Related papers: Indicator Functions: Distilling the Information fr…
Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of…
For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…
Cosmic shear data contains a large amount of cosmological information encapsulated in the non-Gaussian features of the weak lensing mass maps. This information can be extracted using non-Gaussian statistics. We compare the constraining…
We examine the errors on counts in cells extracted from galaxy surveys. The measurement error, related to the finite number of sampling cells, is disentangled from the ``cosmic error'', due to the finiteness of the survey. Using the…
Finite mixture such as the Gaussian mixture is a flexible and powerful probabilistic modeling tool for representing the multimodal distribution widely involved in many estimation and learning problems. The core of it is representing the…
We extend field-level inference to jointly constrain the cosmological parameters $\{A,\omega_{\rm cdm},H_0\}$, in both real and redshift space. Our analyses are based on mock data generated using a perturbative forward model, with noise…
Most state-of-the-art action feature extractors involve differential operators, which act as highpass filters and tend to attenuate low frequency action information. This attenuation introduces bias to the resulting features and generates…
We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed…
Rare events can potentially occur in many applications. When manifested as opportunities to be exploited, risks to be ameliorated, or certain features to be extracted, such events become of paramount significance. Due to their sporadic…
Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation…
We investigate the non-Gaussian features in the distribution of the matter power spectrum multipoles. Using the COVMOS method, we generate 100\,000 mock realisations of dark matter density fields in both real and redshift space across…
We investigate the performance of the scan (maximum likelihood ratio statistic) and of the average likelihood ratio statistic in the problem of detecting a deterministic signal with unknown spatial extent in the prototypical univariate…
Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability…
Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…
The 3D Gaussian splatting methods are getting popular. However, they work directly on the signal, leading to a dense representation of the signal. Even with some techniques such as pruning or distillation, the results are still dense. In…
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
A common assumption in signal processing is that underlying data numerically conforms to a Gaussian distribution. It is commonly utilized in signal processing to describe unknown additive noise in a system and is often justified by citing…
This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the presence of noise. We extend recent advances in doubly…
By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…
We examine how the prior probability distribution of a sensory variable in the environment influences the optimal allocation of neurons and spikes in a population that represents that variable. We start with a conventional response model,…