gaussian impulsive noise." IOP Conference Series: Materials Science and Engineering 1090, no. 1 (March 1, 2021): 012096. http://dx.doi.org/10.1088/1757-899x/1090/1/012096.

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Chong-Yung Chi and J. Mendel. "Viterbi algorithm detector for Bernoulli-Gaussian processes." IEEE Transactions on Acoustics, Speech, and Signal Processing 33, no. 3 (June 1985): 511–19. http://dx.doi.org/10.1109/tassp.1985.1164580.

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Talagrand, Michel. "Gaussian averages, Bernoulli averages, and Gibbs' measures." Random Structures and Algorithms 21, no. 3-4 (October 2002): 197–204. http://dx.doi.org/10.1002/rsa.10059.

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Dissertations / Theses on the topic "Bernoulli-Gaussian"

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Gaerke, Tiffani M. "Characteristic Functions and Bernoulli-Gaussian Impulsive Noise Channels." University of Akron / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1408040080.

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Vu, Hung Van. "Capacities of Bernoulli-Gaussian Impulsive Noise Channels in Rayleigh Fading." University of Akron / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1407370145.

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Boudineau, Mégane. "Vers la résolution "optimale" de problèmes inverses non linéaires parcimonieux grâce à l'exploitation de variables binaires sur dictionnaires continus : applications en astrophysique." Thesis, Toulouse 3, 2019. http://www.theses.fr/2019TOU30020/document.

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Cette thèse s'intéresse à la résolution de problèmes inverses non linéaires exploitant un a priori de parcimonie ; plus particulièrement, des problèmes où les données se modélisent comme la combinaison linéaire d'un faible nombre de fonctions non linéaires en un paramètre dit de " localisation " (par exemple la fréquence en analyse spectrale ou le décalage temporel en déconvolution impulsionnelle). Ces problèmes se reformulent classiquement en un problème d'approximation parcimonieuse linéaire (APL) en évaluant les fonctions non linéaires sur une grille de discrétisation arbitrairement fine du paramètre de localisation, formant ainsi un " dictionnaire discret ". Cependant, une telle approche se heurte à deux difficultés majeures. D'une part, le dictionnaire provenant d'une telle discrétisation est fortement corrélé et met en échec les méthodes de résolution sous-optimales classiques comme la pénalisation L1 ou les algorithmes gloutons. D'autre part, l'estimation du paramètre de localisation, appartenant nécessairement à la grille de discrétisation, se fait de manière discrète, ce qui entraîne une erreur de modélisation. Dans ce travail nous proposons des solutions pour faire face à ces deux enjeux, d'une part via la prise en compte de la parcimonie de façon exacte en introduisant un ensemble de variables binaires, et d'autre part via la résolution " optimale " de tels problèmes sur " dictionnaire continu " permettant l'estimation continue du paramètre de localisation. Deux axes de recherches ont été suivis, et l'utilisation des algorithmes proposés est illustrée sur des problèmes de type déconvolution impulsionnelle et analyse spectrale de signaux irrégulièrement échantillonnés. Le premier axe de ce travail exploite le principe " d'interpolation de dictionnaire ", consistant en une linéarisation du dictionnaire continu pour obtenir un problème d'APL sous contraintes. L'introduction des variables binaires nous permet de reformuler ce problème sous forme de " programmation mixte en nombres entiers " (Mixed Integer Programming - MIP) et ainsi de modéliser de façon exacte la parcimonie sous la forme de la " pseudo-norme L0 ". Différents types d'interpolation de dictionnaires et de relaxation des contraintes sont étudiés afin de résoudre de façon optimale le problème grâce à des algorithmes classiques de type MIP. Le second axe se place dans le cadre probabiliste Bayésien, où les variables binaires nous permettent de modéliser la parcimonie en exploitant un modèle de type Bernoulli-Gaussien. Ce modèle est étendu (modèle BGE) pour la prise en compte de la variable de localisation continue. L'estimation des paramètres est alors effectuée à partir d'échantillons tirés avec des algorithmes de type Monte Carlo par Chaîne de Markov. Plus précisément, nous montrons que la marginalisation des amplitudes permet une accélération de l'algorithme de Gibbs dans le cas supervisé (hyperparamètres du modèle connu). De plus, nous proposons de bénéficier d'une telle marginalisation dans le cas non supervisé via une approche de type " Partially Collapsed Gibbs Sampler. " Enfin, nous avons adapté le modèle BGE et les algorithmes associés à un problème d'actualité en astrophysique : la détection d'exoplanètes par la méthode des vitesses radiales. Son efficacité sera illustrée sur des données simulées ainsi que sur des données réelles
This thesis deals with solutions of nonlinear inverse problems using a sparsity prior; more specifically when the data can be modelled as a linear combination of a few functions, which depend non-linearly on a "location" parameter, i.e. frequencies for spectral analysis or time-delay for spike train deconvolution. These problems are generally reformulated as linear sparse approximation problems, thanks to an evaluation of the nonlinear functions at location parameters discretised on a thin grid, building a "discrete dictionary". However, such an approach has two major drawbacks. On the one hand, the discrete dictionary is highly correlated; classical sub-optimal methods such as L1- penalisation or greedy algorithms can then fail. On the other hand, the estimated location parameter, which belongs to the discretisation grid, is necessarily discrete and that leads to model errors. To deal with these issues, we propose in this work an exact sparsity model, thanks to the introduction of binary variables, and an optimal solution of the problem with a "continuous dictionary" allowing a continuous estimation of the location parameter. We focus on two research axes, which we illustrate with problems such as spike train deconvolution and spectral analysis of unevenly sampled data. The first axis focusses on the "dictionary interpolation" principle, which consists in a linearisation of the continuous dictionary in order to get a constrained linear sparse approximation problem. The introduction of binary variables allows us to reformulate this problem as a "Mixed Integer Program" (MIP) and to exactly model the sparsity thanks to the "pseudo-norm L0". We study different kinds of dictionary interpolation and constraints relaxation, in order to solve the problem optimally thanks to MIP classical algorithms. For the second axis, in a Bayesian framework, the binary variables are supposed random with a Bernoulli distribution and we model the sparsity through a Bernoulli-Gaussian prior. This model is extended to take into account continuous location parameters (BGE model). We then estimate the parameters from samples drawn using Markov chain Monte Carlo algorithms. In particular, we show that marginalising the amplitudes allows us to improve the sampling of a Gibbs algorithm in a supervised case (when the model's hyperparameters are known). In an unsupervised case, we propose to take advantage of such a marginalisation through a "Partially Collapsed Gibbs Sampler." Finally, we adapt the BGE model and associated samplers to a topical science case in Astrophysics: the detection of exoplanets from radial velocity measurements. The efficiency of our method will be illustrated with simulated data, as well as actual astrophysical data
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Barbault, Pierre. "Un ticket pour le sparse : de l'estimation des signaux et des paramètres en problèmes inverses bernoulli-gaussiens." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG049.

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L'imagerie par Magnéto/Électro Encéphalographie (M/EEG) peut servir à reconstruire les foyers d'activité cérébrale en mesurant le champ Électro Magnétique produit par ce dernier. Même si le temps caractéristique des signaux enregistrés est assez faible pour pouvoir envisager un modèle linéaire d'acquisition, le nombre de sources possibles reste très large face au nombre de capteurs. De fait, il s'agit là d'un problème mal posé et de surcroît de grande dimension. Afin de se ramener dans le cadre d'un problème qui admet une hypothèse courante, et qui fait sens pour les neurones, est que les sources sont parcimonieuses i.e. que le nombre de valeurs non-nulles est très petit. On modélise alors le problème d'un point de vue probabiliste en utilisant une distribution a priori Bernoulli-Gaussien (BG) pour les sources. Il existe de nombreuses méthodes qui permettent de résoudre un tel problème, mais la plupart d'entre elles font appel à une connaissance des paramètres de la loi BG. L'objectif de cette thèse est de proposer une approche entièrement non-supervisée qui permet d'estimer les paramètres de la loi BG ainsi que d'estimer les sources si possible. Pour ce faire les algorithmes d'Espérance-Maximisation (EM) sont explorés. Dans un premier temps, le cas le plus simple est traité : celui du débruitage où l'opérateur linéaire est l'identité. Dans ce cadre trois algorithmes sont proposés : Une méthode des Moments basée sur la statistique des données, un EM et un algorithme d'estimation jointe des sources et des paramètres. Les résultats montrent que l'EM initialisé par la méthode des Moments est le meilleur candidat pour l'estimation des paramètres. Dans un second temps, les résultats précédents sont étendus au cas général d'opérateurs linéaires quelconques grâce à l'introduction d'une variable latente. Cette variable, en découplant les sources des observations, permet de dériver des algorithmes dit 'latents' qui alternent entre une étape de descente de gradient et une étape de débruitage qui correspond exactement au problème traité précédemment. Les résultats montrent alors que la stratégie la plus efficace est l'utilisation de l'estimation jointe 'latente' qui initialise l'EM 'latent'. Enfin, la dernière partie de ces travaux est consacrée à des considérations théoriques concernant les choix d'estimateurs joints ou marginaux du support et/ou des sources dans le cas supervisé. Ces travaux montrent que l'on peut encadrer les fonctions de coûts associées aux problèmes marginaux par celles associées à des problèmes joints grâce à une reparamétrisation du problème. Cela permet alors de proposer une stratégie générale d'estimation basée sur l'initialisation d'algorithmes d'estimation marginale par des algorithmes d'estimation jointe
Magneto/Electro Encephalography (M/EEG) imaging can be used to reconstruct focal points of cerebral activity by measuring the Electro Magnetic field produced by it. Even if the characteristic time of the recorded signals is low enough to be able to consider a linear acquisition model, the number of possible sources remains very large compared to the number of sensors. In fact, this is an ill-posed and, moreover, a large-scale problem. In order to reduce it to a 'well-posed' problem, a common assumption, and which makes sense for neurons, is that the sources are sparse i.e. that the number of non-zero values is very small. We then model the problem from a probabilistic point of view using a Bernoulli-Gaussian (BG) a priori for the sources. There are many methods that can solve such a problem, but most of them require knowledge of the parameters of the BG law. The objective of this thesis is to propose a completely unsupervised approach which allows to estimate the parameters of the BG law as well as to estimate the sources if possible. To do this, Expectation-Minimization (EM) algorithms are explored. First, the simplest case is treated: that of denoising where the linear operator is the identity. In this framework, three algorithms are proposed: A Moments method based on data statistics, an EM and a joint estimation algorithm for sources and parameters. The results show that the EM initialized by the Method of Moments is the best candidate for parameter estimation. Secondly, the previous results are extended to the general case of any linear operator thanks to the introduction of a latent variable. This variable, by decoupling the sources from the observations, makes it possible to derive so-called 'latent' algorithms which alternate between a gradient descent step and a denoising step which corresponds exactly to the problem dealt with previously. The results then show that the most effective strategy is the use of the 'latent' joint estimate which initializes the 'latent' EM. Finally, the last part of this work is devoted to theoretical considerations concerning the choice of joint or marginal estimators in the supervised case. In particular with regard to the sources and their supports. This work shows that it is possible to frame marginal problems by joint problems thanks to a reparameterization of the problem. This then makes it possible to propose a general estimation strategy based on the initialization of marginal estimation algorithms by joint estimation algorithms
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Yu, Jia. "Distributed parameter and state estimation for wireless sensor networks." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/28929.

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The research in distributed algorithms is linked with the developments of statistical inference in wireless sensor networks (WSNs) applications. Typically, distributed approaches process the collected signals from networked sensor nodes. That is to say, the sensors receive local observations and transmit information between each other. Each sensor is capable of combining the collected information with its own observations to improve performance. In this thesis, we propose novel distributed methods for the inference applications using wireless sensor networks. In particular, the efficient algorithms which are not computationally intensive are investigated. Moreover, we present a number of novel algorithms for processing asynchronous network events and robust state estimation. In the first part of the thesis, a distributed adaptive algorithm based on the component-wise EM method for decentralized sensor networks is investigated. The distributed component-wise Expectation-Maximization (EM) algorithm has been designed for application in a Gaussian density estimation. The proposed algorithm operates a component-wise EM procedure for local parameter estimation and exploit an incremental strategy for network updating, which can provide an improved convergence rate. Numerical simulation results have illustrated the advantages of the proposed distributed component-wise EM algorithm for both well-separated and overlapped mixture densities. The distributed component-wise EM algorithm can outperform other EM-based distributed algorithms in estimating overlapping Gaussian mixtures. In the second part of the thesis, a diffusion based EM gradient algorithm for density estimation in asynchronous wireless sensor networks has been proposed. Specifically, based on the asynchronous adapt-then-combine diffusion strategy, a distributed EM gradient algorithm that can deal with asynchronous network events has been considered. The Bernoulli model has been exploited to approximate the asynchronous behaviour of the network. Compared with existing distributed EM based estimation methods using a consensus strategy, the proposed algorithm can provide more accurate estimates in the presence of asynchronous networks uncertainties, such as random link failures, random data arrival times, and turning on or off sensor nodes for energy conservation. Simulation experiments have been demonstrated that the proposed algorithm significantly outperforms the consensus based strategies in terms of Mean-Square- Deviation (MSD) performance in an asynchronous network setting. Finally, the challenge of distributed state estimation in power systems which requires low complexity and high stability in the presence of bad data for a large scale network is addressed. A gossip based quasi-Newton algorithm has been proposed for solving the power system state estimation problem. In particular, we have applied the quasi-Newton method for distributed state estimation under the gossip protocol. The proposed algorithm exploits the Broyden- Fletcher-Goldfarb-Shanno (BFGS) formula to approximate the Hessian matrix, thus avoiding the computation of inverse Hessian matrices for each control area. The simulation results for IEEE 14 bus system and a large scale 4200 bus system have shown that the distributed quasi-Newton scheme outperforms existing algorithms in terms of Mean-Square-Error (MSE) performance with bad data.
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De, la Rue Thierry. "Quelques résultats sur les systèmes dynamiques gaussiens réels." Rouen, 1994. https://tel.archives-ouvertes.fr/tel-01546012.

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Le premier chapitre de cette thèse établit que l'entropie d'un système dynamique gaussien est soit nulle, soit infinie, suivant respectivement que sa mesure spectrale est singulière ou non par rapport à la mesure de Lebesgue. Ce résultat est étendu au cas d'une action multidimensionnelle. Dans le second chapitre, on développe un nouveau modèle pour les systèmes gaussiens, qui sont vus comme une transformation de la trajectoire brownienne plane. Cette transformation peut être insérée dans un flot, pour lequel on calcule un mouvement moyen. Ce modèle est utilisé dans le troisième chapitre pour construire deux systèmes gaussiens d'entropie nulle non équivalents au sens de Kakutani: l'un n'est pas lâchement Bernoulli, alors que l'autre, qui est un gaussien-Kronecker, est lâchement Bernoulli. Pour cela, on a aussi besoin de montrer une propriété du mouvement brownien plan: certains angles formes par les accroissements du brownien suffisent pour reconstituer toute la trajectoire
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Guan, Feng-Bo, and 馮博冠. "Parameter Estimations of Condition Gaussian Distribution Given Bernoulli Distribution." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/87455161476925419316.

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碩士
國立中央大學
數學研究所
90
Abstract The sample mean and sample variance of a Gaussian distribution have the following nice statistical properties:(1)both are sufficient,(2)they are independent, (3)sample mean is m.l.e., UMVUE, and method of momemt estimator,(4)sample variance is m.l.e.,method of moment estimator and UMVUE if multiplied by a constant, (5)both estimators have variances achieve the Cramer-Rao lower bound,(6)both estimators are asymptotically efficient.Based on sample obtianed from the conditional Gaussian distribution given Bernoulli distribution,we study conditional sample mean and conditional sample variance and check if they also have the above statistical properties.
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"Bayesian Inference Frameworks for Fluorescence Microscopy Data Analysis." Master's thesis, 2019. http://hdl.handle.net/2286/R.I.53545.

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abstract: In this work, I present a Bayesian inference computational framework for the analysis of widefield microscopy data that addresses three challenges: (1) counting and localizing stationary fluorescent molecules; (2) inferring a spatially-dependent effective fluorescence profile that describes the spatially-varying rate at which fluorescent molecules emit subsequently-detected photons (due to different illumination intensities or different local environments); and (3) inferring the camera gain. My general theoretical framework utilizes the Bayesian nonparametric Gaussian and beta-Bernoulli processes with a Markov chain Monte Carlo sampling scheme, which I further specify and implement for Total Internal Reflection Fluorescence (TIRF) microscopy data, benchmarking the method on synthetic data. These three frameworks are self-contained, and can be used concurrently so that the fluorescence profile and emitter locations are both considered unknown and, under some conditions, learned simultaneously. The framework I present is flexible and may be adapted to accommodate the inference of other parameters, such as emission photophysical kinetics and the trajectories of moving molecules. My TIRF-specific implementation may find use in the study of structures on cell membranes, or in studying local sample properties that affect fluorescent molecule photon emission rates.
Dissertation/Thesis
Masters Thesis Applied Mathematics 2019
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FANTACCI, CLAUDIO. "Distributed multi-object tracking over sensor networks: a random finite set approach." Doctoral thesis, 2015. http://hdl.handle.net/2158/1003256.

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The aim of the present dissertation is to address distributed tracking over a network of heterogeneous and geographically dispersed nodes (or agents) with sensing, communication and processing capabilities. Tracking is carried out in the Bayesian framework and its extension to a distributed context is made possible via an information-theoretic approach to data fusion which exploits consensus algorithms and the notion of Kullback–Leibler Average (KLA) of the Probability Density Functions (PDFs) to be fused. The first step toward distributed tracking considers a single moving object. Consensus takes place in each agent for spreading information over the network so that each node can track the object. To achieve such a goal, consensus is carried out on the local single-object posterior distribution, which is the result of local data processing, in the Bayesian setting, exploiting the last available measurement about the object. Such an approach is called Consensus on Posteriors (CP). The first contribution of the present work is an improvement to the CP algorithm, namely Parallel Consensus on Likelihoods and Priors (CLCP). The idea is to carry out, in parallel, a separate consensus for the novel information (likelihoods) and one for the prior information (priors). This parallel procedure is conceived to avoid underweighting the novel information during the fusion steps. The outcomes of the two consensuses are then combined to provide the fused posterior density. Furthermore, the case of a single highly-maneuvering object is addressed. To this end, the object is modeled as a jump Markovian system and the multiple model (MM) filtering approach is adopted for local estimation. Thus, the consensus algorithms needs to be re-designed to cope with this new scenario. The second contribution has been to devise two novel consensus MM filters to be used for tracking a maneuvering object. The novel consensus-based MM filters are based on the First Order Generalized Pseudo-Bayesian (GPB1) and Interacting Multiple Model (IMM) filters. The next step is in the direction of distributed estimation of multiple moving objects. In order to model, in a rigorous and elegant way, a possibly time-varying number of objects present in a given area of interest, the Random Finite Set (RFS) formulation is adopted since it provides the notion of probability density for multi-object states that allows to directly extend existing tools in distributed estimation to multi-object tracking. The multi-object Bayes filter proposed by Mahler is a theoretically grounded solution to recursive Bayesian tracking based on RFSs. However, the multi-object Bayes recursion, unlike the single-object counterpart, is affected by combinatorial complexity and is, therefore, computationally infeasible except for very small-scale problems involving few objects and/or measurements. For this reason, the computationally tractable Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filtering approaches will be used as a first endeavour to distributed multiobject filtering. The third contribution is the generalisation of the single-object KLA to the RFS framework, which is the theoretical fundamental step for developing a novel consensus algorithm based on CPHD filtering, namely the Consensus CPHD (CCPHD). Each tracking agent locally updates multi-object CPHD, i.e. the cardinality distribution and the PHD, exploiting the multi-object dynamics and the available local measurements, exchanges such information with communicating agents and then carries out a fusion step to combine the information from all neighboring agents. The last theoretical step of the present dissertation is toward distributed filtering with the further requirement of unique object identities. To this end the labeled RFS framework is adopted as it provides a tractable approach to the multi-object Bayesian recursion. The δ- GLMB filter is an exact closed-form solution to the multi-object Bayes recursion which jointly yields state and label (or trajectory) estimates in the presence of clutter, misdetections and association uncertainty. Due to the presence of explicit data associations in the δ-GLMB filter, the number of components in the posterior grows without bound in time. The fourth contribution of this thesis is an efficient approximation of the δ-GLMB filter, namely Marginalized δ-GLMB (Mδ-GLMB), which preserves key summary statistics (i.e. both the PHD and cardinality distribution) of the full labeled posterior. This approximation also facilitates efficient multi-sensor tracking with detection-based measurements. Simulation results are presented to verify the proposed approach. Finally, distributed labeled multi-object tracking over sensor networks is taken into account. The last contribution is a further generalization of the KLA to the labeled RFS framework, which enables the development of two novel consensus tracking filters, namely the Consensus Marginalized δ-Generalized Labeled Multi-Bernoulli (CM-δGLMB) and the Consensus Labeled Multi-Bernoulli (CLMB) tracking filters. The proposed algorithms provide a fully distributed, scalable and computationally efficient solution for multi-object tracking. Simulation experiments on challenging single-object or multi-object tracking scenarios confirm the effectiveness of the proposed contributions.
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Book chapters on the topic "Bernoulli-Gaussian"

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Cho, KyungHyun, Alexander Ilin, and Tapani Raiko. "Improved Learning of Gaussian-Bernoulli Restricted Boltzmann Machines." In Lecture Notes in Computer Science, 10–17. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21735-7_2.

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Ershov, M. A., and A. S. Voroshilov. "UCB Strategy for Gaussian and Bernoulli Multi-armed Bandits." In Communications in Computer and Information Science, 67–78. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-43257-6_6.

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Li, Ziqiang, Xun Cai, and Ti Liang. "Gaussian-Bernoulli Based Convolutional Restricted Boltzmann Machine for Images Feature Extraction." In Neural Information Processing, 593–602. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-46672-9_66.

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Veziroğlu, Merve, Erkan Eziroğlu, and İhsan Ömür Bucak. "PERFORMANCE COMPARISON BETWEEN NAIVE BAYES AND MACHINE LEARNING ALGORITHMS FOR NEWS CLASSIFICATION." In Bayesian Inference - Recent Trends. IntechOpen, 2024. http://dx.doi.org/10.5772/intechopen.1002778.

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The surge in digital content has fueled the need for automated text classification methods, particularly in news categorization using natural language processing (NLP). This work introduces a Python-based news classification system, focusing on Naive Bayes algorithms for sorting news headlines into predefined categories. Naive Bayes is favored for its simplicity and effectiveness in text classification. Our objective includes exploring the creation of a news classification system and evaluating various Naive Bayes algorithms. The dataset comprises BBC News headlines spanning technology, business, sports, entertainment, and politics. Analyzing category distribution and headline length provided dataset insights. Data preprocessing involved text cleaning, stop word removal, and feature extraction with Count Vectorization to convert text into machine-readable numerical data. Four Naive Bayes variants were evaluated: Gaussian, Multinomial, Complement, and Bernoulli. Performance metrics such as accuracy, precision, recall, and F1 score were employed, and Naive Bayes algorithms were compared to other classifiers like Logistic Regression, Random Forest, Linear Support Vector Classification (SVC), Multi-Layer Perceptron (MLP) Classifier, Decision Trees, and K-Nearest Neighbors. The MLP Classifier achieved the highest accuracy, underscoring its effectiveness, while Multinomial and Complement Naive Bayes proved robust in news classification. Effective data preprocessing played a pivotal role in accurate categorization. This work contributes insights into Naive Bayes algorithm performance in news classification, benefiting NLP and news categorization systems.
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Sivia, D. S. "Assigning probabilities." In Data Analysis, 103–26. Oxford University PressOxford, 2006. http://dx.doi.org/10.1093/oso/9780198568315.003.0005.

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Abstract In the preceding three chapters, we have seen how pdfs can be manipulated, with the sum and product rule of probability, to address data analysis problems; little was said, however, about their assignment in the first place. We now turn to this basic question. In addition to justifying the earlier use of the binomial, Gaussian and Poisson distributions, we will have our first encounter with the principle of maximum entropy. In Section 1.2, we outlined how Cox showed that any method of plausible reasoning, which satisfies elementary requirements of logical consistency, must be equivalent to the use of probability theory. While the sum and product rule specify the relationship between pdfs, they do not tell us how to assign them. Are there any general principles to help us do this? The oldest idea dates back to Bernoulli (1713), in what he called the ‘principle of insufficient reason ‘; Keynes (1921) later renamed it the ‘principle of indifference ‘. It states that if we can enumerate a set of basic, mutually exclusive, possibilities, and have no reason to believe that any one of these is more likely to be true than another, then we should assign the same probability to all. If we consider an ordinary die, for example, we can list the six potential outcomes of a roll, where the background information I consists of nothing more than the enumeration of the possibilities. Although our everyday intuition tells us that this assignment is very reasonable, can we justify it in a more fundamental way? The reason for asking this question is that a better understanding of this easy problem might shed light on how to deal with more complicated situations later.
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Conference papers on the topic "Bernoulli-Gaussian"

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Cho, Kyung Hyun, Tapani Raiko, and Alexander Ilin. "Gaussian-Bernoulli deep Boltzmann machine." In 2013 International Joint Conference on Neural Networks (IJCNN 2013 - Dallas). IEEE, 2013. http://dx.doi.org/10.1109/ijcnn.2013.6706831.

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Jones, George, Ángel F. García-Fernández, and Prudence W. H. Wong. "GOSPA-Driven Gaussian Bernoulli Sensor Management." In 2023 26th International Conference on Information Fusion (FUSION). IEEE, 2023. http://dx.doi.org/10.23919/fusion52260.2023.10224220.

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Liu, Lei, Chongwen Huang, Yuhao Chi, Chau Yuen, Yong Liang Guan, and Ying Li. "Sparse Vector Recovery: Bernoulli-Gaussian Message Passing." In 2017 IEEE Global Communications Conference (GLOBECOM 2017). IEEE, 2017. http://dx.doi.org/10.1109/glocom.2017.8254836.

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Vila, Jeremy, and Philip Schniter. "Expectation-maximization Bernoulli-Gaussian approximate message passing." In 2011 45th Asilomar Conference on Signals, Systems and Computers. IEEE, 2011. http://dx.doi.org/10.1109/acssc.2011.6190117.

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Bazot, Cecile, Nicolas Dobigeon, Jean-Yves Tourneret, and Alfred O. Hero. "A Bernoulli-Gaussian model for gene factor analysis." In 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2011. http://dx.doi.org/10.1109/icassp.2011.5947728.

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Bassi, Francesca, Michel Kieffer, and Cagatay Dikici. "Multiterminal source coding of Bernoulli-Gaussian correlated sources." In ICASSP 2009 - 2009 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2009. http://dx.doi.org/10.1109/icassp.2009.4960130.

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Yin, Jianjun, Jianqiu Zhang, and Jin Zhao. "The Gaussian Particle multi-target multi-Bernoulli filter." In 2010 2nd International Conference on Advanced Computer Control. IEEE, 2010. http://dx.doi.org/10.1109/icacc.2010.5486859.

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Garcaa-Fernandez, Angel F., Yuxuan Xia, Karl Granstrom, Lennart Svensson, and Jason L. Williams. "Gaussian implementation of the multi-Bernoulli mixture filter." In 2019 22th International Conference on Information Fusion (FUSION). IEEE, 2019. http://dx.doi.org/10.23919/fusion43075.2019.9011346.

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Chaari, Lotfi, Jean-Yves Toumeret, and Caroline Chaux. "Sparse signal recovery using a Bernoulli generalized Gaussian prior." In 2015 23rd European Signal Processing Conference (EUSIPCO). IEEE, 2015. http://dx.doi.org/10.1109/eusipco.2015.7362676.

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Yildirim, Sinan, A. Taylan Cemgil, and Aysin B. Ertuzun. "A hybrid method for deconvolution of Bernoulli-Gaussian processes." In ICASSP 2009 - 2009 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2009. http://dx.doi.org/10.1109/icassp.2009.4960359.

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