Related papers: Multivariate Integral Perturbation Techniques - I …
Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics…
In a recent work we have introduced a novel approach to study the effect of weak non-linearities in the transfer function on the information transmitted by an analogue channel, by means of a perturbative diagrammatic expansion. We extend…
We describe some new univariate spline quasi-interpolants on uniform partitions of bounded intervals. Then we give some applications to numerical analysis: integration, differentiation and approximation of zeros.
The recent progress in computing gauge theory amplitudes can be extended, in many cases, to theories incorporating gravity. This has improved our understanding of the perturbative expansion of N=8 supergravity supporting the ``no-triangle…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
We present a method for the study of second-order superhorizon perturbations in multi field inflationary models with non trivial kinetic terms. We utilise a change of coordinates in field space to separate isocurvature and adiabatic…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…
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 this paper we provide a comprehensive study of statistical inference in linear and allied models which exhibit some analytic perturbations in their design and covariance matrices. We also indicate a few potential applications. In the…
Recently a covariant approach to cold matter universes in the zero-shear hypersurfaces (or longitudinal) gauge has been developed. This approach reveals the existence of an integrability condition, which does not appear in standard…
We investigate non-Gaussianity in general multiple-field inflation using the formalism we developed in earlier papers. We use a perturbative expansion of the non-linear equations to calculate the three-point correlator of the curvature…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
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…
The ``close limit,'' a method based on perturbations of Schwarzschild spacetime, has proved to be a very useful tool for finding approximate solutions to models of black hole collisions. Calculations carried out with second order…
The evolution of gauge invariant second-order scalar perturbations in a general single field inflationary scenario are presented. Different second order gauge invariant expressions for the curvature are considered. We evaluate…
The quantum theory of cosmological perturbations in single field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well known…
We study multi-propagator angular integrals, a class of phase-space integrals relevant to processes with multiple observed final states and a test-bed for transferring loop-integral technology to phase space integrals without reversed…
This paper considers the robust and efficient implementation of Gaussian process regression with a Student-t observation model. The challenge with the Student-t model is the analytically intractable inference which is why several…
We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each other, the coefficients of the perturbative series become…