Gaussian process

About: Gaussian process is a research topic. Over the lifetime, 18944 publications have been published within this topic receiving 486645 citations. The topic is also known as: Gaussian stochastic process.

Time Series Based Structural Damage Detection Algorithm Using Gaussian Mixtures Modeling

Abstract: In this paper, a time series based detection algorithm is proposed utilizing the Gaussian Mixture Models. The two critical aspects of damage diagnosis that are investigated are detection and extent. The vibration signals obtained from the structure are modeled as autoregressive moving average (ARMA) processes. The feature vector used consists of the first three autoregressive coefficients obtained from the modeling of the vibration signals. Damage is detected by observing a migration of the extracted AR coefficients with damage. A Gaussian Mixture Model (GMM) is used to model the feature vector. Damage is detected using the gap statistic, which ascertains the optimal number of mixtures in a particular dataset. The Mahalanobis distance between the mixture in question and the baseline (undamaged) mixture is a good indicator of damage extent. Application cases from the ASCE Benchmark Structure simulated data have been used to test the efficacy of the algorithm. This approach provides a useful framework for data fusion, where different measurements such as strains, temperature, and humidity could be used for a more robust damage decision.

Second-Order Comparison of Gaussian Random Functions and the Geometry of DNA Minicircles

Abstract: Given two samples of continuous zero-mean iid Gaussian processes on [0,1], we consider the problem of testing whether they share the same covariance structure. Our study is motivated by the problem of determining whether the mechanical properties of short strands of DNA are significantly affected by their base-pair sequence; though expected to be true, had so far not been observed in three-dimensional electron microscopy data. The testing problem is seen to involve aspects of ill-posed inverse problems and a test based on a Karhunen–Loeve approximation of the Hilbert–Schmidt distance of the empirical covariance operators is proposed and investigated. When applied to a dataset of DNA minicircles obtained through the electron microscope, our test seems to suggest potential sequence effects on DNA shape. Supplemental material available online.

On the expectation of the product of four matrix-valued Gaussian random variables

Abstract: The formula for the expectation of the product of four scalar real Gaussian random variables is generalized to matrix-valued (real or complex) Gaussian random variables. As an application of the extended formula, a simple derivation is presented of the covariance matrix of instrumental variable estimates of parameters in multivariable regression models. >

Minimum model error estimation for poorly modeled dynamic systems

Abstract: A novel strategy (which we call "minimum model error'* estimation) for postexperiment optimal state estimation of discretely measured dynamic systems is developed and illustrated for a simple example. The method is especially appropriate for postexperiment estimation of dynamic systems whose presumed state governing equations are known to contain, or are suspected of containing, errors. The hew method accounts for errors in the system dynamic model equations in a rigorous manner. Specifically, the dynamic model error terms in the proposed method do not require the usual Kalman filter-smoother process noise assumptions of zero-mean, symmetrically distributed random disturbances, nor do they require representation by assumed parameterized time series (such as Fourier series); Instead, the dynamic model error terms require no prior assumptions other than piecewise continuity. Estimates of the state histories, as well as the dynamic model errors, are Obtained as part of the solution of a two-point boundary value problem. The state estimates are continuous and optimal in a global sense, yet the algorithm processes the measurements sequentially. The example demonstrates the method and shows it to be quite accurate for state estimation of a poorly modeled dynamic system.

Manifold Gaussian Processes for Regression

Abstract: Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too restrictive. One way to alleviate this limitation is to find a different representation of the data by introducing a feature space. This feature space is often learned in an unsupervised way, which might lead to data representations that are not useful for the overall regression task. In this paper, we propose Manifold Gaussian Processes, a novel supervised method that jointly learns a transformation of the data into a feature space and a GP regression from the feature space to observed space. The Manifold GP is a full GP and allows to learn data representations, which are useful for the overall regression task. As a proof-of-concept, we evaluate our approach on complex non-smooth functions where standard GPs perform poorly, such as step functions and robotics tasks with contacts.