Identifying Latent States for Accurate Nonstationary Time Series Forecasting

核心概念

The core message of this article is to propose a novel method called IDEA (Identifying Disentangled Latent States) that can effectively learn identifiable latent states, including stationary and nonstationary latent variables as well as latent environments, to improve the performance of nonstationary time series forecasting.

要約

The article presents a novel approach called IDEA (Identifying Disentangled Latent States) for nonstationary time series forecasting. The key insights are:

The authors propose a data generation process that models time series data as a combination of stationary and nonstationary latent variables, influenced by latent environment variables that change over time.

The authors provide theoretical guarantees for the identifiability of the latent environment variables, as well as the stationary and nonstationary latent variables, under mild conditions.

Based on the theoretical results, the authors devise the IDEA model, which incorporates an autoregressive hidden Markov model to estimate the latent environments and modular prior networks to identify the stationary and nonstationary latent variables.

Experiments on both synthetic and real-world benchmark datasets demonstrate that IDEA outperforms state-of-the-art nonstationary forecasting methods, highlighting its advantages in accurately capturing the temporal distribution shifts and disentangling the stationary and nonstationary dependencies.

統計

The article presents several key metrics and figures to support the proposed approach:

The authors generate synthetic datasets with different time lag dependencies to evaluate the identifiability of latent variables and the transition matrix.
The authors report the Mean Correlation Coefficient (MCC) to measure the identifiability of stationary and nonstationary latent variables, as well as the Mean Square Error (MSE) to evaluate the identifiability of the transition matrix.
The authors also report the accuracy of latent environment estimation on the synthetic datasets.
On real-world benchmark datasets, the authors report the Mean Squared Error (MSE) and Mean Absolute Error (MAE) for various forecasting horizons to compare the performance of IDEA against state-of-the-art baselines.

引用

"To solve this problem, we propose to learn IDentifiable latEnt stAtes (IDEA) to detect when the distribution shifts occur. Beyond that, we further disentangle the stationary and nonstationary latent states to learn how the latent states change."
"Under mild conditions, we show that latent environments and stationary/nonstationary variables are identifiable."
"Evaluation of simulation and eight real-world benchmark datasets demonstrate the accuracy of latent environment estimation and identification of latent states, as well as the effectiveness of real-world applications."

抽出されたキーインサイト

When and How: Learning Identifiable Latent States for Nonstationary Time Series Forecasting

by Zijian Li,Ru... 場所 arxiv.org 04-16-2024

https://arxiv.org/pdf/2402.12767.pdf

深掘り質問

What are some potential real-world applications of the IDEA model beyond time series forecasting, where identifying latent states could be beneficial

The IDEA model's capability to identify latent states in nonstationary time series data can be applied to various real-world scenarios beyond time series forecasting. One potential application is anomaly detection in complex systems such as cybersecurity. By identifying identifiable latent states, the model can help in detecting unusual patterns or behaviors in network traffic data, indicating potential security threats. Another application could be in healthcare, where the model can be used to analyze patient data and identify latent states related to specific health conditions or disease progression. This can aid in early diagnosis, personalized treatment plans, and monitoring patient health over time. Additionally, in financial markets, the IDEA model can be utilized for risk management by identifying latent states related to market trends, volatility, or anomalies, helping in making informed investment decisions.

How could the IDEA model be extended to handle more complex temporal dependencies, such as long-range dependencies or hierarchical structures in the time series data

To handle more complex temporal dependencies, such as long-range dependencies or hierarchical structures in time series data, the IDEA model can be extended in several ways. One approach is to incorporate attention mechanisms that can capture long-range dependencies by allowing the model to focus on relevant parts of the input sequence. This can help in capturing relationships between distant time steps and improving forecasting accuracy. Additionally, hierarchical modeling techniques can be implemented to capture dependencies at different levels of granularity in the data. By hierarchically organizing the latent states, the model can learn complex patterns and relationships within the data, leading to more accurate and interpretable results.

Given the theoretical guarantees provided in the paper, are there any limitations or assumptions that may restrict the applicability of the IDEA model in certain scenarios, and how could these be addressed

While the IDEA model provides theoretical guarantees for identifying latent states in nonstationary time series data, there are some limitations and assumptions that may restrict its applicability in certain scenarios. One limitation is the assumption of smooth and positive density functions for the latent variables, which may not hold true in all real-world datasets. To address this, robust modeling techniques can be employed to handle noisy or irregular data distributions. Another limitation is the requirement of prior knowledge about the number of latent environments, which may not always be available. This can be addressed by incorporating techniques for automatic determination of the number of latent environments, such as model selection criteria or Bayesian nonparametric methods. Additionally, the model's performance may be impacted by the complexity of the data and the presence of outliers. Robust training procedures and outlier detection mechanisms can help mitigate these challenges and improve the model's robustness in diverse scenarios.