Related papers: Minimum-entropy causal inference and its applicati…
Wiener and Granger have introduced an intuitive concept of causality between two variables which is based on the idea that an effect never occurs before its cause. Later, Geweke has generalized this concept to a multivariate Granger…
Four different Granger causality-based methods - one linear and three nonlinear (Granger Causality, Kernel Granger Causality, large-scale Nonlinear Granger Causality, and Neural Network Granger Causality) were used for assessment and…
Robust characterization of dynamic causal interactions in multivariate biomedical signals is essential for advancing computational and algorithmic methods in biomedical imaging. Conventional approaches, such as Dynamic Bayesian Networks…
Inferring the causal direction and causal effect between two discrete random variables X and Y from a finite sample is often a crucial problem and a challenging task. However, if we have access to observational and interventional data, it…
The cross entropy (CE) method is a model based search method to solve optimization problems where the objective function has minimal structure. The Monte-Carlo version of the CE method employs the naive sample averaging technique which is…
Granger causality method analyzes the time series causalities without building a complex causality graph. However, the traditional Granger causality method assumes that the causalities lie between time series channels and remain constant,…
Introduced more than a half century ago, Granger causality has become a popular tool for analyzing time series data in many application domains, from economics and finance to genomics and neuroscience. Despite this popularity, the validity…
Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially…
This article investigates the causality structure of financial time series. We concentrate on three main approaches to measuring causality: linear Granger causality, kernel generalisations of Granger causality (based on ridge regression and…
Causal inference from observational data following the restricted structural causal model (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or nonlinearity.…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data…
A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used…
At present, multi-electrode array (MEA) approach and optical recording allow us to acquire plant electrical activity with higher spatio-temporal resolution. To understand the dynamic information flow of the electrical signaling system and…
The Gaussian Process Convolution Model (GPCM; Tobar et al., 2015a) is a model for signals with complex spectral structure. A significant limitation of the GPCM is that it assumes a rapidly decaying spectrum: it can only model smooth…
Gaussian mixture models (GMMs) are fundamental statistical tools for modeling heterogeneous data. Due to the nonconcavity of the likelihood function, the Expectation-Maximization (EM) algorithm is widely used for parameter estimation of…
We propose a geometric model-free causality measurebased on multivariate delay embedding that can efficiently detect linear and nonlinear causal interactions between time series with no prior information. We then exploit the proposed causal…
Hawkes processes are a special class of temporal point processes which exhibit a natural notion of causality, as occurrence of events in the past may increase the probability of events in the future. Discovery of the underlying influence…
In this work we use numerical simulation to investigate how the temporal length of the data affects the reliability of the estimates of brain connectivity from EEG time--series. We assume that the neural sources follow a stable MultiVariate…
The Expectation-Maximization (EM) algorithm for mixture models often results in slow or invalid convergence. The popular convergence proof affirms that the likelihood increases with Q; Q is increasing in the M -step and non-decreasing in…