21 papers · ranked by Valyu relevance
Daniel Robert-Nicoud, Andreas Krause, Viacheslav Borovitskiy
Various applications ranging from robotics to climate science require modeling signals on non-Euclidean domains, such as the sphere. Gaussian process models on manifolds have recently been proposed for such tasks, in particular when uncertainty quantification is needed. In the manifold setting, vectorvalued signals can…
Michael Hutchinson, Alexander Terenin, Viacheslav Borovitskiy, So Takao + 2 more
'So Takao' 'Yee Whye Teh' 'Marc Peter Deisenroth'] Gaussian processes are machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-making systems. Motivated by a desire to deploy Gaussian processes in novel areas of…
Alexander Terenin
This thesis is dedicated to the several hundred Twitter users who thought what I was working on was interesting enough to give it a read, or a comment. Thanks to you, my experiment in writing a thesis in an open-source manner visible to the public was a resounding success. Getting the opportunity to write this thesis…
Miao Huang, Junda Ying, Yuxuan Wang, Haijun Zhou + 2 more
Cell phenotype transition (CPT) plays a pivotal role in various biological processes like development. Recent advancements in single-cell sequencing techniques have uncovered that cell transition dynamics during development are confined on low-dimensional manifolds. However, existing methods are inadequate for directly…
Shane Barratt
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian distribution. We also derive useful results regarding the expected value of…
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…
Abhranil Das, Wilson S. Geisler
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary widely across models. Besides some special cases where these integrals are easy…
Congzhou M Sha, Jian Wang, Nikolay V Dokholyan
Molecular dynamics (MD) is the primary computational method by which modern structural biology explores macromolecule structure and function. Boltzmann generators have been proposed as an alternative to MD, by replacing the integration of molecular systems over time with the training of generative neural networks. This…
Lei Zhang, Huiliang Shang, Yandan Lin, Tiefeng Li
The 6D Pose estimation is a crux in many applications, such as visual perception, autonomous navigation, and spacecraft motion. For robotic grasping, the cluttered and self-occlusion scenarios bring new challenges to the this field. Currently, society uses CNNs to solve this problem. The CNN models will suffer high…
Hongyan Wang, Yanping Bai, Jing Ren, Peng Wang + 4 more
Through extensive literature review, it has been found that sparse Bayesian learning (SBL) is mainly applied to traditional scalar hydrophones and is rarely applied to vector hydrophones. This article proposes a direction of arrival (DOA) estimation method for vector hydrophones based on SBL (Vector-SBL). Firstly…
Eric Schulz, Maarten Speekenbrink, Andreas Krause
This tutorial introduces the reader to Gaussian process regression as a tool to model, actively explore and exploit unknown functions. Gaussian process regression is a powerful, non-parametric Bayesian approach towards regression problems that can be utilized in exploration and exploitation scenarios. This tutorial…
Amelia Carolina Sparavigna
It is important, for further applying the q-Gaussian Tsallis functions, to discuss how they can generalize asymmetric and pseudo-Voigtian functions. Some remarks about Voigt functions are also stressed, regarding the behavior of the wings of Raman spectral components. The use of Voigt and pseudo-Voigt functions implies…
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…
Sara Giarrusso, Paola Gori-Giorgi, Federica Agostini
We generalize the definitions of local scalar potentials named vkin and vN−1, which are relevant to properly describe phenomena such as molecular dissociation with density-functional theory, to the case in which the electronic wavefunction corresponds to a complex current-carrying state. In such a case, an extra term…
James M. Chappell, Azhar Iqbal, John G. Hartnett, Derek Abbott
—There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs' three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body rotations and vectors defined in Clifford geometric algebra. With such a range…
Rui Wang, Yue Wang, Yanping Li, Wenming Cao + 3 more
'Wei Xiang'] Direction-of-arrival (DOA) estimation plays an important role in array signal processing, and the Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is one of the typical super resolution algorithms for direction finding in an electromagnetic vector-sensor (EMVS) array…
Kristopher T. Jensen, Ta-Chu Kao, Jasmine T. Stone, Guillaume Hennequin
Latent variable models are ubiquitous in the exploratory analysis of neural population recordings, where they allow researchers to summarize the activity of large populations of neurons in lower dimensional ‘latent’ spaces. Existing methods can generally be categorized into (i) Bayesian methods that facilitate flexible…
Hermann G. Matthies, Alexander Litvinenko, Bojana Rosić, Elmar Zander
'Elmar Zander'] The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a…
Authors not listed
NMR chemical shifts depend on the applied magnetic flux density, and this becomes more and more important as stronger and stronger magnetic fields are becoming available. Herein, we develop a theory of the field dependence of NMR shifts of paramagnetic molecules in solution. Our derivation leads to two distinct…
Tagir Akhmetshin, Arkadii Lin, Timur Madzhidov, Alexandre Varnek
Autoencoders represent a promising technique for the inverse quantitative structure-activity relationship (QSAR) task. However, undesirable bias, such as atom ordering, affects the neighbourhood behaviour of autoencoders’ latent space and, consequently, usage of the latent vectors as variables in machine-learning…
Pablo Bernal-Polo, Humberto Martínez-Barberá
The problem of attitude estimation is broadly addressed using the Kalman filter formalism and unit quaternions to represent attitudes. This paper is also included in this framework, but introduces a new viewpoint from which the notions of “multiplicative update” and “covariance correction step” are conceived in a…