skip to main content


Title: Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models
In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are particularly challenging in such nonstationary environments. In this paper, we study causal discovery and forecasting for nonstationary time series. By exploiting a particular type of state-space model to represent the processes, we show that nonstationarity helps to identify the causal structure, and that forecasting naturally benefits from learned causal knowledge. Specifically, we allow changes in both causal strengths and noise variances in the nonlinear state-space models, which, interestingly, renders both the causal structure and model parameters identifiable. Given the causal model, we treat forecasting as a problem in Bayesian inference in the causal model, which exploits the time-varying property of the data and adapts to new observations in a principled manner. Experimental results on synthetic and real-world data sets demonstrate the efficacy of the proposed methods.  more » « less
Award ID(s):
1829681
NSF-PAR ID:
10125751
Author(s) / Creator(s):
Date Published:
Journal Name:
Proceedings of the 36th International Conference on Machine Learning
Page Range / eLocation ID:
2901-2910
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    In this paper, a method for real-time forecasting of the dynamics of structures experiencing nonstationary inputs is described. This is presented as time series predictions across different timescales. The target applications include hypersonic vehicles, space launch systems, real-time prognostics, and monitoring of high-rate and energetic systems. This work presents numerical analysis and experimental results for the real-time implementation of a Fast Fourier Transform (FFT)-based approach for time series forecasting. For this preliminary study, a testbench structure that consists of a cantilever beam subjected to nonstationary inputs is used to generate experimental data. First, the data is de-trended, then the time series data is transferred into the frequency domain, and measures for frequency, amplitude, and phase are obtained. Thereafter, select frequency components are collected, transformed back to the time domain, recombined, and then the trend in the data is restored. Finally, the recombined signals are propagated into the future to the selected prediction horizon. This preliminary time series forecasting work is done offline using pre-recorded experimental data, and the FFT-based approach is implemented in a rolling window configuration. Here learning windows of 0.1, 0.5, and 1 s are considered with different computation times simulated. Results demonstrate that the proposed FFT-based approach can maintain a constant prediction horizon at 1 s with sufficient accuracy for the considered system. The performance of the system is quantified using a variety of metrics. Computational speed and prediction accuracy as a function of training time and learning window lengths are examined in this work. The algorithm configuration with the shortest learning window (0.1 s) is shown to converge faster following the nonstationary when compared to algorithm configuration with longer learning windows.

     
    more » « less
  2. Han, Jae-Hung ; Shahab, Shima ; Yang, Jinkyu (Ed.)
    Hard real-time time-series forecasting of temporal signals has applications in the field of structural health monitoring and control. Particularly for structures experiencing high-rate dynamics, examples of such structures include hypersonic vehicles and space infrastructure. This work reports on the development of a coupled softwarehardware algorithm for deterministic and low-latency online time-series forecasting of structural vibrations that is capable of learning over nonstationary events and adjusting its forecasted signal following an event. The proposed algorithm uses an ensemble of multi-layer perceptrons trained offline on experimental and simulated data relevant to the structure. A dynamic attention layer is then used to selectively scale the outputs of the individual models to obtain a unified forecasted signal over the considered prediction horizon. The scalar values of the dynamic attention layer are continuously updated by quantifying the error between the signal’s measured value and its previously predicted value. Deterministic timing of the proposed algorithm is achieved through its deployment on a field programmable gate array. The performance of the proposed algorithm is validated on experimental data taken on a test structure. Results demonstrate that a total system latency of 25.76 µs can be achieved on a Kintex-7 70T FPGA with sufficient accuracy for the considered system. 
    more » « less
  3. Abstract

    We introduce two novel nonparametric forecasting methods designed for functional time series (FTS), namely, functional singular spectrum analysis (FSSA) recurrent and vector forecasting. Our algorithms rely on extracted signals obtained from the FSSA method and innovative recurrence relations to make predictions. These techniques are model‐free, capable of predicting nonstationary FTS and utilize a computational approach for parameter selection. We also employ a bootstrap algorithm to assess the goodness‐of‐prediction. Through comprehensive evaluations on both simulated and real‐world climate data, we showcase the effectiveness of our techniques compared to various parametric and nonparametric approaches for forecasting nonstationary stochastic processes. Furthermore, we have implemented these methods in theRfssaR package and developed a shiny web application for interactive exploration of the results.

     
    more » « less
  4. Abstract

    Magnetic polarity inversion lines (PILs) detected in solar active regions have long been recognized as arguably the most essential feature for triggering instabilities such as flares and eruptive events (i.e., eruptive flares and coronal mass ejections). In recent years, efforts have been focused on using features engineered from PILs for solar eruption prediction. However, PIL rasters and metadata are often generated as by-products and are not accessible for public use, which limits their utilization in data-intensive space weather analytics applications. We introduce a large-scale publicly available PIL data set covering practically the entire solar cycle 24 for applying to various space weather forecasting and analytics tasks. The data set is created using both radial magnetic field (B_r) and line-of-sight (B_LoS) magnetograms from the Solar Dynamics Observatory’s Helioseismic and Magnetic Imager Active Region Patches (HARP) that involve 4090 HARP series ranging from 2010 May to 2019 March. This data set includes three PIL-related binary masks of rasters: the actual PILs as per the spatial analysis of the magnetograms, the region of polarity inversion, and the convex hull of PILs, along with time-series-structured metadata extracted from these masks. We also provide a preliminary exploratory analysis of selected features aiming to correlate time series of feature metadata and eruptive activity originating from active regions. We envision that this comprehensive PIL data set will complement existing data sets used for space weather forecasting and benefit research in related areas, specifically in better understanding the PIL structure, evolution, and role in eruptions.

     
    more » « less
  5. Summary

    We propose to model a spatio-temporal random field that has nonstationary covariance structure in both space and time domains by applying the concept of the dimension expansion method in Bornn et al. (2012). Simulations are conducted for both separable and nonseparable space-time covariance models, and the model is also illustrated with a streamflow dataset. Both simulation and data analyses show that modeling nonstationarity in both space and time can improve the predictive performance over stationary covariance models or models that are nonstationary in space but stationary in time.

     
    more » « less