Multivariate Time Series Data Causal Discovery
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Date
2021-10-05
Authors
Chang, Bo Yuan
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
One of the goals for Artificial Intelligence is to achieve human-like intelligence. To that
end, several solutions were proposed over the decades, where causal structure discovery
was proposed as a viable tool for enabling human-like reasoning. It can be treated as two
stages, first causal discovery that examines the cause-effect relationships between variables,
which are then used in the second stage, referred to as causal parameter inference, to
perform causal inference using counterfactual/logic-like reasoning similar to how human
beings approach a problem. Generally speaking, there are two types of causal discovery
algorithms: those that work with random variables and those that work with time series
data. The focus of this thesis will be on the latter.
Performing causal studies on real world dataset is very challenging for time series data
as it is prevalent to run into missing values. Currently, all existing causal algorithms require
evenly-sampled time series data which unfortunately are not always available.
In this thesis I proposed a systems that can address this difficulties that is hindering
causal learning on real world datasets. The proposed system performs causal discovery
using time series data with missing entries (i.e., sparsely sampled data at varying intervals).
The solution put forward for this task is comprised of two parts: data filling with Gaussian
Process Regression, and causal learning using a the traditional Vector Autoregressive Model
or Machine Learning based approach. For the first part, experiments have shown that
Gaussian Process Regression outperformed all the benchmark filling techniques such as
K Nearest Neighbour regression, Parametric Linear filling as well as random variable
filling. The obtained Root Mean Square Error for GPR filled was the smallest under across
all filling percentages, comfortably beating benchmark algorithms by margins (RMSE
difference varies from 0.05 to 1.5). As for the second part, an Echo State Network for
causal learning is used due to its fast running time and higher prediction capabilities when
compared with other causal learning algorithms available in the industry such as algorithms
like Structural Expectation Maximization (SEM), and Subsampled Linear Auto-Regression
Absolute Coefficients algorithm (SLARAC). When working with a 10 percent missing
entries, the proposed system is capable of obtaining an MCC score of 0.31 on a -1 to +1
scale where +1 represents perfect prediction and -1 represents complete no usefulness of
the result. The MCC score received from the proposed system significantly outperformed
other methods such as SEM and SLARAC. To showcase the ability of the proposed system
to adapt causal relationships on real world engineering applications, the experiment was
conducted using a chemical refinery dataset called the Tennessee Eastman (TE) dataset.
Description
Keywords
time series, data filling, Granger Causality, machine learning, causal inference
LC Keywords
Time-series analysis—Computer programs, Machine learning