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Related papers: Optimally-Weighted Herding is Bayesian Quadrature

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We study a nonparametric approach to Bayesian computation via feature means, where the expectation of prior features is updated to yield expected kernel posterior features, based on regression from learned neural net or kernel features of…

Machine Learning · Statistics 2022-08-11 Liyuan Xu , Yutian Chen , Arnaud Doucet , Arthur Gretton

The kernel herding algorithm is used to construct quadrature rules in a reproducing kernel Hilbert space (RKHS). While the computational efficiency of the algorithm and stability of the output quadrature formulas are advantages of this…

Numerical Analysis · Mathematics 2022-07-18 Kazuma Tsuji , Ken'ichiro Tanaka

Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…

Quantum Physics · Physics 2021-09-22 Samuel P. Nolan , Augusto Smerzi , Luca Pezzè

Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…

Quantum Physics · Physics 2024-02-06 Frederic Rapp , Marco Roth

This article concerns testing for equality of distribution between groups. We focus on screening variables with shared distributional features such as common support, modes and patterns of skewness. We propose a Bayesian testing method…

Methodology · Statistics 2016-02-19 Eric F. Lock , David B. Dunson

Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can…

Methodology · Statistics 2021-10-29 Yuling Yao , Gregor Pirš , Aki Vehtari , Andrew Gelman

Kernel methods have recently attracted resurgent interest, showing performance competitive with deep neural networks in tasks such as speech recognition. The random Fourier features map is a technique commonly used to scale up kernel…

Machine Learning · Computer Science 2018-02-01 Tri Dao , Christopher De Sa , Christopher Ré

High throughput technologies have become the practice of choice for comparative studies in biomedical applications. Limited number of sample points due to sequencing cost or access to organisms of interest necessitates the development of…

Methodology · Statistics 2018-07-17 Ariana Broumand , Siamak Zamani Dadaneh

Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…

Machine Learning · Computer Science 2023-02-15 Brian Staber , Sébastien Da Veiga

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…

Machine Learning · Computer Science 2012-06-22 Samuel Gershman , Matt Hoffman , David Blei

We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…

Numerical Analysis · Mathematics 2022-10-12 Satoshi Hayakawa , Harald Oberhauser , Terry Lyons

Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick…

Machine Learning · Statistics 2011-08-15 Ferenc Huszár , Simon Lacoste-Julien

We propose Bayesian extensions of two nonparametric regression methods which are kernel and mutual $k$-nearest neighbor regression methods. Derived based on Gaussian process models for regression, the extensions provide distributions for…

Machine Learning · Computer Science 2016-08-05 Hyun-Chul Kim

The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the…

Machine Learning · Statistics 2017-08-01 Francois-Xavier Briol , Chris J. Oates , Jon Cockayne , Wilson Ye Chen , Mark Girolami

In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…

Statistics Theory · Mathematics 2017-12-14 Elisabeth Gassiat , Judith Rousseau , Elodie Vernet

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…

Machine Learning · Statistics 2023-02-14 A. Duncan , N. Nuesken , L. Szpruch

Bayesian optimization is a popular formalism for global optimization, but its computational costs limit it to expensive-to-evaluate functions. A competing, computationally more efficient, global optimization framework is optimistic…

Machine Learning · Computer Science 2022-09-05 Julia Grosse , Cheng Zhang , Philipp Hennig

We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…

Machine Learning · Statistics 2011-10-25 Cedric Archambeau , Francis Bach

The Bayesian evidence, crucial ingredient for model selection, is arguably the most important quantity in Bayesian data analysis: at the same time, however, it is also one of the most difficult to compute. In this paper we present a…

Methodology · Statistics 2024-05-14 Stefano Rinaldi , Gabriele Demasi , Walter Del Pozzo , Otto A. Hannuksela

We propose a practical Bayesian optimization method over sets, to minimize a black-box function that takes a set as a single input. Because set inputs are permutation-invariant, traditional Gaussian process-based Bayesian optimization…

Machine Learning · Statistics 2021-01-26 Jungtaek Kim , Michael McCourt , Tackgeun You , Saehoon Kim , Seungjin Choi