Browsing by Subject "Gaussian processes"
Now showing 1 - 8 of 8
Results Per Page
Sort Options
Item Algorithms and data structures for cache-efficient computation: theory and experimental evaluation(2007-08) Chowdhury, Rezaul Alam; Ramachandran, VijayaItem Bayesian learning methods for neural coding(2013-12) Park, Mi Jung; Pillow, Jonathan W.; Bovik, Alan C. (Alan Conrad), 1958-A primary goal in systems neuroscience is to understand how neural spike responses encode information about the external world. A popular approach to this problem is to build an explicit probabilistic model that characterizes the encoding relationship in terms of a cascade of stages: (1) linear dimensionality reduction of a high-dimensional stimulus space using a bank of filters or receptive fields (RFs); (2) a nonlinear function from filter outputs to spike rate; and (3) a stochastic spiking process with recurrent feedback. These models have described single- and multi-neuron spike responses in a wide variety of brain areas. This dissertation addresses Bayesian methods to efficiently estimate the linear and non-linear stages of the cascade encoding model. In the first part, the dissertation describes a novel Bayesian receptive field estimator based on a hierarchical prior that flexibly incorporates knowledge about the shapes of neural receptive fields. This estimator achieves error rates several times lower than existing methods, and can be applied to a variety of other neural inference problems such as extracting structure in fMRI data. The dissertation also presents active learning frameworks developed for receptive field estimation incorporating a hierarchical prior in real-time neurophysiology experiments. In addition, the dissertation describes a novel low-rank model for the high dimensional receptive field, combined with a hierarchical prior for more efficient receptive field estimation. In the second part, the dissertation describes new models for neural nonlinearities using Gaussian processes (GPs) and Bayesian active learning algorithms in closed-loop neurophysiology experiments to rapidly estimate neural nonlinearities. The dissertation also presents several stimulus selection criteria and compare their performance in neural nonlinearity estimation. Furthermore, the dissertation presents a variation of the new models by including an additional latent Gaussian noise source, to infer the degree of over-dispersion in neural spike responses. The proposed model successfully captures various mean-variance relationships in neural spike responses and achieves higher prediction accuracy than previous models.Item Edge detection in noisy images using directional diffusion with log filters(Texas Tech University, 1996-08) Liu, ChangImage noise reduction and edge detection have been important image processing techniques. Traditional isotropic image smoothing reduces noise at the cost of image blurring. Anisotropic smoothing tries to maintain the image features, while reducing noise. This thesis presents an anisotropic smoothing implementation that only uses a 3-by-3 window, and therefore is easy to implement in hardware. Edge detection is also studied in this thesis. A pre-processing technique is proposed to do position dependent brightness correction. This technique makes edge thresholding easier. We also present an algorithm that implements Gaussian filtering more accurately than Gauss-Hermite integration at the cost of an insignificant increase in computing complexity.Item Experimental investigation of stochastic vibration of nonlinear structures(Texas Tech University, 1986-12) Sullivan, Douglas GrantThe purpose of this experimental investigation is to measure the dynamic response of an aeroelastic structure involving nonlinear coupling to random parametric vibration. Two main series of tests are conducted under two different bandwidths. The first test corresponds to isolation of the first normal mode natural frequency. The second test corresponds to a bandwidth which covers the second normal mode frequency. The tests are conducted when the structure is tuned internally such that the second normal mode frequency is twice the first normal mode frequency. Experimental measurements are processed to estimate the response mean squares. The influence of excitation spectral density level and internal detuning on the response mean squares is examined. The results confirm regions of instability as predicted in harmonic excitation but there is no evidence of the well known saturation phenomenon. The results differ from the theoretical results obtained for the same model under white band random excitation. This disagreement is mainly due to the fact that the excitation is represented by a physical white noise process in the analytical model while it is a band— limited process in the actual experiment.Item Gaussian Process Modeling and Computation in Engineering Applications(2014-07-08) Pourhabib, ArashBig Data refers to the complexity, high-dimensionality, and high volume of information which are common features in many contemporary engineering applications. In the context of Big Data, however, specific treatments are required to successfully apply and implement Gaussian processes. This dissertation discusses new methodologies for solving three critical problems: analysis of spatial-temporal systems for wind energy applications; multi-fidelity analysis for nano-manufacturing systems; and predictive modeling for large datasets. First, we develop a spatial-temporal model for local wind fields in a wind farm with more than 200 wind turbines. Our framework utilizes the correlation among the derivatives of wind speeds to find a neighborhood of predictors. We extend the model to incorporate the wind direction as a variable to define regimes and fit a separate model for each regime. We consider other meteorological measurements, such as air pressure and temperature, by calculating a theoretical wind called the geostrophic wind to enhance the model's predictive power. We present the model in an optimization framework and solve it through numerical techniques. We compare the model's performance with some alternatives in order to demonstrate its prediction accuracy. Second, we consider a multi-fidelity analysis for predicting the Young's modules of buckypaper, a nano-manufactured product. The data for this problem derive from expensive, but accurate, physical experiments and an inexpensive, but less accurate, simulation model. The practice of integrating such data with different levels of accuracy is called multi-fidelity analysis. The challenge is that some of the input variables in the physical experiments are difficult to measure. We formulate the problem by introducing latent variables and then imputing unobserved latent variables in a two-step process: defining the functional relationship between observed and latent variables, and finding the optimal relationship by minimizing the distance between them. We demonstrate that this problem can be understood as a case of non-isometric curve to surface matching. Third, we apply Gaussian process regression to large datasets. We propose a Bayesian Site Selection (BSS) approach which approximates the likelihood of the Gaussian process by using unobserved variables called pseudo-inputs. The BSS framework enables us to learn both the number and the location of the pseudo-inputs simultaneously through reversible jump Markov chain Monte Carlo methods. Testing the proposed method on both real and artificial datasets shows that the BSS approach provides a sensible trade-off between the prediction accuracy and computation time.Item Hessian-based response surface approximations for uncertainty quantification in large-scale statistical inverse problems, with applications to groundwater flow(2013-08) Flath, Hannah Pearl; Ghattas, Omar N.Subsurface flow phenomena characterize many important societal issues in energy and the environment. A key feature of these problems is that subsurface properties are uncertain, due to the sparsity of direct observations of the subsurface. The Bayesian formulation of this inverse problem provides a systematic framework for inferring uncertainty in the properties given uncertainties in the data, the forward model, and prior knowledge of the properties. We address the problem: given noisy measurements of the head, the pdf describing the noise, prior information in the form of a pdf of the hydraulic conductivity, and a groundwater flow model relating the head to the hydraulic conductivity, find the posterior probability density function (pdf) of the parameters describing the hydraulic conductivity field. Unfortunately, conventional sampling of this pdf to compute statistical moments is intractable for problems governed by large-scale forward models and high-dimensional parameter spaces. We construct a Gaussian process surrogate of the posterior pdf based on Bayesian interpolation between a set of "training" points. We employ a greedy algorithm to find the training points by solving a sequence of optimization problems where each new training point is placed at the maximizer of the error in the approximation. Scalable Newton optimization methods solve this "optimal" training point problem. We tailor the Gaussian process surrogate to the curvature of the underlying posterior pdf according to the Hessian of the log posterior at a subset of training points, made computationally tractable by a low-rank approximation of the data misfit Hessian. A Gaussian mixture approximation of the posterior is extracted from the Gaussian process surrogate, and used as a proposal in a Markov chain Monte Carlo method for sampling both the surrogate as well as the true posterior. The Gaussian process surrogate is used as a first stage approximation in a two-stage delayed acceptance MCMC method. We provide evidence for the viability of the low-rank approximation of the Hessian through numerical experiments on a large scale atmospheric contaminant transport problem and analysis of an infinite dimensional model problem. We provide similar results for our groundwater problem. We then present results from the proposed MCMC algorithms.Item Stationary response of liquid free surface under wide-band random parametric excitation(Texas Tech University, 1983-05) Soundararajan, AravamudhanThe stationary response of a liquid free surface in a partially filled cylindrical container, to a wide band random parametric excitation, is investigated. Two analytical approaches are employed. The first is the Gaussian closure scheme to truncate the infinite hierarchy moment equations obtained through the Fokker-Planck equation, and the second is the Stratonovich stochastic averaging approach. The validity of the two solutions is examined by comparing the two analytically predicted probability densities with the one obtained through experiments. The comparison reveals poor agreement with the Gaussian probability density. In contrast, the probability density derived by the averaging method agrees very well with the experimental density.Item Transfer learning for classification of spatially varying data(2010-08) Jun, Goo; Ghosh, Joydeep; Aggarwal, J. K.; Crawford, Melba M.; Caramanis, Constantine; Sanghavi, Sujay; Grauman, KristenMany real-world datasets have spatial components that provide valuable information about characteristics of the data. In this dissertation, a novel framework for adaptive models that exploit spatial information in data is proposed. The proposed framework is mainly based on development and applications of Gaussian processes. First, a supervised learning method is proposed for the classification of hyperspectral data with spatially adaptive model parameters. The proposed algorithm models spatially varying means of each spectral band of a given class using a Gaussian process regression model. For a given location, the predictive distribution of a given class is modeled by a multivariate Gaussian distribution with spatially adjusted parameters obtained from the proposed algorithm. The Gaussian process model is generally regarded as a good tool for interpolation, but not for extrapolation. Moreover, the uncertainty of the predictive distribution increases as the distance from the training instances increases. To overcome this problem, a semi-supervised learning algorithm is presented for the classification of hyperspectral data with spatially adaptive model parameters. This algorithm fits the test data with a spatially adaptive mixture-of-Gaussians model, where the spatially varying parameters of each component are obtained by Gaussian process regressions with soft memberships using the mixture-of-Gaussian-processes model. The proposed semi-supervised algorithm assumes a transductive setting, where the unlabeled data is considered to be similar to the training data. This is not true in general, however, since one may not know how many classes may existin the unexplored regions. A spatially adaptive nonparametric Bayesian framework is therefore proposed by applying spatially adaptive mechanisms to the mixture model with infinitely many components. In this method, each component in the mixture has spatially adapted parameters estimated by Gaussian process regressions, and spatial correlations between indicator variables are also considered. In addition to land cover and land use classification applications based on hyperspectral imagery, the Gaussian process-based spatio-temporal model is also applied to predict ground-based aerosol optical depth measurements from satellite multispectral images, and to select the most informative ground-based sites by active learning. In this application, heterogeneous features with spatial and temporal information are incorporated together by employing a set of covariance functions, and it is shown that the spatio-temporal information exploited in this manner substantially improves the regression model. The conventional meaning of spatial information usually refers to actual spatio-temporal locations in the physical world. In the final chapter of this dissertation, the meaning of spatial information is generalized to the parametrized low-dimensional representation of data in feature space, and a corresponding spatial modeling technique is exploited to develop a nearest-manifold classification algorithm.