Continuous-Space Gaussian Process Regression and Generalized Wiener Filtering with Application to Learning Curves
نویسندگان
چکیده
Gaussian process regression is a machine learning paradigm, where the regressor functions are modeled as realizations from an a priori Gaussian process model. We study abstract continuous-space Gaussian regression problems where the training set covers the whole input space instead of consisting of a finite number of distinct points. The model can be used for analyzing theoretical properties of Gaussian process regressors. In this paper, we present the general continuous-space Gaussian process regression equations and discuss their close connection with Wiener filtering. We apply the results to estimation of learning curves as functions of training set size and input dimensionality.
منابع مشابه
Application of Model-Based Estimation to Time-Delay Estimation of Ultrasonic Testing Signals
Time-Delay-Estimation (TDE) has been a topic of interest in many applications in the past few decades. The emphasis of this work is on the application of model-based estimation (MBE) for TDE of ultrasonic signals used in ultrasonic thickness gaging. Ultrasonic thickness gaging is based on precise measurement of the time difference between successive echoes which reflect back from the back wall ...
متن کاملSpeech Enhancement Using Gaussian Mixture Models, Explicit Bayesian Estimation and Wiener Filtering
Gaussian Mixture Models (GMMs) of power spectral densities of speech and noise are used with explicit Bayesian estimations in Wiener filtering of noisy speech. No assumption is made on the nature or stationarity of the noise. No voice activity detection (VAD) or any other means is employed to estimate the input SNR. The GMM mean vectors are used to form sets of over-determined system of equatio...
متن کاملTO APPEAR IN SPECIAL ISSUE: ADVANCES IN KERNEL-BASED LEARNING FOR SIGNAL PROCESSING IN THE IEEE SIGNAL PROCESSING MAGAZINE 1 Spatio-Temporal Learning via Infinite-Dimensional Bayesian Filtering and Smoothing
Gaussian process based machine learning is a powerful Bayesian paradigm for non-parametric non-linear regression and classification. In this paper, we discuss connections of Gaussian process regression with Kalman filtering, and present methods for converting spatio-temporal Gaussian process regression problems into infinite-dimensional state space models. This formulation allows for use of com...
متن کاملSpatio-Temporal Learning via Infinite-Dimensional Bayesian Filtering and Smoothing
Gaussian process based machine learning is a powerful Bayesian paradigm for non-parametric non-linear regression and classification. In this paper, we discuss connections of Gaussian process regression with Kalman filtering, and present methods for converting spatio-temporal Gaussian process regression and classification problems into infinite-dimensional state space models. This formulation al...
متن کاملRelativistic diffusion processes and random walk models
The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As is well known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equa...
متن کامل