Bayesian approach

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A Sparse Bayesian Approach for Joint Feature Selection and Classifier Learning

A Sparse Bayesian Approach for Joint Feature Selection and Classifier Learning

space. On the other hand, Automatic Relevance Determination (ARD) [18] has been used to estimate scaling factors on features in different types of classifiers. In kernel classifiers such as Support Vector Machines a Bayesian method for model selection was proposed by Seeger [19], where a maximum a posteriori (MAP) criterion on the parameters is imposed using a vari- ational approach. Nevertheless, there exist only a few embedded methods addressing the feature selection problem in connection with non-parametric classifiers up to now. An embedded approach for the quadratic 1-norm SVM was suggested by Zhu et al. [20], while Jebara and Jaakkola [21] developed a feature selection method as an extension to the so-called maximum en- tropy discrimination. Li at al [22] used a two stepwise forward procedure for the same compacting model problem. Recently, Krishnapuram et al. [23] developed a joint classifier and feature optimization method for kernel clas- sifiers. The method shows promising results in high dimensional data sets. Nevertheless, the resulting kernel classifier model is learned by the Expec- tation Maximization algorithm and the computational complexity becomes unpractical for large training data sets.
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33 Lee mas

Bayesian analysis of polarization measurements

Bayesian analysis of polarization measurements

integrating the posterior distribution over the subset. If the prob- ability is greater than 50%, the hypothesis is accepted. If it is less than 50%, it is rejected. The simplicity of these tests is one of the benefits of the Bayesian approach. The subset need not consist of more than a single point but in that case the associated probabil- ity will usually be infinitesimal unless distributions are allowed for priors. In the next section, priors will be introduced that use a delta function at the origin to represent the probability that a source has negligible polarization. After the measurement, one may compute the posterior odds for the origin (a single point) to test if the measurement is consistent with zero. One of the ben- efits of ˆ p 0,MED is that it naturally performs this test for a delta function at the origin.
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15 Lee mas

Scaling relations of the colour detected cluster RzCS 052 at z=1 016 and some other high redshift clusters

Scaling relations of the colour detected cluster RzCS 052 at z=1 016 and some other high redshift clusters

halo occupation number for this cluster is only marginally consistent with what was expected assuming a self-similar evolution of cluster scaling relations, suggesting perhaps a break of them at z ∼ 1. We also rule out a strong galaxy merging activity between z = 1 and today. Finally, we present a Bayesian approach to measuring cluster velocity dispersions and X-ray luminosities in the presence of a background: we critically reanalyse recent claims for X-ray underluminous clusters using these techniques and find that the clusters can be accommodated within the existing L X –σ v relation.
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11 Lee mas

Bayesian Reliability, Availability and Maintainability Analysis for Hardware Systems Described Through Continuous Time Markov Chains

Bayesian Reliability, Availability and Maintainability Analysis for Hardware Systems Described Through Continuous Time Markov Chains

The standard approach to RAM estimation of CTMC HW systems com- putes Maximum Likelihood Estimates (MLEs) for the involved parameters of the CTMC, substitutes parameters by the MLEs, computes the equilibrium dis- tribution, and, consequently, estimates the long-term fraction of time that the system remains in ON and OFF configurations. However, this approach usually underrepresents uncertainty in the parameters, as discussed in Glynn (1986) or Berger and R´ıos Insua (1998). Thus, we adopt here a Bayesian approach that fully acknowledges the uncertainty present and takes advantage of all informa- tion available. Moreover, we adopt a more short-term oriented approach.
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26 Lee mas

Bayesian statistics in genetics

Bayesian statistics in genetics

In many cases, Bayesian methods can address the question of interest more directly than a classical approach. Two examples from the literature, the first from the field of population genetics and the second from linkage analysis, illustrate this point. In a large, randomly mating population that is free of disturbing forces, allele and genotypic fre- quencies do not change and are related in a simple way. The population is said to conform to Hardy–Weinberg equilib- rium (HWE). In a classical setting, one tests for whether the population is exactly in HWE and then looks for evidence against this null hypothesis. However, in many cases, the experimenter does not believe that the population is exactly in HWE and might fail to reject a false null hypothesis. A Bayesian approach can reflect a more relevant question, which might be ‘are departures from HWE large enough to be important?’ The size of departure that is important varies with the context. We addressed this question in the context of forensic science, where an important departure in human populations was suggested by the United States National Research Council (NRC) 12 .
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5 Lee mas

Environment, mathematics and the best solution to stop natural world destruction

Environment, mathematics and the best solution to stop natural world destruction

Several statistical studies (usually textbooks) use Bayesian statistics in a rather primitive way, changing prior ideas after observations, therefore, additional assumptions should be made to obtain solid results. A modern Bayesian approach ought to lead toward correct decision making, assign- ing looses or gains to particular actions, in order to find a fairly optimal solution. To be able to succeed in this task, we need specific models and its assignment of parameters (calibration), more precisely than those pos- tulated in Sterns report, seemingly by the rule of thumb. Nowadays, this approach represents the Nirvana and cannot generate reasonable deci-
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9 Lee mas

Phylogeography Takes a Relaxed Random Walk in Continuous Space and Time

Phylogeography Takes a Relaxed Random Walk in Continuous Space and Time

Indeed, samples are often continuously distributed and less amenable to discretized sampling schemes. To ac- commodate such sampling, Lemmon AR and Lemmon EM (2008) have recently presented a maximum likelihood method for estimating dispersal across a continuous land- scape. For continuous geographic coordinates (latitude and longitude), Brownian diffusion (BD) finds analogues to the Markov chain transition model (Schluter et al. 1997). Such BD models have found repeated use since the formal- ization of statistical phylogenetics (Edwards and Cavalli- Sforza 1964; Cavalli-Sforza and Edwards 1967; Felsenstein 1973, 1985). Although statistical inference on a continu- ous landscape sets a milestone in phylogeographic analyses, Lemmon AR and Lemmon EM (2008) also note that such models will benefit significantly from a Bayesian implemen- tation. In particular, a Bayesian approach permits the easy integration of different sources of uncertainty and also af- fords more flexible incorporation of geographic information systems data.
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9 Lee mas

Decision boundary for discrete Bayesian network classifiers

Decision boundary for discrete Bayesian network classifiers

Moreover, the resulting bounds for the number of decision functions representable are strictly upper bounds since the subspaces generated by the different Bayesian networks considered are not in general position. What happens in the case of subspaces not in general position? Clearly we have to define some other property to characterize the position of a subspace with respect to orthants in some given basis and try to count the number of such intersected orthants. With similar geometric results we will be able to precisely count the number of decision functions representable by a given Bayesian network classifier, and we will be able to compute the gain in expressivity from simple to more complicated Bayesian network classifiers.
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25 Lee mas

TítuloRobust Precoding with Bayesian Error Modeling for Limited Feedback MU MISO Systems

TítuloRobust Precoding with Bayesian Error Modeling for Limited Feedback MU MISO Systems

Most of the work on precoding with erroneous CSI was motivated by a Time Division Duplex (TDD) setup, where the transmitter can estimate the CSI during the transmission in the opposite direction [13], [14]. This approach however is difficult due to the necessity of very good calibration [20]. Contrarily, we focus on the more difficult case, where the CSI is obtained by the receivers and fed back to the transmitter. In this case, calibration errors are estimated as being part of the CSI and, therefore, no special problems arise from calibration. Additionally, the feedback of CSI enables precoding in Frequency Division Duplex (FDD) systems, where the transmitter is unable to obtain the CSI during reception, because the channels are not reciprocal.
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25 Lee mas

Learning Tractable Bayesian Networks

Learning Tractable Bayesian Networks

Scanagatta et al. [2016] proposed a method (called k-greedy) for learning bounded tree- width BNs from very large datasets. Before performing the structure search, k-greedy initial- izes a cache of candidate parent sets for each node using the approach of Scanagatta et al. [2015]. Then, it samples the space of orderings of variables, performing the next steps for each order. First, an initial structure with the first k + 1 variables in the order is learned. Depending on the value of k, k-greedy uses either an exact [Cussens, 2011] or an approxi- mate [Scanagatta et al., 2015] structure learning method. Second, the structure incrementally grows according to the chosen order, ensuring that at each step the moral graph of the struc- ture is a partial k-tree. This process is repeated until the maximum allowed execution time is met. More recently, Scanagatta et al. [2018b] improved k-greedy by proposing a heuris- tic score for choosing the order in which the variables are visited. This heuristic ranks the variables by comparing the highest-scoring parent set with the lowest scoring parent set that do not exceed the treewidth bound. The resultant method is called k-MAX. As the former, k-MAX requires predefining a maximum execution time to explore the space of solutions. Ex- tensive experiments showed that both approaches consistently outperform some of the above methods [Parviainen et al., 2014; Nie et al., 2014, 2017] for learning bounded treewidth BNs. A limitation of k-greedy and k-MAX is that they only learn BNs whose reverse topological order, when used as an EO, has at most width k.
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142 Lee mas

Prediction in health domain using Bayesian networks optimization based on induction learning techniques

Prediction in health domain using Bayesian networks optimization based on induction learning techniques

The Bayesian networks can make the classification task, a particular case of prediction, that it is characterized to have a single variable of the database (class) that we desire to predict, whereas all the others are the data evidence of the case that we desire to classify. A great amount of variables in the database can exist; some of them directly related to the class variable but also other variables that have not direct influence on the class.

9 Lee mas

Pronóstico de grandes sismos mediante el análisis de semiperiodicidad de procesos puntuales etiquetadosForecast of large earthquakes through semi-periodicity analysis of labeled point processes

Pronóstico de grandes sismos mediante el análisis de semiperiodicidad de procesos puntuales etiquetadosForecast of large earthquakes through semi-periodicity analysis of labeled point processes

Large  earthquakes  have  semi-­‐periodic  behavior  as  a  result  of  critically  self-­‐organized  processes  of  stress   accumulation  and  release  in  seismogenic  regions.  Hence,  large  earthquakes  in  a  given  region  constitute   semi-­‐periodic  sequences  with  recurrence  times  varying  slightly  from  periodicity.  In  previous  studies,  it   has  been  shown  that  it  is  possible  to  identify  these  sequences  through  Fourier  analysis  of  the  occurrence   time  series  of  large  earthquakes  from  a  given  region,  by  realizing  that  not  all  earthquakes  in  the  region   need  belong  to  the  same  sequence,  since  there  can  be  more  than  one  process  of  stress  accumulation   and  release  in  the  region.  Sequence  identification  can  be  used  to  forecast  earthquake  occurrence  with   well   determined   confidence   bounds.This   work   presents   improvements   on   the   above   mentioned   sequence   identification   and   forecasting   method:   a)   Considers   the   influence   of   earthquake   size   on   the   spectral   analysis,   and   its   importance   in   semi-­‐periodic   sequences   identification,   which   means   that   earthquake  occurrence  times  are  treated  as  a  labeled  point  process.  b)  Uses  an  improved  estimation  of   non-­‐randomness  probability.  c)  Improves  the  estimation  upper  limit  uncertainties  to  use  in  forecasts.  d)   Uses   Bayesian   analysis   to   evaluate   aftcast   (forecast   done   a   posteriori)   performance.   e)   Estimates   the   forecast  robustness  through  Monte  Carlo  simulation  of  noise  in  magnitude  data.  This  improved  method   was   successfully   tested   on   synthetic   data   and   subsequently   applied   to   real   data   from   some   specific   regions:   the   southwestern   coast   of   Mexico   and   the   northeastern   Japan   Arc.   Semi-­‐periodic   sequences   with  high  non-­‐randomness  probability  were  identified:  1  sequence  of  nine  events  with   ! !M ≥ 7.4  in  Mexico   and  1  sequence  of  four  events  with   ! !M ≥ 8.0  in  Japan.  Aftcasts  were  successfully  done  for  each  of  the  last   events   in   the   identified   sequences,   and   the   aftcast   probabilities   were   upgraded   through   Bayesian   analysis  and  compared  with  the  updated  forecast  probability  for  the  sequence  including  the  last  event.   The  forecast  probabilities  for  intervals  two  standard  deviations  wide  are  larger  than  the  corresponding   Poissonian  occurrence  probabilities,  and  the  probability  gains  are  significant.    
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78 Lee mas

Bayesian analysis of textual data

Bayesian analysis of textual data

Table 5.4 presents the proportion of times each one of the three disputed texts is correctly attributed to the author that actually wrote it. These proportions are estimates of the long run (frequentist) probability that the method correctly classifies the disputed text to the actual author. The first row of that table, for example, indicates that the decision tree approach correctly classifies D1 to be by Author 1 in 639 out of the 1000 realizations, the support vector machine approach does that 588 times and the logistic regression ap- proach does that 653 times, all compared to the 733 times that the Bayesian multinomial approach correctly classifies D1. Different from the Bayesian multinomial method, the three top-of-the-counter alternative supervised classification approaches considered here do not allow for an open-set classification framework, because they can not handle the hypothesis that neither Author 1 nor Author 2 wrote a text. Hence, no proportion of correct classifications can be provided for DU under these alternative approaches. Table 5.4 indicates that the Bayesian multinomial method implemented with a uniform prior for the multinomial parameters performs better than the logistic regression based approach and that, in turn, the logistic regression approach performs better than the decision tree and the support vector machine based approaches. The performance of the three alternative methods considered is specially poor in the five training texts per author scenario, because they are designed to work with many training samples and not just a few.
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195 Lee mas

The evolution of ecomorphological traits within the Abrothrichini (Rodentia : Sigmodontinae): A Bayesian phylogenetics approach

The evolution of ecomorphological traits within the Abrothrichini (Rodentia : Sigmodontinae): A Bayesian phylogenetics approach

j . We estimated the aspects of trait evolution using a Bayesian MCMC framework (Pagel et al., 2004), selecting the parameter val- ues from the chains that gave the highest value of likelihood given the model of evolution. In this sense, the likelihood values distribu- tion for different aspects of trait evolution provide a direct measure of their relative goodness-of-fit to the data. However, we used the Bayes factors (Gelman et al., 1995) to compare an observed j mod- el with the null hypothesis models of j = 0 and j = 1. The Bayes factor compares two posterior probability distributions, by asking which is larger after adjusting for differences between the models in terms of the numbers of parameters they use. Models with more parameters are expected to fit the data better by chance, and so the Bayes factor attaches a penalty to each extra parameter. Given marginal likelihoods (p(D/M)) for two different models (M), the log-Bayes factor is defined as:
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8 Lee mas

A. J. Drummond, A. Rambaut, B. Shapiro, and O. G. Pybus - Bayesian skyline plots

A. J. Drummond, A. Rambaut, B. Shapiro, and O. G. Pybus - Bayesian skyline plots

To investigate the behavior of the Bayesian skyline plot model, we analyzed two simulated data sets using our MCMC method. We followed Strimmer and Pybus (2001) and performed the following simulations: (1) Coales- cent trees were simulated under two demographic models, hðtÞ 50:05 (constant) and hðtÞ 5e 1000t (exponential). These models approximately represent the history and genetic diversity of animal mitochondrial DNA (mtDNA) se- quences. In these demographic models, time is measured in mutations per site. (2) Sequences were simulated down the trees using the HKY (Hasegawa, Kishino, and Yano 1985) model (transition/transversion ratio 5 10; nucleotide frequencies A 5 0.3, C5 0.25, G 5 0.15, and T 5 0.3) with a uniform mutation rate among sites. The constant-model sequence alignment was 500 base pairs (bp) in length, and the exponential-model alignment was 1,500 bp long. (3) The resulting sequence alignments were then analyzed using the MCMC method described above. In both analyses, the number of groups (m) was set to 12, and MCMC chains were run for 10,000,000 iterations, of which the first 1% was discarded to allow for burn-in. The substitution model used was HKY, and the transition/transversion ratio was coestimated along with the parameters of the Bayesian sky- line plot and the ancestral genealogy. Genealogies and model parameters were sampled every 1,000 iterations, and the results are summarized as a Bayesian skyline plot, shown in figure 2.
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8 Lee mas

Detection and tracking of multiple targets using wireless sensor networks - Detección y seguimiento de múltiples blancos en redes inalámbricas de sensores

Detection and tracking of multiple targets using wireless sensor networks - Detección y seguimiento de múltiples blancos en redes inalámbricas de sensores

properly and estimate the target states. Conventional particle filters with finite number of particles fail to do the former and estimators based on the MMSE fail to do the latter. This section explains why this information cannot be properly extracted using MMSE estimators based on conventional particle filters and, then addresses how to extract target labelling information when there are a fixed and known number of targets. Therefore, the following discussion is based on this case. There are two usual approaches to represent the multitarget state in multiple target tracking from the Bayesian perspective. One uses sets [131] and the other uses vectors as done in this thesis. Usual set notation implies that targets are not labelled and, thus, one is not interested in knowing which target state estimate corresponds to each target [185] unless explicit labels are included in the target states [129]. Adopting the usual (unlabelled) set notation implies that all that matters is to estimate the target states. Contrarily, in vector notation, the order implicit in the components of a vector implies that targets are labelled when the number of targets is fixed and known as pointed out in Section 4.3 3 . Therefore, in this case, if the posterior PDF of the multitarget state is known, the information regarding target labels is included in the posterior, i.e., the probability that a target state estimate corresponds to a given target. It should be noted that if labelled set notation is used, the procedure to extract target labelling information is exactly the same as the one indicated in this section, which uses vector notation, because of the bijection that exists between labelled sets and vectors as indicated in Appendix B.
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311 Lee mas

Contributions to Bayesian network learning with applications to neuroscience

Contributions to Bayesian network learning with applications to neuroscience

In real life problems, continuous data may not fit any standard parametric distribution. Therefore, the assumption of a parametric shape might yield misleading conclusions or re- sults. Non-parametric density estimation is used to avoid the parametric assumptions in probabilistic modeling and reasoning [218, 462]. Non-parametric estimation techniques can be classified in four categories [201]: histograms, orthogonal series, kernels and splines. His- tograms are based on transforming the continuous data into discrete data. Discretization is one of the most widely used approaches for data transformation, and a large number of dis- cretization techniques have been proposed in the literature [208, 527]. However, important information can be lost during the discretization process. A different approach approxi- mates probability densities by an orthogonal series expansion using, e.g., Hermite, Fourier or trigonometric orthonormal systems of functions. Their main drawback is that the resulting estimate is frequently not a proper density (non-negative and integrating to one). Recently, KDE has received a lot of attention because it provides a flexible and powerful tool for non- parametric density estimation. However, KDE has to save and analyze the complete training dataset to evaluate the density of each data point. Also, bandwidth selection for KDE can be challenging and a lot of different approaches have been proposed for finding bandwidth values that accurately model the data without overfitting [87, 283]. Finally, splines are piecewise polynomial curves frequently used for approximating arbitrary functions.
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346 Lee mas

Prediction of Federal Funds Target Rate: a dynamic logistic Bayesian Model averaging approach

Prediction of Federal Funds Target Rate: a dynamic logistic Bayesian Model averaging approach

Table 5 lists the complete set of 7 potential predictors we use in our analysis. It is worth mentioning that variables measured at a quarterly frequency, such as Expected y/y GDP (data gathered from Bloomberg’s survey), are transformed to monthly observations by keeping the value constant for the three months within the quarter. This approach is a common market practice because during the three- month period no new information about the variable is revealed. Since the first group of predictors is subject to revisions after their initial release, the currently available time series is different from the one that was the FOMC’s members’ disposal at the time they met; therefore, we decided to employ data as available on a real-time basis in order to make our empirical analysis as realistic as possible.
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27 Lee mas

Robust techniques for multiple target tracking and fully adaptive radar = Técnicas robustas para seguimiento de múltiples blancos y radar adaptativo

Robust techniques for multiple target tracking and fully adaptive radar = Técnicas robustas para seguimiento de múltiples blancos y radar adaptativo

limited class of problems [152], so that one generally has to rely on approximations. The performance of these approximations depends on several factors, with attention being often dedicated primarily to the form of the dynamic and measurement models. Nevertheless, a key factor for performance of these types of methods is the dimension of the space in which the state of the system can take values. If the dimension of the state space is high, as a general rule, the performance of approximated Bayesian filtering techniques severely drops. Common examples of high-dimensional state estimation problems are the tracking of multiple targets in surveillance applications or meteorological estimation in large areas. There is therefore a great interest in the development of robust Bayesian filtering methods which can accurately provide estimates in high-dimensional state spaces. In Part I of this thesis, this problem is tackled, proposing different methods for high-dimensional Bayesian filtering. These methods were conceived with an eye on their application to the problem of multiple target tracking (MTT). However, we wish to emphasize that these methods can be used in a wide range of applications for high-dimensional filtering besides MTT. With this purpose in mind, the proposed methods are first presented and derived in a general setting, and then, their performance is illustrated in MTT scenarios.
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291 Lee mas

The design of a Bayesian Network for mobility management in Wireless Sensor Networks

The design of a Bayesian Network for mobility management in Wireless Sensor Networks

This paper proposes a Bayesian network (BN) approach for making explicit the structural and parametric components of a movement context using WSN metadata. The aim is to infer mobility management requirements when a spatial coverage is incorrectly covering a Region of Interest (ROI), regardless the network connectivity. The BN approach provides several advantages regarding to the probabilistic representation of a movement context, the inference of mobility management requirements based on such a context, and the dynamic updating of the movement context every time new metadata are retrieved from the WSN. Previous research works in WSNs have used a similar approach focusing on energy management (Elnahrawy and Nath 2004) and prediction of sensor movement directions (Coles et al. 2009). The main contribution of our work is the analysis of how well a ROI is being covered by mobile sensors, and what are the requirements to improve that coverage given a movement context. A controlled experiment was carried out and the results show that, when the ROI is not being sufficiently covered by a WSN, the BN can probabilistically infer different mobility management requirements, based on a given movement context. Two movement contexts have been used to illustrate this approach. They are related to whether the sensing is being carried out in an emergency situation or not.
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6 Lee mas

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