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Related papers: Variational Implicit Processes

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Like many numerical methods, solvers for initial value problems (IVPs) on ordinary differential equations estimate an analytically intractable quantity, using the results of tractable computations as inputs. This structure is closely…

Numerical Analysis · Mathematics 2017-08-14 Michael Schober , Simo Särkkä , Philipp Hennig

Deep Gaussian processes (DGPs) provide a rich class of models that can better represent functions with varying regimes or sharp changes, compared to conventional GPs. In this work, we propose a novel inference method for DGPs for computer…

Machine Learning · Statistics 2022-08-18 Deyu Ming , Daniel Williamson , Serge Guillas

Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…

Transformed Gaussian Processes (TGPs) are stochastic processes specified by transforming samples from the joint distribution from a prior process (typically a GP) using an invertible transformation; increasing the flexibility of the base…

Machine Learning · Computer Science 2023-11-03 Francisco Javier Sáez-Maldonado , Juan Maroñas , Daniel Hernández-Lobato

We present a new approach to automatic amortized inference in universal probabilistic programs which improves performance compared to current methods. Our approach is a variation of inference compilation (IC) which leverages deep neural…

Machine Learning · Computer Science 2019-10-29 William Harvey , Andreas Munk , Atılım Güneş Baydin , Alexander Bergholm , Frank Wood

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

Machine Learning · Computer Science 2010-02-23 Yuan Qi , Ahmed H. Abdel-Gawad , Thomas P. Minka

Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…

Machine Learning · Computer Science 2021-02-26 Juan Maroñas , Oliver Hamelijnck , Jeremias Knoblauch , Theodoros Damoulas

Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs,…

Machine Learning · Statistics 2017-11-15 Hugh Salimbeni , Marc Deisenroth

Gaussian processes (GPs) are non-parametric Bayesian models that are widely used for diverse prediction tasks. Previous work in adding strong privacy protection to GPs via differential privacy (DP) has been limited to protecting only the…

Machine Learning · Computer Science 2021-11-12 Antti Honkela , Laila Melkas

Sparse Gaussian processes and various extensions thereof are enabled through inducing points, that simultaneously bottleneck the predictive capacity and act as the main contributor towards model complexity. However, the number of inducing…

Machine Learning · Computer Science 2021-07-27 Anders Kirk Uhrenholt , Valentin Charvet , Bjørn Sand Jensen

Deep neural networks excel at function approximation, yet they are typically trained from scratch for each new function. On the other hand, Bayesian methods, such as Gaussian Processes (GPs), exploit prior knowledge to quickly infer the…

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…

Machine Learning · Statistics 2015-03-23 Yarin Gal , Richard Turner

Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that…

Machine Learning · Statistics 2018-11-13 Marton Havasi , José Miguel Hernández-Lobato , Juan José Murillo-Fuentes

A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. Algorithms are proposed to detect changes in such i.p.i.d.…

Statistics Theory · Mathematics 2018-10-31 Taposh Banerjee , Prudhvi Gurram , Gene Whipps

We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational…

Machine Learning · Computer Science 2023-11-23 Maria Bånkestad , Jens Sjölund , Jalil Taghia , Thomas B. Schöon

Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the…

Computation · Statistics 2021-03-10 Topi Paananen , Juho Piironen , Paul-Christian Bürkner , Aki Vehtari

Solving high-dimensional Bayesian inverse problems (BIPs) with the variational inference (VI) method is promising but still challenging. The main difficulties arise from two aspects. First, VI methods approximate the posterior distribution…

Numerical Analysis · Mathematics 2023-02-23 Yingzhi Xia , Qifeng Liao , Jinglai Li

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

Machine Learning · Statistics 2016-06-24 Christos Louizos , Max Welling

The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general…

Data Analysis, Statistics and Probability · Physics 2017-02-01 Ethan Atkins , Matthias Morzfeld , Alexandre J. Chorin

Invariants are a set of properties over program attributes that are expected to be true during the execution of a program. Since developing those invariants manually can be costly and challenging, there are a myriad of approaches that…

Robotics · Computer Science 2020-12-15 Meriel Stein , Sebastian Elbaum , Lu Feng , Shili Sheng