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Among the best known quantities obtainable from photon correlation measurements are the $g^{(m)}$~correlation functions. Here, we introduce a new procedure to evaluate these correlation functions based on higher-order factorial cumulants…
Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social…
Implicit particle filtering is a sequential Monte Carlo method for data assim- ilation, designed to keep the number of particles manageable by focussing attention on regions of large probability. These regions are found by min- imizing, for…
Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce the…
Correlation coefficient is usually used to measure the correlation degree between two time signals. However, its performance will drop or even fail if the signals are noised. Based on the time-frequency phase spectrum (TFPS) provided by…
In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to…
We consider the reflection from a random medium of light with short coherence length. We found that the second order correlation function of light can have a peak in a direction where the reflection angle is equal to angle of incidence.…
Hamiltonian moments in Fourier space - expectation values of the unitary evolution operator under a Hamiltonian at different times - provide a convenient framework to understand quantum systems. They offer insights into the energy…
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically…
In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF)…
We derive new time-space tradeoff lower bounds and algorithms for exactly computing statistics of input data, including frequency moments, element distinctness, and order statistics, that are simple to calculate for sorted data. We develop…
Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…
The analysis of low dimensional factorial designs with possible interactions is a relevant issue. Instead of the common pre-tests for interaction, a simultaneous inference procedure of the primary factor at the respective level of the…
We address the problem of inferring the causal direction between two variables by comparing the least-squares errors of the predictions in both possible directions. Under the assumption of an independence between the function relating cause…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an…
The learning of the physical world relies on sensing and data post-processing. When the signals are weak, multidimensional and correlated, the performance of learning is often bottlenecked by the quality of sensors, calling for integrating…
Inferring cluster structure in microarray datasets is a fundamental task for the -omic sciences. A fundamental question in Statistics, Data Analysis and Classification, is the prediction of the number of clusters in a dataset, usually…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
Anomaly detection aims to identify observations that deviate from the typical pattern of data. Anomalous observations may correspond to financial fraud, health risks, or incorrectly measured data in practice. We show detecting anomalies in…
As a well-known clustering algorithm, Fuzzy C-Means (FCM) allows each input sample to belong to more than one cluster, providing more flexibility than non-fuzzy clustering methods. However, the accuracy of FCM is subject to false detections…