28 papers · ranked by Valyu relevance
Fabian Berns, Jan Hüwel, Christian Beecks
Gaussian process models (GPMs) are widely regarded as a prominent tool for learning statistical data models that enable interpolation, regression, and classification. These models are typically instantiated by a Gaussian Process with a zero-mean function and a radial basis covariance function. While these default…
Zoubin Ghahramani
Modelling is fundamental to many fields of science and engineering. A model can be thought of as a representation of possible data one could predict from a system. The probabilistic approach to modelling uses probability theory to express all aspects of uncertainty in the model. The probabilistic approach is synonymous…
Jamie Fairbrother, Christopher Nemeth, Maxime Rischard, Johanni Brea + 1 more
'Thomas Pinder'] Gaussian processes are a class of flexible nonparametric Bayesian tools that are widely used across the sciences, and in industry, to model complex data sources. Key to applying Gaussian process models is the availability of well-developed open source software, which is available in many programming…
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…
Peter S. Swain, Keiran Stevenson, Allen Leary, Luis F. Montano-Gutierrez + 3 more
'Luis F. Montano-Gutierrez' 'Ivan B.N. Clark' 'Jackie Vogel' 'Teuta Pilizota'] Often the time derivative of a measured variable is of as much interest as the variable itself. For a growing population of biological cells, for example, the population's growth rate is typically more important than its size. Here we…
Andrew Gordon Wilson, Elad Gilboa, Arye Nehorai, John P. Cunningham
Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework – GPatt – enabling automatic pattern extrapolation with Gaussian processes on large multidimensional datasets. GPatt unifies and extends highly expressive kernels and fast exact…
Mark Ebden
If we expect the underlying function f(x) to be linear, and can make some assumptions about the input data, we might use a least-squares method to fit a straight line (linear regression). Moreover, if we suspect f(x) may also be quadratic, cubic, or even nonpolynomial, we can use the principles of model selection to…
Allen Ross, Jason Lloyd-Price, Ali Rahnavard
Identifying meaningful associations from small-sample longitudinal data is challenging, especially in low signal-to-noise environments where the Gaussian likelihood assumption does not hold. We introduce two methods to algorithmically perform variable selection with sparse, irregularly sampled, longitudinal count data…
Jörn Tebbe, Andreas Besginow, Markus Lange-Hegermann
— Model Predictive Control evolved as the state of the art paradigm for safety critical control tasks. Controlas-Inference approaches thereof model the constrained optimization problem as a probabilistic inference problem. The constraints have to be implemented into the inference model. A recently introduced…
Julian D. Karch, Andreas M. Brandmaier, Manuel C. Voelkle
In this article, we extend the Bayesian nonparametric regression method Gaussian Process Regression to the analysis of longitudinal panel data. We call this new approach Gaussian Process Panel Modeling (GPPM). GPPM provides great flexibility because of the large number of models it can represent. It allows classical…
Peter S. Swain, Keiran Stevenson, Allen Leary, Luis F. Montano-Gutierrez + 3 more
Often the time-derivative of a measured variable is of as much interest as the variable itself. For a growing population of biological cells, for example, the population's growth rate is typically more important than its size. Here we introduce a non-parametric method to infer first and second time-derivatives as a…
Roland Preuss, Udo von Toussaint, Frank Nielsen, Frédéric Barbaresco + 2 more
'Ali Mohammad-Djafari' 'Martino Trassinelli'] Data for complex plasma-wall interactions require long-running and expensive computer simulations. Furthermore, the number of input parameters is large, which results in low coverage of the (physical) parameter space. Unpredictable occasions of outliers create a need to…
Juan J. L. Velázquez, Luis A. Escamilla, Purba Mukherjee, J. Alberto Vázquez
Processes Regression Authors: ['Juan J. L. Velázquez' 'Luis A. Escamilla' 'Purba Mukherjee' 'J. Alberto Vázquez'] The current accelerated expansion of the Universe remains ones of the most intriguing topics in modern cosmology, driving the search for innovative statistical techniques. Recent advancements in machine…
Paul Rigby, Oscar Pizarro, Stefan B. Williams, Freddie Salsbury Jr
We propose a method for estimating the clustering parameters in a Neyman-Scott Poisson process using Gaussian process regression. It is assumed that the underlying process has been observed within a number of quadrats, and from this sparse information the distribution is modelled as a Gaussian process. The clustering…
Sunny Cui, Elizabeth C. Yoo, Didong Li, Krzysztof Laudanski + 1 more
Gaussian processes (GPs) are a versatile nonparametric model for nonlinear regression and have been widely used to study spatiotemporal phenomena. However, standard GPs offer limited interpretability and generalizability for datasets with naturally occurring hierarchies. With large-scale, rapidly-updating electronic…
Marius Marinescu, Alberto Olivares, Ernesto Staffetti, Junzi Sun + 1 more
'Chi-Hua Chen'] Wind velocity field knowledge is crucial for the future air traffic management paradigm and is key in many applications, such as aircraft performance studies. This paper addresses the problem of spatio-temporal windc velocity field estimation. The north and east wind components within a given air space…
Kanta Matsunaga, Takuto Harada, Shintaro Harada, Akinori Sato + 4 more
Density Prediction between an Insulator and a Semiconductor by Gaussian Process Regression Models for a Modified Process Authors: ['Kanta Matsunaga' 'Takuto Harada' 'Shintaro Harada' 'Akinori Sato' 'Shota Terai' 'Mutsunori Uenuma' 'Tomoyuki Miyao' 'Yukiharu Uraoka'] During data-driven process condition optimization on…
Nuha BinTayyash, Sokratia Georgaka, ST John, Sumon Ahmed + 3 more
The negative binomial distribution is a good model for counts data from both bulk and single-cell RNA-sequencing (RNA-seq). Gaussian process (GP) regression provides a useful non-parametric approach for modeling temporal or spatial changes in gene expression. However, currently available GP regression methods that…
Bohan Xu, Rayus Kuplicki, Sandip Sen, Martin P. Paulus
Normative modeling, a group of methods used to quantify an individual’s deviation from some expected trajectory relative to observed variability around that trajectory, has been used to characterize subject heterogeneity. Gaussian Processes Regression includes an estimate of variable uncertainty across the input…
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…
Baptiste Py, Adeleke Maradesa, Francesco Ciucci
Electrochemical impedance spectroscopy (EIS) is a widespread characterization technique used to study electrochemical systems. However, several shortcomings still limit the application of this technique. First, EIS data is intrinsically noisy, hindering spectra regression and prediction at unknown frequencies. Second…
Aryan Deshwal, Cory Simon, Janardhan Rao Doppa
Given a gas storage or separation task, we wish to search a library of nanoporous materials (NPMs) for the one with the optimal adsorption property. The high cost of measuring the adsorption property of an NPM, whether in the lab or a simulation, precludes exhaustive search. We explain, demonstrate, and advocate…
Chenxi Sui, Ziyang Jiang, Genesis Higueros, David Carlson + 1 more
High-performance batteries are poised for electrification of vehicles and therefore mitigate greenhouse gas emissions, which, in turn, promote a sustainable future. However, the design of optimized batteries is challenging due to the nonlinear governing physics and electrochemistry. Recent advancements have…
Sterling Baird, Jason R. Hall, Taylor D. Sparks
Would you rather search for a line inside a cube or a point inside a square? This type of solution degeneracy often exists in physics-based simulations and wet-lab experiments, but constraining these degeneracies is often unsupported or difficult to implement in many optimization packages, requiring additional time and…
Martin Seifrid, Stanley Lo, Dylan Choi, Gary Tom + 12 more
Martin Seifrid 1 , Stanley Lo 2 , Dylan G. Choi 3 , Gary Tom 2 , My Linh Le 3 , Kunyu Li 3 , Rahul Sankar 3 , Hoai-Thanh Vuong 3 , Hiba Wakidi 3 , Ahra Yi 3 , Ziyue Zhu 3 , Nora Schopp 3 , Aaron Peng 3 , Benjamin Luginbuhl 3 , Thuc-Quyen Nguyen 3 , Alán Aspuru-Guzik 2
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…
Sterling Baird, Jason R. Hall, Taylor D. Sparks
Would you rather search for a line inside a cube or a point inside a square? Physics-based simulations and wet-lab experiments often have symmetries (degeneracies) that allow reducing problem dimensionality or search space, but constraining these degeneracies is often unsupported or difficult to implement in many…
Steen Lysgaard, Paul C. Jennings, Jens Strabo Hummelshøj, Thomas Bligaard + 1 more
A machine learning (ML) model is trained on-the-fly as a computationally inexpensive energy predictor before analyzing how to augment convergence in Genetic Algorithm (GA)-based approaches by using the ML model as a surrogate. This leads to a machine learning accelerated genetic algorithm (MLaGA) combining robust…