Assessing Granger-Causality in the Southern Humboldt Current Ecosystem Using Cross-Spectral Methods

Recently, it has been shown that the information flow and causality between two time series can be inferred in a rigorous and quantitative sense, and, besides, the resulting causality can be normalized. A corollary that follows is, in the linear limit, causation implies correlation, while correlation does not imply causation. Now suppose there is an event A taking a harmonic form (sine/cosine), and it generates through some process another event B so that B always lags A by a phase of π/2. Here the causality is obviously seen, while by computation the correlation is, however, zero. This apparent contradiction is rooted in the fact that a harmonic system always leaves a single point on the Poincaré section; it does not add information. That is to say, though the absolute information flow from A to B is zero, i.e., TA→B=0, the total information increase of B is also zero, so the normalized TA→B, denoted as τA→B, takes the form of 00. By slightly perturbing the system with some noise, solving a stochastic differential equation, and letting the perturbation go to zero, it can be shown that τA→B approaches 100%, just as one would have expected.

Section: The Solutionmentioning

confidence: 99%

A Note on Causation versus Correlation in an Extreme Situation

Liang

Yang

2021

“…4. On 4-feature setting, we take H (4) [Y ] = H[Y |X 7 , X 8 , X 9 , X 10 ] = 1.6278, which is significantly smaller than H (3) [Y ]. As expected, this is an evidence of effect of curse of dimensionality.…”

Section: [Example-6]mentioning

confidence: 99%

Learned Practical Guidelines for Evaluating Conditional Entropy and Mutual Information in Discovering Major Factors of Response-vs.-Covariate Dynamics

Chen

Hsieh

Chou

2022

We reformulate and reframe a series of increasingly complex parametric statistical topics into a framework of response-vs.-covariate (Re-Co) dynamics that is described without any explicit functional structures. Then we resolve these topics’ data analysis tasks by discovering major factors underlying such Re-Co dynamics by only making use of data’s categorical nature. The major factor selection protocol at the heart of Categorical Exploratory Data Analysis (CEDA) paradigm is illustrated and carried out by employing Shannon’s conditional entropy (CE) and mutual information (I[Re;Co]) as the two key Information Theoretical measurements. Through the process of evaluating these two entropy-based measurements and resolving statistical tasks, we acquire several computational guidelines for carrying out the major factor selection protocol in a do-and-learn fashion. Specifically, practical guidelines are established for evaluating CE and I[Re;Co] in accordance with the criterion called [C1:confirmable]. Following the [C1:confirmable] criterion, we make no attempts on acquiring consistent estimations of these theoretical information measurements. All evaluations are carried out on a contingency table platform, upon which the practical guidelines also provide ways of lessening the effects of the curse of dimensionality. We explicitly carry out six examples of Re-Co dynamics, within each of which, several widely extended scenarios are also explored and discussed.

“…Contreras-Reyes et al [ 50 ] used the frequency-domain Granger-causality method to test the statistical significance of causality between two time series and determine the direction of causality on the drivers of pelagic species’ biological indicators. Since the Granger causality coefficient is used in two stationary time series, its application is limited.…”

Section: Related Workmentioning

confidence: 99%

Distributed Deep Fusion Predictor for a Multi-Sensor System Based on Causality Entropy

Jin

et al. 2021

Trend prediction based on sensor data in a multi-sensor system is an important topic. As the number of sensors increases, we can measure and store more and more data. However, the increase in data has not effectively improved prediction performance. This paper focuses on this problem and presents a distributed predictor that can overcome unrelated data and sensor noise: First, we define the causality entropy to calculate the measurement’s causality. Then, the series causality coefficient (SCC) is proposed to select the high causal measurement as the input data. To overcome the traditional deep learning network’s over-fitting to the sensor noise, the Bayesian method is used to obtain the weight distribution characteristics of the sub-predictor network. A multi-layer perceptron (MLP) is constructed as the fusion layer to fuse the results from different sub-predictors. The experiments were implemented to verify the effectiveness of the proposed method by meteorological data from Beijing. The results show that the proposed predictor can effectively model the multi-sensor system’s big measurement data to improve prediction performance.