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Risk, Unexpected Uncertainty, and Estimation Uncertainty: Bayesian Learning in Unstable Settings

Payzan-LeNestour, Elise; Bossaerts, Peter
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
47.77961%
Recently, evidence has emerged that humans approach learning using Bayesian updating rather than (model-free) reinforcement algorithms in a six-arm restless bandit problem. Here, we investigate what this implies for human appreciation of uncertainty. In our task, a Bayesian learner distinguishes three equally salient levels of uncertainty. First, the Bayesian perceives irreducible uncertainty or risk: even knowing the payoff probabilities of a given arm, the outcome remains uncertain. Second, there is (parameter) estimation uncertainty or ambiguity: payoff probabilities are unknown and need to be estimated. Third, the outcome probabilities of the arms change: the sudden jumps are referred to as unexpected uncertainty. We document how the three levels of uncertainty evolved during the course of our experiment and how it affected the learning rate. We then zoom in on estimation uncertainty, which has been suggested to be a driving force in exploration, in spite of evidence of widespread aversion to ambiguity. Our data corroborate the latter. We discuss neural evidence that foreshadowed the ability of humans to distinguish between the three levels of uncertainty. Finally, we investigate the boundaries of human capacity to implement Bayesian learning. We repeat the experiment with different instructions...

Disentangling preferences, inertia and learning in brand choice models

Shin, Sangwoo (1973 - ); Horsky, Dan
Fonte: University of Rochester Publicador: University of Rochester
Tipo: Tese de Doutorado Formato: Number of Pages:ix, 70 leaves
Português
Relevância na Pesquisa
57.579844%
Thesis (Ph. D.)--University of Rochester. William E. Simon Graduate School of Business Administration, 2008.; The forces that influence a consumer in brand choice: preferences, experiences, and marketing mix have been of great interest to marketing scientists. The vast literature based on static survey data points to consumers using multi-attribute utilities in making a choice. At the same time the vast literature of scanner panel data based studies points to the existence of state dependence (in various functional forms) in brand choices in frequently purchased product markets. Using a unique dataset that contains stated preferences (survey) and actual purchase data (scanner panel) for the same group of consumers I attempt to untangle the effects of preference heterogeneity and state dependence, and to determine the exact nature of the latter. I propose a hierarchical model in which consumers within the same product category are heterogeneous in the order of the brand choice process and its parameters as well as in their preferences and responsiveness to marketing mix. The proposed model is designed to encompass side by side three different types of consumer experience based behavior: zero-order, inertia and learning. Two sources of state dependence...

Probabilistic and fuzzy reasoning in simple learning classifier systems

Muruzábal, Jorge
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /04/1995 Português
Relevância na Pesquisa
57.28901%
This paper is concerned with the general stimulus-response problem as addressed by a variety of simple learning c1assifier systems (CSs). We suggest a theoretical model from which the assessment of uncertainty emerges as primary concern. A number of representation schemes borrowing from fuzzy logic theory are reviewed, and sorne connections with a well-known neural architecture revisited. In pursuit of the uncertainty measuring goal, usage of explicit probability distributions in the action part of c1assifiers is advocated. Sorne ideas supporting the design of a hybrid system incorpo'rating bayesian learning on top of the CS basic algorithm are sketched.

Computationally Efficient Bayesian Learning of Gaussian Process State Space Models

Svensson, Andreas; Solin, Arno; Särkkä, Simo; Schön, Thomas B.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/06/2015 Português
Relevância na Pesquisa
57.5128%
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting the problem onto a set of approximate eigenfunctions derived from the prior covariance structure. Learning under this family of models can be conducted using a carefully crafted particle MCMC algorithm. This scheme is computationally efficient and yet allows for a fully Bayesian treatment of the problem. Compared to conventional system identification tools or existing learning methods, we show competitive performance and reliable quantification of uncertainties in the model.

Compressed Sensing for Energy-Efficient Wireless Telemonitoring of Noninvasive Fetal ECG via Block Sparse Bayesian Learning

Zhang, Zhilin; Jung, Tzyy-Ping; Makeig, Scott; Rao, Bhaskar D.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
57.28901%
Fetal ECG (FECG) telemonitoring is an important branch in telemedicine. The design of a telemonitoring system via a wireless body-area network with low energy consumption for ambulatory use is highly desirable. As an emerging technique, compressed sensing (CS) shows great promise in compressing/reconstructing data with low energy consumption. However, due to some specific characteristics of raw FECG recordings such as non-sparsity and strong noise contamination, current CS algorithms generally fail in this application. This work proposes to use the block sparse Bayesian learning (BSBL) framework to compress/reconstruct non-sparse raw FECG recordings. Experimental results show that the framework can reconstruct the raw recordings with high quality. Especially, the reconstruction does not destroy the interdependence relation among the multichannel recordings. This ensures that the independent component analysis decomposition of the reconstructed recordings has high fidelity. Furthermore, the framework allows the use of a sparse binary sensing matrix with much fewer nonzero entries to compress recordings. Particularly, each column of the matrix can contain only two nonzero entries. This shows the framework, compared to other algorithms such as current CS algorithms and wavelet algorithms...

Sparse Signal Recovery with Temporally Correlated Source Vectors Using Sparse Bayesian Learning

Zhang, Zhilin; Rao, Bhaskar D.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
57.5128%
We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorithms do not consider such temporal correlations and thus their performance degrades significantly with the correlations. In this work, we propose a block sparse Bayesian learning framework which models the temporal correlations. In this framework we derive two sparse Bayesian learning (SBL) algorithms, which have superior recovery performance compared to existing algorithms, especially in the presence of high temporal correlations. Furthermore, our algorithms are better at handling highly underdetermined problems and require less row-sparsity on the solution matrix. We also provide analysis of the global and local minima of their cost function, and show that the SBL cost function has the very desirable property that the global minimum is at the sparsest solution to the MMV problem. Extensive experiments also provide some interesting results that motivate future theoretical research on the MMV model.; Comment: The final version with some typos corrected. Codes can be downloaded at: http://dsp.ucsd.edu/~zhilin/TSBL_code.zip

Tractable Bayesian Learning of Tree Belief Networks

Meila, Marina; Jaakkola, Tommi S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/01/2013 Português
Relevância na Pesquisa
57.5128%
In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and can be completely determined analytically in polynomial time. This follows from two main results: First, we show that factored distributions over spanning trees in a graph can be integrated in closed form. Second, we examine priors over tree parameters and show that a set of assumptions similar to (Heckerman and al. 1995) constrain the tree parameter priors to be a compactly parameterized product of Dirichlet distributions. Beside allowing for exact Bayesian learning, these results permit us to formulate a new class of tractable latent variable models in which the likelihood of a data point is computed through an ensemble average over tree structures.; Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000)

Spatiotemporal Sparse Bayesian Learning with Applications to Compressed Sensing of Multichannel Physiological Signals

Zhang, Zhilin; Jung, Tzyy-Ping; Makeig, Scott; Pi, Zhouyue; Rao, Bhaskar D.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
57.5128%
Energy consumption is an important issue in continuous wireless telemonitoring of physiological signals. Compressed sensing (CS) is a promising framework to address it, due to its energy-efficient data compression procedure. However, most CS algorithms have difficulty in data recovery due to non-sparsity characteristic of many physiological signals. Block sparse Bayesian learning (BSBL) is an effective approach to recover such signals with satisfactory recovery quality. However, it is time-consuming in recovering multichannel signals, since its computational load almost linearly increases with the number of channels. This work proposes a spatiotemporal sparse Bayesian learning algorithm to recover multichannel signals simultaneously. It not only exploits temporal correlation within each channel signal, but also exploits inter-channel correlation among different channel signals. Furthermore, its computational load is not significantly affected by the number of channels. The proposed algorithm was applied to brain computer interface (BCI) and EEG-based driver's drowsiness estimation. Results showed that the algorithm had both better recovery performance and much higher speed than BSBL. Particularly, the proposed algorithm ensured that the BCI classification and the drowsiness estimation had little degradation even when data were compressed by 80%...

Bayesian Learning in Undirected Graphical Models: Approximate MCMC algorithms

Murray, Iain; Ghahramani, Zoubin
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/07/2012 Português
Relevância na Pesquisa
57.5128%
Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov Chain Monte Carlo) schemes giving the correct equilibrium distribution over parameters. While this intractability, due to the partition function, is familiar to those performing parameter optimisation, Bayesian learning of posterior distributions over undirected model parameters has been unexplored and poses novel challenges. we propose several approximate MCMC schemes and test on fully observed binary models (Boltzmann machines) for a small coronary heart disease data set and larger artificial systems. While approximations must perform well on the model, their interaction with the sampling scheme is also important. Samplers based on variational mean- field approximations generally performed poorly, more advanced methods using loopy propagation, brief sampling and stochastic dynamics lead to acceptable parameter posteriors. Finally, we demonstrate these techniques on a Markov random field with hidden variables.; Comment: Appears in Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI2004)

Pattern-Coupled Sparse Bayesian Learning for Recovery of Block-Sparse Signals

Fang, Jun; Shen, Yanning; Li, Hongbin; Wang, Pu
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/11/2013 Português
Relevância na Pesquisa
57.5128%
We consider the problem of recovering block-sparse signals whose structures are unknown \emph{a priori}. Block-sparse signals with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. However, the knowledge of the block structure is usually unavailable in practice. In this paper, we develop a new sparse Bayesian learning method for recovery of block-sparse signals with unknown cluster patterns. Specifically, a pattern-coupled hierarchical Gaussian prior model is introduced to characterize the statistical dependencies among coefficients, in which a set of hyperparameters are employed to control the sparsity of signal coefficients. Unlike the conventional sparse Bayesian learning framework in which each individual hyperparameter is associated independently with each coefficient, in this paper, the prior for each coefficient not only involves its own hyperparameter, but also the hyperparameters of its immediate neighbors. In doing this way, the sparsity patterns of neighboring coefficients are related to each other and the hierarchical model has the potential to encourage structured-sparse solutions. The hyperparameters, along with the sparse signal, are learned by maximizing their posterior probability via an expectation-maximization (EM) algorithm. Numerical results show that the proposed algorithm presents uniform superiority over other existing methods in a series of experiments.

Fast Marginalized Block Sparse Bayesian Learning Algorithm

Liu, Benyuan; Zhang, Zhilin; Fan, Hongqi; Fu, Qiang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
57.28901%
The performance of sparse signal recovery from noise corrupted, underdetermined measurements can be improved if both sparsity and correlation structure of signals are exploited. One typical correlation structure is the intra-block correlation in block sparse signals. To exploit this structure, a framework, called block sparse Bayesian learning (BSBL), has been proposed recently. Algorithms derived from this framework showed superior performance but they are not very fast, which limits their applications. This work derives an efficient algorithm from this framework, using a marginalized likelihood maximization method. Compared to existing BSBL algorithms, it has close recovery performance but is much faster. Therefore, it is more suitable for large scale datasets and applications requiring real-time implementation.

Impulsive Noise Mitigation in Powerline Communications Using Sparse Bayesian Learning

Lin, Jing; Nassar, Marcel; Evans, Brian L.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/03/2013 Português
Relevância na Pesquisa
57.21097%
Additive asynchronous and cyclostationary impulsive noise limits communication performance in OFDM powerline communication (PLC) systems. Conventional OFDM receivers assume additive white Gaussian noise and hence experience degradation in communication performance in impulsive noise. Alternate designs assume a parametric statistical model of impulsive noise and use the model parameters in mitigating impulsive noise. These receivers require overhead in training and parameter estimation, and degrade due to model and parameter mismatch, especially in highly dynamic environments. In this paper, we model impulsive noise as a sparse vector in the time domain without any other assumptions, and apply sparse Bayesian learning methods for estimation and mitigation without training. We propose three iterative algorithms with different complexity vs. performance trade-offs: (1) we utilize the noise projection onto null and pilot tones to estimate and subtract the noise impulses; (2) we add the information in the data tones to perform joint noise estimation and OFDM detection; (3) we embed our algorithm into a decision feedback structure to further enhance the performance of coded systems. When compared to conventional OFDM PLC receivers, the proposed receivers achieve SNR gains of up to 9 dB in coded and 10 dB in uncoded systems in the presence of impulsive noise.; Comment: To appear in IEEE Journal on Selected Areas of Communications

The Annealing Sparse Bayesian Learning Algorithm

Liu, Benyuan; Fan, Hongqi; Lu, Zaiqi; Fu, Qiang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
57.459937%
In this paper we propose a two-level hierarchical Bayesian model and an annealing schedule to re-enable the noise variance learning capability of the fast marginalized Sparse Bayesian Learning Algorithms. The performance such as NMSE and F-measure can be greatly improved due to the annealing technique. This algorithm tends to produce the most sparse solution under moderate SNR scenarios and can outperform most concurrent SBL algorithms while pertains small computational load.; Comment: The update equation in the annealing process was too empirical for practical usage. This paper need to be revised in order to be printed on the arxiv.org

Bayesian Learning for Low-Rank matrix reconstruction

Sundin, Martin; Rojas, Cristian R.; Jansson, Magnus; Chatterjee, Saikat
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/01/2015 Português
Relevância na Pesquisa
57.28901%
We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between the latent variable models and several low-rank promoting penalty functions. The relations justify the use of Kronecker structured covariance matrices in a Gaussian based prior. In the methods, we use evidence approximation and expectation-maximization to learn the model parameters. The performance of the methods is evaluated through extensive numerical simulations.; Comment: Submitted to IEEE Transactions on Signal Processing

Sparse Bayesian Learning for EEG Source Localization

Saha, Sajib; de Hoog, Frank; Nesterets, Ya. I.; Rana, Rajib; Tahtali, M.; Gureyev, T. E.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/01/2015 Português
Relevância na Pesquisa
57.21097%
Purpose: Localizing the sources of electrical activity from electroencephalographic (EEG) data has gained considerable attention over the last few years. In this paper, we propose an innovative source localization method for EEG, based on Sparse Bayesian Learning (SBL). Methods: To better specify the sparsity profile and to ensure efficient source localization, the proposed approach considers grouping of the electrical current dipoles inside human brain. SBL is used to solve the localization problem in addition with imposed constraint that the electric current dipoles associated with the brain activity are isotropic. Results: Numerical experiments are conducted on a realistic head model that is obtained by segmentation of MRI images of the head and includes four major components, namely the scalp, the skull, the cerebrospinal fluid (CSF) and the brain, with appropriate relative conductivity values. The results demonstrate that the isotropy constraint significantly improves the performance of SBL. In a noiseless environment, the proposed method was 1 found to accurately (with accuracy of >75%) locate up to 6 simultaneously active sources, whereas for SBL without the isotropy constraint, the accuracy of finding just 3 simultaneously active sources was <75%. Conclusions: Compared to the state-of-the-art algorithms...

Hierarchical sparse Bayesian learning: theory and application for inferring structural damage from incomplete modal data

Huang, Yong; Beck, James L.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/03/2015 Português
Relevância na Pesquisa
57.740703%
Structural damage due to excessive loading or environmental degradation typically occurs in localized areas in the absence of collapse. This prior information about the spatial sparseness of structural damage is exploited here by a hierarchical sparse Bayesian learning framework with the goal of reducing the source of ill-conditioning in the stiffness loss inversion problem for damage detection. Sparse Bayesian learning methodologies automatically prune away irrelevant or inactive features from a set of potential candidates, and so they are effective probabilistic tools for producing sparse explanatory subsets. We have previously proposed such an approach to establish the probability of localized stiffness reductions that serve as a proxy for damage by using noisy incomplete modal data from before and after possible damage. The core idea centers on a specific hierarchical Bayesian model that promotes spatial sparseness in the inferred stiffness reductions in a way that is consistent with the Bayesian Ockham razor. In this paper, we improve the theory of our previously proposed sparse Bayesian learning approach by eliminating an approximation and, more importantly, incorporating a constraint on stiffness increases. Our approach has many appealing features that are summarized at the end of the paper. We validate the approach by applying it to the Phase II simulated and experimental benchmark studies sponsored by the IASC-ASCE Task Group on Structural Health Monitoring. The results show that it can reliably detect...

Cramer Rao-Type Bounds for Sparse Bayesian Learning

Prasad, Ranjitha; Murthy, Chandra R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
57.459937%
In this paper, we derive Hybrid, Bayesian and Marginalized Cram\'{e}r-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compressible Student-t prior distribution. We derive CRBs that encompass the deterministic or random nature of the unknown parameters of the prior distribution and the regression noise variance. We extend the MCRB to the case where the compressible vector is distributed according to a general compressible prior distribution, of which the generalized Pareto distribution is a special case. We use the derived bounds to uncover the relationship between the compressibility and Mean Square Error (MSE) in the estimates. Further, we illustrate the tightness and utility of the bounds through simulations, by comparing them with the MSE performance of two popular SBL-based estimators. It is found that the MCRB is generally the tightest among the bounds derived and that the MSE performance of the Expectation-Maximization (EM) algorithm coincides with the MCRB for the compressible vector. Through simulations, we demonstrate the dependence of the MSE performance of SBL based estimators on the compressibility of the vector for several values of the number of observations and at different signal powers.; Comment: Accepted for publication in the IEEE Transactions on Signal Processing...

Big Learning with Bayesian Methods

Zhu, Jun; Chen, Jianfei; Hu, Wenbo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 24/11/2014 Português
Relevância na Pesquisa
47.88741%
Explosive growth in data and availability of cheap computing resources have sparked increasing interest in Big learning, an emerging subfield that studies scalable machine learning algorithms, systems, and applications with Big Data. Bayesian methods represent one important class of statistic methods for machine learning, with substantial recent developments on adaptive, flexible and scalable Bayesian learning. This article provides a survey of the recent advances in Big learning with Bayesian methods, termed Big Bayesian Learning, including nonparametric Bayesian methods for adaptively inferring model complexity, regularized Bayesian inference for improving the flexibility via posterior regularization, and scalable algorithms and systems based on stochastic subsampling and distributed computing for dealing with large-scale applications.; Comment: 21 pages, 6 figures

Bayesian Learning for Earthquake Engineering Applications and Structural Health Monitoring

Oh, Chang Kook
Fonte: Earthquake Engineering Research Laboratory Publicador: Earthquake Engineering Research Laboratory
Tipo: Report or Paper; PeerReviewed Formato: application/pdf
Publicado em 17/09/2007 Português
Relevância na Pesquisa
47.854653%
Parallel to significant advances in sensor hardware, there have been recent developments of sophisticated methods for quantitative assessment of measured data that explicitly deal with all of the involved uncertainties, including inevitable measurement errors. The existence of these uncertainties often causes numerical instabilities in inverse problems that make them ill-conditioned. The Bayesian methodology is known to provide an efficient way to alleviate this illconditioning by incorporating the prior term for regularization of the inverse problem, and to provide probabilistic results which are meaningful for decision making. In this work, the Bayesian methodology is applied to inverse problems in earthquake engineering and especially to structural health monitoring. The proposed methodology of Bayesian learning using automatic relevance determination (ARD) prior, including its kernel version called the Relevance Vector Machine, is presented and applied to earthquake early warning, earthquake ground motion attenuation estimation, and structural health monitoring, using either a Bayesian classification or regression approach. The classification and regression are both performed in three phases: (1) Phase I (feature extraction phase): Determine which features from the data to use in a training dataset; (2) Phase II (training phase): Identify the unknown parameters defining a model by using a training dataset; and (3) Phase III (prediction phase): Predict the results based on the features from new data. This work focuses on the advantages of making probabilistic predictions obtained by Bayesian methods to deal with all uncertainties and the good characteristics of the proposed method in terms of computationally efficient training...

Risk, Unexpected Uncertainty, and Estimation Uncertainty: Bayesian Learning in Unstable Settings

Payzan-LeNestour, Elise; Bossaerts, Peter
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Article; PeerReviewed Formato: application/pdf; application/pdf; application/pdf; application/pdf; application/pdf; application/pdf
Publicado em /01/2011 Português
Relevância na Pesquisa
47.77961%
Recently, evidence has emerged that humans approach learning using Bayesian updating rather than (model-free) reinforcement algorithms in a six-arm restless bandit problem. Here, we investigate what this implies for human appreciation of uncertainty. In our task, a Bayesian learner distinguishes three equally salient levels of uncertainty. First, the Bayesian perceives irreducible uncertainty or risk: even knowing the payoff probabilities of a given arm, the outcome remains uncertain. Second, there is (parameter) estimation uncertainty or ambiguity: payoff probabilities are unknown and need to be estimated. Third, the outcome probabilities of the arms change: the sudden jumps are referred to as unexpected uncertainty. We document how the three levels of uncertainty evolved during the course of our experiment and how it affected the learning rate. We then zoom in on estimation uncertainty, which has been suggested to be a driving force in exploration, in spite of evidence of widespread aversion to ambiguity. Our data corroborate the latter. We discuss neural evidence that foreshadowed the ability of humans to distinguish between the three levels of uncertainty. Finally, we investigate the boundaries of human capacity to implement Bayesian learning. We repeat the experiment with different instructions...