Time-series forecasting through recurrent topology

Abstract

Time-series forecasting is a practical goal in many areas of science and engineering. Common approaches for forecasting future events often rely on highly parameterized or black-box models. However, these are associated with a variety of drawbacks including critical model assumptions, uncertainties in their estimated input hyperparameters, and computational cost. All of these can limit model selection and performance. Here, we introduce a learning algorithm that avoids these drawbacks. A variety of data types including chaotic systems, macroeconomic data, wearable sensor recordings, and population dynamics are used to show that Forecasting through Recurrent Topology (FReT) can generate multi-step-ahead forecasts of unseen data. With no free parameters or even a need for computationally costly hyperparameter optimization procedures in high-dimensional parameter space, the simplicity of FReT offers an attractive alternative to complex models where increased model complexity may limit interpretability/explainability and impose unnecessary system-level computational load and power consumption constraints.

Implementing Gait Kinematic Trajectory Forecasting Models on an Embedded System

“…Artificial neural networks are a type of artificial intelligence technology that mimics the human brain’s powerful ability to recognize patterns [ 39 ]. These models have been used successfully for modelling a broad range of time-series data [ 36 , 38 , 41 , 42 ]. The task of the artificial neural network is to model the underlying data-generating process during training so that valid forecasts can be made when the parameterized model is subsequently presented with new input data [ 35 ].…”

“…An obvious prerequisite for adaptive model building is the ability for CL to be completed quickly. However, modern prediction models are inherently complex, often requiring hyperparameter optimization and tuning in high-dimensional parameter space [ 1 , 6 , 35 , 36 , 37 , 38 ]. Increasing the number of parameter weights, which is inextricably linked with model architecture complexity, also increases computation time [ 39 ].…”

“…Local topological recurrence analysis represents a new computational approach we developed for identifying emergent recurring patterns in a signal’s surface topology [ 40 ]. Recently, we have expanded on the theoretical and practical properties of local topological recurrence analysis to provide a simple solution for time-series forecasting [ 38 ]. Forecasting through Recurrent Topology (FReT) identifies recurring patterns in local signal shapes to reveal unique memory traces embedded in a time-series signal that can be used to forecast a system’s upcoming time evolution [ 38 ].…”

“…Recently, we have expanded on the theoretical and practical properties of local topological recurrence analysis to provide a simple solution for time-series forecasting [ 38 ]. Forecasting through Recurrent Topology (FReT) identifies recurring patterns in local signal shapes to reveal unique memory traces embedded in a time-series signal that can be used to forecast a system’s upcoming time evolution [ 38 ]. Furthermore, unlike many other types of models, there is no need for computationally costly optimization and tuning procedures [ 38 ].…”

“…Forecasting through Recurrent Topology (FReT) identifies recurring patterns in local signal shapes to reveal unique memory traces embedded in a time-series signal that can be used to forecast a system’s upcoming time evolution [ 38 ]. Furthermore, unlike many other types of models, there is no need for computationally costly optimization and tuning procedures [ 38 ]. FReT’s simplicity may therefore enable new capabilities for CL to incorporate current dynamic signal information into forecasting.…”