Summary of On the Approximability Of Stationary Processes Using the Arma Model, by Anand Ganesh et al.
On the Approximability of Stationary Processes using the ARMA Model
by Anand Ganesh, Babhrubahan Bose, Anand Rajagopalan
First submitted to arxiv on: 20 Aug 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Probability (math.PR); Methodology (stat.ME)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper aims to bridge a significant gap in theoretical literature on stationary random variables by exploring Autoregressive Moving Average (ARMA) models. Building upon the spectral lemma connecting supnorm-based function approximation to random variable approximation, the authors provide quantitative bounds for ARMA model approximations. This leads to several key findings, including the identification of a class of stationary processes where guarantees are feasible, an idealized process that resists good ARMA approximation, and exact bounds for a specific example process. The paper’s approach uses generating functions rather than spectral measures, focusing on random variable approximation error instead of prediction error. This work contributes to a deeper understanding of ARMA models and their applications in various fields. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at something called Autoregressive Moving Average (ARMA) models. These are important tools for understanding how things change over time. The authors use a special trick called the spectral lemma to help them figure out how well these models work. They find that some types of random processes can be approximated really well using ARMA models, while others might not be as easily understood. The paper also shows an example where they calculate exactly how well an ARMA model works for a specific type of process. |
Keywords
» Artificial intelligence » Autoregressive
