Related papers: On the probabilistic approach for Gaussian Berezin…
A recovery map effectively cancels the action of a quantum operation to a partial or full extent. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are…
Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the…
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…
We demonstrate how path integrals often used in problems of theoretical physics can be adapted to provide a machinery for performing Bayesian inference in function spaces. Such inference comes about naturally in the study of inverse…
In a previous work, we developed an algorithm for the computation of incomplete Bessel functions, which pose as a numerical challenge, based on the $G_{n}^{(1)}$ transformation and Slevinsky-Safouhi formula for differentiation. In the…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
This paper is the first in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. Our immediate motivation is a specific model, involving…
A new generalization of the modified Bessel function of the second kind $K_{z}(x)$ is studied. Elegant series and integral representations, a differential-difference equation and asymptotic expansions are obtained for it thereby…
We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…
The Hermite polynomials are ubiquitous but can be difficult to work with due to their unwieldy definition in terms of derivatives. To remedy this, we showcase an underappreciated Gaussian integral formula for the Hermite polynomials, which…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
Two recent landmark experiments have performed Gaussian boson sampling (GBS) with a non-programmable linear interferometer and threshold detectors on up to 144 output modes (see Refs.~\onlinecite{zhong_quantum_2020,zhong2021phase}). Here we…
We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…
A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using…
A bosonic-fermionic correspondence allows an analytic definition of functional super derivative, in particular, and a bosonic functional calculus, in general, on Bargmann- Gelfand triples for the second super quantization. A Feynman…
The eigenvalues of an arbitrary quaternionic matrix have a joint probability distribution function first derived by Ginibre. We show that there exists a mapping of this system onto a fermionic field theory and then use this mapping to…
Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…
This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a supervised manner, that can be time-consuming and partly…
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…