Don’t FReT: A simple solution to predict complex dynamics

Forecasting through Recurrent Topology (FReT) offers a new approach to decode and forecast time-evolving dependencies in a time-series that reduces computational complexity and cost.
Don’t FReT: A simple solution to predict complex dynamics
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Time-series data: What is it and why do we want to predict it?

Time-series data consists of a series of data points that have natural temporal ordering. Time-series data is ubiquitous and can be used to help us better understand the principles and mechanisms underlying natural and biological systems. One practical use of these datasets is to develop effective forecasting models that can describe the behaviour of the relevant system. Time-series forecasting has numerous applications across a variety of scientific and engineering disciplines, as well as for informing policy. However, because time-series data is complex and dynamic in nature, being able to forecast it is one of the most challenging tasks in machine learning.

The misconception: Complex problems require complex solutions

Unlike classical memoryless Markovian processes that assume that an unknown future event depends only on the present state, time-series data often retain long-lived memory traces. As detecting these memory traces is particularly challenging for complex time-series, we tend to look to increasingly more complex solutions, such as artificial neural network models, to decode this type of information. Yet, the performance of these models critically depends on an appropriate model design which can require computationally costly hyperparameter optimization and tuning. Unfortunately, even with an appropriately designed model, we are still not guaranteed top performance.

FReT: A simple solution for complex problems

A few years ago, we developed Local Topological Recurrence Analysis (LoTRA). The basic premise of LoTRA is that time-series data has shape and recurring patterns within this shape that can reveal important information. It was initially developed for applications related to Neuroscience/Neurology, where, for instance, it was able to improve the diagnostic accuracy of Parkinson’s disease through the analysis of clinical time-series data. It turns out that the theoretical and practical properties of LoTRA have much broader applications for data science.

As reported in Nature’s Communications Engineering, we propose a LoTRA-inspired algorithm that provides a simple solution to time-series forecasting. Forecasting through Recurrent Topology (FReT) identifies recurring patterns in local shape to reveal unique memory traces that can be used to predict future events. Additionally, unlike complex models, there is no need for computationally costly optimization and tuning procedures. In fact, FReT may serve as a general-purpose algorithm as its versatility has been demonstrated using various types of time-series data including chaotic systems, macroeconomic data, wearable sensor recordings, and population dynamics.

FReT: An attractive alternative to complex models

Many complex prediction models can be limited because the performance of these models highly depends on the chosen model architecture. Moreover, modern prediction models often require tuning and optimization that may impose system-level constraints related to computational load, power consumption, and the cost of machine learning projects. FReT’s simplicity enables new capabilities for adaptive learning to rapidly incorporate current dynamic signal information into forecasting. This will be an important step towards prioritizing computationally efficient algorithms that can simplify the integration of time-series forecasting into real-world applications.

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Time Series Analysis
Mathematics and Computing > Mathematics > Computational Mathematics and Numerical Analysis > Computational Science and Engineering > Computational Neuroscience > Dynamical Systems > Time Series Analysis
Machine Learning
Mathematics and Computing > Computer Science > Artificial Intelligence > Machine Learning

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