Reconstructing the unmeasured causal drivers of complex time series from observed response data represents a fundamental challenge across various scientific domains. Latent variables, including genetic controls or environmental factors, are important in determining system dynamics but are rarely measured. Challenges with current methods come from the noise of the data, the high system size, and the inherent capabilities of the algorithms in handling nonlinear interactions. This will be of great help in modeling, predicting, and controlling high-dimensional systems in systems biology, ecology, and fluid dynamics.
Commonly used techniques for causal driver reconstruction often rely on signal processing or machine learning frameworks. Some common ones include joint information methods, neural network applications, and dynamic attractor reconstruction. Although these methods work well in some cases, they have important limitations. Most want large, high-quality datasets that are rarely available in real-world applications. They are more prone to measurement noise, resulting in lower reconstruction accuracy. Some require computationally expensive algorithms and thus are not suitable for real-time applications. In addition, many models lack physical principles, which limits their interpretation and applicability across domains.
Researchers from the University of Texas are introducing a physics-based unsupervised learning framework called SHREC (Synchronized Iterators) to reconstruct causal drivers from time series data. The method is based on the concept of skew-product dynamical systems and topological data analysis. Innovations include the use of recurrent events in time series to infer common causal structures among responses, the construction of a truncated consensus recurrence graph to reveal hidden driver dynamics, and the introduction of new network embeddings that adapt noise to different data sets using simple fuzzy structures. Unlike existing methods, the SHREC framework captures noisy and nonlinear data well, requires little parameter adjustment, and provides useful insight into the physical dynamics underlying driver response systems.
The SHREC algorithm is implemented in several stages. The measured response time series are mapped into weighted recurrent networks by topological embedding, where an affinity matrix is constructed for each time series based on nearest neighbor distances and variable thresholds. Recurrence graphs are compiled from each time series to obtain a consistency graph that captures the ensemble dynamics. Different time drivers have been linked and decomposed by public detection algorithms, including the Leiden method, to provide different equivalence classes. For continuous drivers, on the other hand, the Laplacian decomposition of the graph reveals the temporal modes corresponding to the states of the drivers. The algorithm was tested on a variety of data: gene expression, plankton abundance, and turbulent flow. It has shown excellent reconstruction of drivers under challenging conditions such as loud noise and missing data. The structure of the framework is based on graph-based actions. Therefore, it avoids expensive gradient-based optimization and makes it computationally efficient.
SHREC performed remarkably well and consistently on benchmark challenge datasets. The approach successfully reconstructs causal determinants from gene expression datasets, thus revealing key regulatory components, even in the presence of sparse and noisy data. In experiments involving turbulent flow, this method successfully obtained sinusoidal forcing characteristics, showing superiority over conventional signal processing techniques. Regarding environmental datasets, SHREC has revealed temperature-induced trends in plankton populations, despite very little information, thus demonstrating its robustness to incomplete and noisy data. Comparisons with other methods have highlighted the increased accuracy and efficiency of SHREC in calculations, especially in the presence of high levels of noise and complex non-linear dependencies. These findings highlight its broad applicability and reliability in many fields.
SHREC is a physics-based unsupervised learning framework that enables the reconstruction of observable causal drivers from complex time series data. This new method tackles the difficult obstacles of today's techniques, including the tendency to noise and high computational costs, by using the properties of iteration and topological embedding. SHREC's successful performance on diverse datasets underscores its broad applicability with the ability to develop AI-based modeling in biology, physics, and engineering disciplines. This approach improves the accuracy of the causal driver reconstruction and, at the same time, lays down a framework based on the principles of dynamical systems theory and sheds new light on important aspects of information transfer within interconnected systems.
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Aswin AK is a consultant at MarkTechPost. He is pursuing his Dual Degree at the Indian Institute of Technology, Kharagpur. He is passionate about data science and machine learning, which brings a strong academic background and practical experience in solving real-life domain challenges.
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