Related papers: Gradient of Probability Density Functions based Co…
The Forward-Forward (FF) learning algorithm provides a bottom-up alternative to backpropagation (BP) for training neural networks, relying on a layer-wise "goodness" function with well-designed negative samples for contrastive learning.…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
Double hybrid density functional theory arguably sits on the seamline between wavefunction methods and DFT: it represents a special case of Rung 5 on the "Jacobs Ladder" of John P. Perdew. For large and chemically diverse benchmarks such as…
Dempster-Shafer theory is widely applied in uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. A distance between two basic probability assignments(BPAs) presents a measure of performance…
Intermittency in MHD turbulence has been analyzed using high resolution 2D numerical simulations. We show that the Probability Distribution Functions (PDFs) of the fluctuations of the Elsasser fields, magnetic field and velocity field…
Photometric wide-field surveys are imaging the sky in unprecedented detail. These surveys face a significant challenge in efficiently estimating galactic photometric redshifts while accurately quantifying associated uncertainties. In this…
Among dissimilarities between probability distributions, the Kernel Stein Discrepancy (KSD) has received much interest recently. We investigate the properties of its Wasserstein gradient flow to approximate a target probability distribution…
The standard model of classical Density Functional Theory for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated Fundamental…
In a world blessed with a great diversity of loss functions, we argue that that choice between them is not a matter of taste or pragmatics, but of model. Probabilistic depencency graphs (PDGs) are probabilistic models that come equipped…
The spherical-radial decomposition (SRD) is an efficient method for estimating probabilistic functions and their gradients defined over finite-dimensional elliptical distributions. In this work, we generalize the SRD to infinite stochastic…
Conditional density estimation (CDE) is a fundamental task in machine learning that aims to model the full conditional law $\mathbb{P}(\mathbf{y} \mid \mathbf{x})$, beyond mere point prediction (e.g., mean, mode). A core challenge is…
Probability distribution functions (PDFs) of column densities are an established tool to characterize the evolutionary state of interstellar clouds. Using simulations, we show to what degree their determination is affected by noise,…
We continue to explore the hypothesis that neuronal populations represent and process analog variables in terms of probability density functions (PDFs). A neural assembly encoding the joint probability density over relevant analog variables…
In massive MIMO systems, the matched filter (MF) beamforming is attractive technique due to its extremely low complexity of implementation compared to those high-complexity decomposition-based beamforming techniques such as zero-forcing,…
This paper studies the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large block-lengths. The perception measure is based on a divergence between the distributions of the source and…
Probability density function (PDF) of passive scalar dissipation ${\cal P} (\epsilon)$ is found analytically in the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime) in two dimensions. The tail of PDF at…
While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and challenging. We introduce an efficient, geometric approach for…
We propose a function-valued evaluation metric for generative models based on the relative density ratio (RDR) designed to characterize distributional differences between real and generated samples. As an evaluation metric, the RDR function…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
We utilize the probability distribution function (PDF) of normalized convergence maps reconstructed from the Subaru Hyper Suprime-Cam (HSC) Y1 shear catalogue, in combination with the power spectrum, to measure the matter clustering…