Gaussian function

About: Gaussian function is a research topic. Over the lifetime, 7073 publications have been published within this topic receiving 171197 citations. The topic is also known as: Gaussian.

Prediction with Gaussian processes: from linear regression to linear prediction and beyond

Abstract: The main aim of this paper is to provide a tutorial on regression with Gaussian processes. We start from Bayesian linear regression, and show how by a change of viewpoint one can see this method as a Gaussian process predictor based on priors over functions, rather than on priors over parameters. This leads in to a more general discussion of Gaussian processes in section 4. Section 5 deals with further issues, including hierarchical modelling and the setting of the parameters that control the Gaussian process, the covariance functions for neural network models and the use of Gaussian processes in classification problems.

Locality-sensitive binary codes from shift-invariant kernels

Abstract: This paper addresses the problem of designing binary codes for high-dimensional data such that vectors that are similar in the original space map to similar binary strings. We introduce a simple distribution-free encoding scheme based on random projections, such that the expected Hamming distance between the binary codes of two vectors is related to the value of a shift-invariant kernel (e.g., a Gaussian kernel) between the vectors. We present a full theoretical analysis of the convergence properties of the proposed scheme, and report favorable experimental performance as compared to a recent state-of-the-art method, spectral hashing.

Auditory filter shapes derived with noise stimuli

Abstract: A wide‐band noise having a deep notch with sharp edges was used to mask a tone. The notch was centered on the tone, and threshold was measured as the width of the notch was increased from 0.0 to 0.8 times the tone frequency (0.5, 1.0, or 2.0 kHz). The spectrum level of the noise was 40 dB SPL. If it is assumed that the auditory filter is reasonably symmetric at these intensities, then the shape of the filter centered on the tone can be estimated from the first derivative of the curve relating tone threshold to the width of the notch in the noise. The 3‐dB bandwidths of the filters obtained were about 0.13 of their center frequency. In the region of the passband, the Gaussian curve provides a good approximation to the shape of the derived filters. The equivalent rectangular bandwidths of the Gaussian approximations are about 0.20 of their center frequency, which is comparable to the critical‐band estimates of R. Zwicker, G. Flottorp, and S. S. Stevens [’’Critical bandwidth in loudness summation,’’ J. Acoust. Soc. Am. 29, 548–557 (1957)]. The Gaussian approximation cannot be used outside the passband, because the tails of the derived filters do not fall as fast as the Gaussian curve. Subject Classification: [43]65.58, [43]65.35; [43]80.50.

Universal quantum computation with continuous-variable cluster states.

Abstract: We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.