scholarly journals Towards a Framework for Observational Causality from Time Series: When Shannon Meets Turing

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 426 ◽  
Author(s):  
David Sigtermans
Keyword(s):  
Time Series ◽  
Theoretical Analysis ◽  
Communication Channels ◽  
Transfer Entropy ◽  
Total Effect ◽  
Bivariate Analysis ◽  
Transmission Of Information ◽  
Data Processing Inequality ◽  
Tensor Multiplication ◽  
Causal Structures

We propose a tensor based approach to infer causal structures from time series. An information theoretical analysis of transfer entropy (TE) shows that TE results from transmission of information over a set of communication channels. Tensors are the mathematical equivalents of these multichannel causal channels. The total effect of subsequent transmissions, i.e., the total effect of a cascade, can now be expressed in terms of the tensors of these subsequent transmissions using tensor multiplication. With this formalism, differences in the underlying structures can be detected that are otherwise undetectable using TE or mutual information. Additionally, using a system comprising three variables, we prove that bivariate analysis suffices to infer the structure, that is, bivariate analysis suffices to differentiate between direct and indirect associations. Some results translate to TE. For example, a Data Processing Inequality (DPI) is proven to exist for transfer entropy.

scholarly journals Towards a Framework for Observational Causality from Time Series: When Shannon Meets Turing

2020 ◽  
Author(s):  
David Sigtermans
Keyword(s):  
Time Series ◽  
Single Channel ◽  
Communication Channels ◽  
Transfer Entropy ◽  
Bivariate Analysis ◽  
Noisy Channels ◽  
Transmission Of Information ◽  
Data Processing Inequality ◽  
Causal Structures

We propose a novel tensor-based formalism for inferring causal structures from time series. An information theoretical analysis of transfer entropy (TE), shows that TE results from transmission of information over a set of communication channels. Tensors are the mathematical equivalents of these multi-channel causal channels. A multi-channel causal channel is a generalization of a discrete memoryless channel (DMC). We consider a DMC as a single-channel causal channel. Investigation of a system comprising three variables shows that in our formalism, bivariate analysis suffices to differentiate between direct and indirect relations. For this to be true, we have to combine the output of multi-channel causal channels with the output of single-channel causal channels. We can understand this result when we consider the role of noise. Subsequent transmission of information over noisy channels can never result in less noisy transmission overall. This implies that a Data Processing Inequality (DPI) exists for transfer entropy.

scholarly journals Learning in Feedforward Neural Networks Accelerated by Transfer Entropy

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 102 ◽  
Author(s):  
Adrian Moldovan ◽  
Angel Caţaron ◽  
Răzvan Andonie
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Information Transfer ◽  
Feedforward Neural Networks ◽  
Theoretical Method ◽  
Transfer Entropy ◽  
Training Algorithms ◽  
Training Algorithm ◽  
Neural Connections ◽  
Feedback Connections

Current neural networks architectures are many times harder to train because of the increasing size and complexity of the used datasets. Our objective is to design more efficient training algorithms utilizing causal relationships inferred from neural networks. The transfer entropy (TE) was initially introduced as an information transfer measure used to quantify the statistical coherence between events (time series). Later, it was related to causality, even if they are not the same. There are only few papers reporting applications of causality or TE in neural networks. Our contribution is an information-theoretical method for analyzing information transfer between the nodes of feedforward neural networks. The information transfer is measured by the TE of feedback neural connections. Intuitively, TE measures the relevance of a connection in the network and the feedback amplifies this connection. We introduce a backpropagation type training algorithm that uses TE feedback connections to improve its performance.

"Blend-then-Index" or "Index-then-Blend": A Theoretical Analysis for Generating High-resolution NDVI Time Series by STARFM

2018 ◽  
Vol 84 (2) ◽  
pp. 65-73 ◽  
Author(s):  
Xuehong Chen ◽  
Meng Liu ◽  
Xiaolin Zhu ◽  
Jin Chen ◽  
Yanfei Zhong ◽  
...  
Keyword(s):  
Time Series ◽  
High Resolution ◽  
Theoretical Analysis ◽  
Ndvi Time Series

What Can We Make of Unsubstantiated Child Abuse Reports? A New Approach

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Michael Malcolm
Keyword(s):  
Time Series ◽  
Child Abuse ◽  
Theoretical Analysis ◽  
General Public ◽  
Child Outcomes ◽  
Empirical Approach ◽  
Previous Literature ◽  
New Approach ◽  
Data Generating Process ◽  
Statistical Time

AbstractOnly about a quarter of child abuse reports are ultimately substantiated, which has caused some concern among policymakers and the general public. But previous literature suggests that unsubstantiated and substantiated reports may not be much different from each other in terms of child outcomes. We present a Bayesian theoretical analysis of the data-generating process underlying maltreatment substantiation, and then take a new empirical approach by examining the statistical time-series relationship between substantiated and unsubstantiated reports. We show that the two series are cointegrated. This suggests that unsubstantiated reports are not mostly malicious or unfounded, but that they emanate from the same signals as verifiable, substantiated abuse.

scholarly journals The Impact of the Oil Sector on Commodity Prices: Correlation or Causation?

2010 ◽  
Vol 42 (3) ◽  
pp. 477-485 ◽  
Author(s):  
Sayed H. Saghaian
Keyword(s):  
Time Series ◽  
Graph Theory ◽  
Causal Structure ◽  
Commodity Prices ◽  
Oil Prices ◽  
Causal Link ◽  
Energy Markets ◽  
Oil Sector ◽  
The Impact ◽  
Causal Structures

The interconnections of agriculture and energy markets have increased through the rise in the new biofuel agribusinesses and the oil-ethanol-corn linkages. The question is whether these linkages have a causal structure by which oil prices affect commodity prices and through these links, instability is transferred from energy markets to already volatile agricultural markets. In this article, we present empirical results using contemporary time-series analysis and Granger causality supplemented by a directed graph theory modeling approach to identify the links and plausible contemporaneous causal structures among energy and commodity variables. The results show that although there is a strong correlation among oil and commodity prices, the evidence for a causal link from oil to commodity prices is mixed.

scholarly journals Efficient Transfer Entropy Analysis of Non-Stationary Neural Time Series

PLoS ONE ◽  
2014 ◽  
Vol 9 (7) ◽  
pp. e102833 ◽  
Author(s):  
Patricia Wollstadt ◽  
Mario Martínez-Zarzuela ◽  
Raul Vicente ◽  
Francisco J. Díaz-Pernas ◽  
Michael Wibral
Keyword(s):  
Time Series ◽  
Transfer Entropy ◽  
Entropy Analysis ◽  
Efficient Transfer

Multiscale Symbolic Phase Transfer Entropy in Financial Time Series Classification

2017 ◽  
Vol 16 (02) ◽  
pp. 1750019 ◽  
Author(s):  
Ningning Zhang ◽  
Aijing Lin ◽  
Pengjian Shang
Keyword(s):  
Time Series ◽  
Pharmaceutical Industry ◽  
Phase Transfer ◽  
Financial Time Series ◽  
Market Mechanism ◽  
Transfer Entropy ◽  
Aviation Industry ◽  
Financial Time ◽  
High Degree ◽  
Degree Of Similarity

We address the challenge of classifying financial time series via a newly proposed multiscale symbolic phase transfer entropy (MSPTE). Using MSPTE method, we succeed to quantify the strength and direction of information flow between financial systems and classify financial time series, which are the stock indices from Europe, America and China during the period from 2006 to 2016 and the stocks of banking, aviation industry and pharmacy during the period from 2007 to 2016, simultaneously. The MSPTE analysis shows that the value of symbolic phase transfer entropy (SPTE) among stocks decreases with the increasing scale factor. It is demonstrated that MSPTE method can well divide stocks into groups by areas and industries. In addition, it can be concluded that the MSPTE analysis quantify the similarity among the stock markets. The symbolic phase transfer entropy (SPTE) between the two stocks from the same area is far less than the SPTE between stocks from different areas. The results also indicate that four stocks from America and Europe have relatively high degree of similarity and the stocks of banking and pharmaceutical industry have higher similarity for CA. It is worth mentioning that the pharmaceutical industry has weaker particular market mechanism than banking and aviation industry.

Sign in / Sign up

Export Citation Format

Share Document