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Sparse variational approximations are popular methods for scaling up inference and learning in Gaussian processes to larger datasets. For $N$ training points, exact inference has $O(N^3)$ cost; with $M \ll N$ features, state of the art…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
Calibrating for direction-dependent ionospheric distortions in visibility data is one of the main technical challenges that must be overcome to advance low-frequency radio astronomy. In this paper, we propose a novel probabilistic,…
The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…
Sensors in high-precision mechatronic systems require accurate calibration, which is achieved using test beds that, in turn, require even more accurate calibration. The aim of this paper is to develop a cascaded calibration method for…
The knowledge of the exact structure of the optical system PSF enables a high-quality image reconstruction in fluorescence microscopy. Accurate PSF models account for the vector nature of light and the phase and amplitude modifications.…
Numerical simulation of continuous variable quantum state preparation is a necessary tool for optimization of existing quantum information processing protocols. A powerful instrument for such simulation is the numerical computation in the…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
Iterative phase retrieval algorithms are widely used in digital optics for their efficiency and simplicity. Conventionally, these algorithms do not consider aberrations as they assume an ideal, aberration-free optical system. Here, we…
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the…
In this paper, we investigate Gaussian process regression models where inputs are subject to measurement error. In spatial statistics, input measurement errors occur when the geographical locations of observed data are not known exactly.…
Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…
We propose a method to map the conventional optical interferometry setup into quantum circuits. The unknown phase shift inside a Mach-Zehnder interferometer in the presence of photon loss is estimated by simulating the quantum circuits. For…
Bayesian inference is useful to obtain a predictive distribution with a small generalization error. However, since posterior distributions are rarely evaluated analytically, we employ the variational Bayesian inference or sampling method to…
We study the problem of estimating a function of many parameters acquired by sensors that are distributed in space, e.g., the spatial gradient of a field. We restrict ourselves to a setting where the distributed sensors are probed with…
Advances in photonics require photon-number resolved simulations of quantum optical experiments with Gaussian states. We demonstrate a simple and versatile method to simulate the photon statistics of general multimode Gaussian states. The…
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…
A Gaussian process has been one of the important approaches for emulating computer simulations. However, the stationarity assumption for a Gaussian process and the intractability for large-scale dataset limit its availability in practice.…
Process variations are a major concern in today's chip design since they can significantly degrade chip performance. To predict such degradation, existing circuit and MEMS simulators rely on Monte Carlo algorithms, which are typically too…
This work presents a novel method for extracting potential barrier distributions from experimental fusion cross sections. We utilize a simple Gaussian process regression (GPR) framework to model the observed cross sections as a function of…