2,984 research outputs found
Structure-Based Bayesian Sparse Reconstruction
Sparse signal reconstruction algorithms have attracted research attention due
to their wide applications in various fields. In this paper, we present a
simple Bayesian approach that utilizes the sparsity constraint and a priori
statistical information (Gaussian or otherwise) to obtain near optimal
estimates. In addition, we make use of the rich structure of the sensing matrix
encountered in many signal processing applications to develop a fast sparse
recovery algorithm. The computational complexity of the proposed algorithm is
relatively low compared with the widely used convex relaxation methods as well
as greedy matching pursuit techniques, especially at a low sparsity rate.Comment: 29 pages, 15 figures, accepted in IEEE Transactions on Signal
Processing (July 2012
Bayesian Lattice Filters for Time-Varying Autoregression and Time-Frequency Analysis
Modeling nonstationary processes is of paramount importance to many
scientific disciplines including environmental science, ecology, and finance,
among others. Consequently, flexible methodology that provides accurate
estimation across a wide range of processes is a subject of ongoing interest.
We propose a novel approach to model-based time-frequency estimation using
time-varying autoregressive models. In this context, we take a fully Bayesian
approach and allow both the autoregressive coefficients and innovation variance
to vary over time. Importantly, our estimation method uses the lattice filter
and is cast within the partial autocorrelation domain. The marginal posterior
distributions are of standard form and, as a convenient by-product of our
estimation method, our approach avoids undesirable matrix inversions. As such,
estimation is extremely computationally efficient and stable. To illustrate the
effectiveness of our approach, we conduct a comprehensive simulation study that
compares our method with other competing methods and find that, in most cases,
our approach performs superior in terms of average squared error between the
estimated and true time-varying spectral density. Lastly, we demonstrate our
methodology through three modeling applications; namely, insect communication
signals, environmental data (wind components), and macroeconomic data (US gross
domestic product (GDP) and consumption).Comment: 49 pages, 16 figure
Feature selection for chemical sensor arrays using mutual information
We address the problem of feature selection for classifying a diverse set of chemicals using an array of metal oxide sensors. Our aim is to evaluate a filter approach to feature selection with reference to previous work, which used a wrapper approach on the same data set, and established best features and upper bounds on classification performance. We selected feature sets that exhibit the maximal mutual information with the identity of the chemicals. The selected features closely match those found to perform well in the previous study using a wrapper approach to conduct an exhaustive search of all permitted feature combinations. By comparing the classification performance of support vector machines (using features selected by mutual information) with the performance observed in the previous study, we found that while our approach does not always give the maximum possible classification performance, it always selects features that achieve classification performance approaching the optimum obtained by exhaustive search. We performed further classification using the selected feature set with some common classifiers and found that, for the selected features, Bayesian Networks gave the best performance. Finally, we compared the observed classification performances with the performance of classifiers using randomly selected features. We found that the selected features consistently outperformed randomly selected features for all tested classifiers. The mutual information filter approach is therefore a computationally efficient method for selecting near optimal features for chemical sensor arrays
The Automatic Statistician: A Relational Perspective
Department of Computer EngineeringGaussian Processes (GPs) provide a general and analytically tractable way of capturing complex time-varying, nonparametric functions. The time varying parameters of GPs can be explained as a composition of base kernels such as linear, smoothness or periodicity in that covariance kernels are closed under addition and multiplication. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of time-series data by treating unknown time-series data nonparametrically using GPs. Unfortunately, learning a composite covariance kernel with a single time-series dataset often
results in less informative kernels instead of finding qualitative distinct descriptions. We address this issue by proposing a relational kernel learning which can model relationship between sets of data and find shared structure among the time series datasets. We show the shared structure can help learning more accurate models for sets of regression problems with some synthetic data, US top market capitalization stock data and US house sales index data.ope
Inference and Optimization of Real Edges on Sparse Graphs - A Statistical Physics Perspective
Inference and optimization of real-value edge variables in sparse graphs are
studied using the Bethe approximation and replica method of statistical
physics. Equilibrium states of general energy functions involving a large set
of real edge-variables that interact at the network nodes are obtained in
various cases. When applied to the representative problem of network resource
allocation, efficient distributed algorithms are also devised. Scaling
properties with respect to the network connectivity and the resource
availability are found, and links to probabilistic Bayesian approximation
methods are established. Different cost measures are considered and algorithmic
solutions in the various cases are devised and examined numerically. Simulation
results are in full agreement with the theory.Comment: 21 pages, 10 figures, major changes: Sections IV to VII updated,
Figs. 1 to 3 replace
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