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.

Variational inference for latent variables and uncertain inputs in Gaussian processes

Abstract: The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where the latent projection variables are maximised over rather than integrated out. In this paper we present a Bayesian method for training GP-LVMs by introducing a non-standard variational inference framework that allows to approximately integrate out the latent variables and subsequently train a GP-LVM by maximising an analytic lower bound on the exact marginal likelihood. We apply this method for learning a GP-LVM from i.i.d. observations and for learning non-linear dynamical systems where the observations are temporally correlated. We show that a benefit of the variational Bayesian procedure is its robustness to overfitting and its ability to automatically select the dimensionality of the non-linear latent space. The resulting framework is generic, flexible and easy to extend for other purposes, such as Gaussian process regression with uncertain or partially missing inputs. We demonstrate our method on synthetic data and standard machine learning benchmarks, as well as challenging real world datasets, including high resolution video data.

Sparse and Semi-supervised Visual Mapping with the S^3GP

Abstract: This paper is about mapping images to continuous output spaces using powerful Bayesian learning techniques. A sparse, semi-supervised Gaussian process regression model (S3GP) is introduced which learns a mapping using only partially labelled training data. We show that sparsity bestows efficiency on the S3GP which requires minimal CPU utilization for real-time operation; the predictions of uncertainty made by the S3GP are more accurate than those of other models leading to considerable performance improvements when combined with a probabilistic filter; and the ability to learn from semi-supervised data simplifies the process of collecting training data. The S3GP uses a mixture of different image features: this is also shown to improve the accuracy and consistency of the mapping. A major application of this work is its use as a gaze tracking system in which images of a human eye are mapped to screen coordinates: in this capacity our approach is efficient, accurate and versatile.

Adaptive Double Subspace Signal Detection in Gaussian Background—Part I: Homogeneous Environments

Abstract: In this two-part paper, we consider the problem of adaptive multidimensional/multichannel signal detection in Gaussian noise with unknown covariance matrix. The test data (primary data) is assumed as a collection of sample vectors, arranged as the columns of a rectangular data array. The rows and columns of the signal matrix are both assumed to lie in known subspaces, but with unknown coordinates. Due to this feature of the signal structure, we name this kind of signal as the double subspace signal. Part I of this paper focuses on the adaptive detection in homogeneous environments, while Part II deals with the adaptive detection in partially homogeneous environments. Precisely, in this part, we derive the generalized likelihood ratio test (GLRT), Rao test, Wald test, as well as their two-step variations, in homogeneous environments. Three types of spectral norm tests (SNTs) are also introduced. All these detectors are shown to possess the constant false alarm rate (CFAR) property. Moreover, we discuss the differences between them and show how they work. Another contribution is that we investigate various special cases of these detectors. Remarkably, some of them are well-known existing detectors, while some others are still new. At the stage of performance evaluation, conducted by Monte Carlo simulations, both matched and mismatched signals are dealt with. For each case, more than one scenario is considered.

Efficient nonparametric n -body force fields from machine learning

Abstract: The authors present a scheme to construct classical $n$-body force fields using Gaussian Process (GP) Regression, appropriately mapped over explicit n-body functions (M-FFs). The procedure is possible, and will yield accurate forces, whenever prior knowledge allows to restrict the interactions to a finite order $n$, so that the ``universal approximator'' resolving power of standard GPs or Neural Networks is not needed. Under these conditions, the proposed construction preserves flexibility of training, systematically improvable accuracy, and a clear framework for validation of the underlying machine learning technique. Moreover, the M-FFs are as fast as classical parametrized potentials, since they avoid lengthy summations over database entries or weight parameters.