27 papers · ranked by Valyu relevance
Olga Korotkova
A generalization of the classic Gaussian random variable to the family of Multi-Gaussian (MG) random variables characterized by shape parameter M > 0, in addition to the mean and the standard deviation, is introduced. The probability density function of the MG family members is the alternating series of the Gaussian…
Krzysztof Domino
The primary goal of computer engineering is the analysis of data. Such data are often large data sets distributed according to various distribution models. In this manuscript, we focus on the analysis of non-Gaussian distributed data. In the case of univariate data analysis, we discuss stochastic processes with…
Zexun Chen, Bo Wang, Alexander N. Gorban
Gaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to re-formulate the matrix-variate Gaussian distribution as a multivariate normal distribution. Although it is effective in many cases, re-formulation is not always workable…
Zexun Chen, Jun Fan, Kuo Wang
Gaussian processes occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong results. The common use of Gaussian processes is in connection with problems related to estimation, detection, and many statistical or machine learning models. With the fast…
Kenric P. Nelson
1 d d , where d is the dimension of the argument of the multivariate coupled-exponential. The coupled-Gaussian distribution is defined such that the argument of the coupled-exponential depends on the coupled-moments but not the coupling parameter. The multivariate version of the coupled-product is defined such that the…
Charalambos D. Charalambous, Jan H. van Schuppen, Shu-Chuan Chu
Examined in this paper is the Gray and Wyner source coding for a simple network of correlated multivariate Gaussian random variables, $Y_{1}:Ω\rightarrowRp_{1}$ and $Y_{2}:Ω\rightarrowRp_{2}$. The network consists of an encoder that produces two private rates $R_{1}$ and $R_{2}$, and a common rate $R_{0}$, and two…
Sheng Wang, Emily Flynn, Russ B. Altman
Molecular interaction networks are our basis for understanding functional interdependencies among genes. Network embedding approaches analyze these complicated networks by representing genes as low-dimensional vectors based on the network topology. These low-dimensional vectors have recently become the building blocks…
Carlos Martí-Gómez, Juannan Zhou, Wei-Chia Chen, Justin B. Kinney + 1 more
Multiplex assays of variant effect (MAVEs) allow the functional characterization of an unprecedented number of sequence variants in both gene regulatory regions and protein coding sequences. This has enabled the study of nearly complete combinatorial libraries of mutational variants and revealed the widespread…
Victor Vicente-Palacios, Santiago Vicente-Tavera, P. Ignacio Dorado-Díaz, Antonio Sanchez-Puente + 6 more
A new statistical analysis methodology, “Multivariate Gaussian Subspatial Regression” (MGSR), has been applied to randomized clinical trial data collected from percutaneous coronary intervention (PCI) patients, which combines the descriptive quality of Factorial Techniques and the predictive power of Gaussian…
Robin A. A. Ince, Bruno L. Giordano, Christoph Kayser, Guillaume A. Rousselet + 2 more
We begin by reviewing the statistical framework of information theory as applicable to neuroimaging data analysis. A major factor hindering wider adoption of this framework in neuroimaging is the difficulty of estimating information theoretic quantities in practice. We present a novel estimation technique that combines…
Sanjeena Subedi, Utkarsh J. Dang
Modern biological data are often multivariate discrete counts, and there has been a dearth of statistical distributions to directly model such counts in an efficient manner. While mixed Poisson distributions, e.g., negative binomial distribution, are often the distribution of choice for univariate data, multivariate…
Takoua Jendoubi, Korbinian Strimmer
Background Canonical correlation analysis (CCA) is a classic statistical tool for investigating complex multivariate data. Correspondingly, it has found many diverse applications, ranging from molecular biology and medicine to social science and finance. Intriguingly, despite the importance and pervasiveness of CCA…
Olga Egorova, Roohollah Hafizi, David C. Woods, Graeme Day
The prediction of crystal structures from first principles requires highly accurate energies for large numbers of putative crystal structures. The accuracy of solid state density functional theory (DFT) calculations is often required, but hundreds or more structures can be present in the low energy region of interest…
Authors not listed
Solving optimization problems, especially for nonlinear and constrained systems, is a challenge. Decades of specialized algorithms have been developed for general and special cases of root finding, minimization (including constraints), for parameter estimation, and mapping connected spaces. These approaches typically…
Qingyang Zhang, Xuan Shi
Gaussian Bayesian networks have become a widely used framework to estimate directed associations between joint Gaussian variables, where the network structure encodes decomposition of multivariate normal density into local terms. However, the resulting estimates can be inaccurate when normality assumption is moderately…
Théo Galy-Fajou, Valerio Perrone, Manfred Opper, Pierre Alquier
Variational inference is a powerful framework, used to approximate intractable posteriors through variational distributions. The de facto standard is to rely on Gaussian variational families, which come with numerous advantages: they are easy to sample from, simple to parametrize, and many expectations are known in…
Yuanqing Lu, Timur Fazletdinov, Zhiwen Pan, Katrin Wondraczek + 1 more
The synthesis of nanoscale particles and particle aggregates from liquid or gaseous precursors is affected by a variety of trade-off relations, for example, in terms of product composition, yield, or energy efficiency. Machine-supported process evaluation and learning (ML) of these relations enables optimization…
E. Bura, S. Duarte, L. Forzani, E. Smucler + 1 more
Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalized linear…
Authors not listed
Optimizing the synthesis conditions of advanced materials is challenging, especially when outcomes are subject to inherent experimental uncertainties. Bayesian optimization is a popular tool for accelerating materials discovery, but its standard risk-neutral framework overlooks the variability of outcomes under…
Raphaël Liégeois, Timothy O. Laumann, Abraham Z. Snyder, Juan Zhou + 1 more
Resting-state functional connectivity is a powerful tool for studying human functional brain networks. Temporal fluctuations in functional connectivity, i.e., dynamic functional connectivity (dFC), are thought to reflect dynamic changes in brain organization and non-stationary switching of discrete brain states.…
Authors not listed
Elucidating Collective Variables (CVs) for biomolecular dynamics is crucial for understanding numerous biological processes. By leveraging the tensor-train data structure, a multilinear version of the AMUSE (Algorithm for Multiple Unknown Signals) algorithm for Koopman approximation (AMUSEt) was recently developed to…
David A. Clifton, Lei Clifton, Samuel Hugueny, Lionel Tarassenko
Novelty detection involves the construction of a “model of normality”, and then classifies test data as being either “normal” or “abnormal” with respect to that model. For this reason, it is often termed one-class classification. The approach is suitable for cases in which examples of “normal” behaviour are commonly…
Baishuai Zuo, Chuancun Yin, Jing Yao
In this paper, we propose the multivariate range Value-at-Risk (MRVaR) and the multivariate range covariance (MR-Cov) as two risk measures and explore their desirable properties in risk management. In particular, we explain that such range-based risk measures are appropriate for risk management of regulation and…
Didong Li, Wenpin Tang, Sudipto Banerjee
Gaussian processes are widely employed as versatile modelling and predictive tools in spatial statistics, functional data analysis, computer modelling and diverse applications of machine learning. They have been widely studied over Euclidean spaces, where they are specified using covariance functions or covariograms…
Amelia Carolina Sparavigna
Previous studies (Sparavigna, 2023) have demonstrated the Tsallis q-Gaussian functions suitable for the analysis of Raman spectra. Here we consider two asymmetric forms of them, with the aim of further improving the fitting of Raman spectra. The first asymmetric form, that we are here proposing for the first time, is a…
Authors not listed
Atmospheric dispersion models are a key component for characterizing methane emissions on oil and gas sites. While some model implementations with varying degrees of complexity are available, existing regulatory-grade dispersion models are cumbersome to apply within an inversion framework on a routine operational level…
Amelia Carolina Sparavigna
In an article by Thibault et al., 2002, we can find measurements of Raman linewidths in the Q branch of carbon monoxide, for mixtures with Argon at different temperatures. A plot is available for the Q(5) line with a fitted Voigt function. Here we show that a q-Gaussian Tsallis function can be used for fitting this…