Related papers: Spectral Inference under Complex Temporal Dynamics

Extracting the spectral representations of the neural processes that underlie spiking activity is key to understanding how the brain rhythms mediate cognitive functions. While spectral estimation of continuous time-series is well studied,…

Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…

Time Resolved Correlation (TRC) is a recently introduced light scattering technique that allows to detect and quantify dynamic heterogeneities. The technique is based on the analysis of the temporal evolution of the speckle pattern…

Hyperspectral imaging provides detailed information about the scanned objects, as it captures their spectral characteristics within a large number of wavelength bands. Classification of such data has become an active research topic due to…

Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of…

Spectra derived from fast Fourier transform (FFT) analysis of time-domain data intrinsically contain statistical fluctuations whose distribution depends on the number of accumulated spectra contributing to a measurement. The tail of this…

Power spectral densities are often interpreted through ensemble averages and long-time asymptotics. In many experiments, however, only a single finite record is available, so spectral estimators remain broadly distributed and the usual…

The covariance function and the variogram play very important roles in modelling and in prediction of spatial and spatio-temporal data. The assumption of second order stationarity, in space and time, is often made in the analysis of spatial…

Continuous symmetries are fundamental to many scientific and learning problems, yet they are often unknown a priori. Existing symmetry discovery approaches typically search directly in the space of transformation generators or rely on…

This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data…

A fast simulation framework for stochastic Volterra processes based on Random Fourier Features (RFF) approximation of the kernel is developed. After recalling the main properties of Volterra processes and reviewing existing numerical…

Signal Temporal Logic (STL) inference seeks to extract human-interpretable rules from time-series data, but existing methods lack formal confidence guarantees for the inferred rules. Conformal prediction (CP) is a technique that can provide…

Spatiotemporal learning is challenging due to the intricate interplay between spatial and temporal dependencies, the high dimensionality of the data, and scalability constraints. These challenges are further amplified in scientific domains,…

We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints…

In network analysis, developing a unified theoretical framework that can compare methods under different models is an interesting problem. This paper proposes a partial solution to this problem. We summarize the idea of using separation…

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, audio, and 3D scenes. However, existing INR frameworks -- including MLPs with Fourier features, SIREN, and multiresolution…

Conformal inference is a popular tool for constructing prediction intervals (PI). We consider here the scenario of post-selection/selective conformal inference, that is PIs are reported only for individuals selected from an unlabeled test…

Several recent studies advocate the use of spectral discriminators, which evaluate the Fourier spectra of images for generative modeling. However, the effectiveness of the spectral discriminators is not well interpreted yet. We tackle this…

Characterizing the long term behavior of dynamical systems given limited measurements is a common challenge throughout the physical and biological sciences. This is a challenging task due to the sparsity and noise inherent to empirical…

We consider the problem of joint simultaneous confidence band (JSCB) construction for regression coefficient functions of time series scalar-on-function linear regression when the regression model is estimated by roughness penalization…