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Model Agnostic Time Series Analysis via Matrix Estimation
Machine Learning · Submitted 25 Feb 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Through synthetic and real-world datasets, we demonstrate that our algorithm outperforms standard software packages (including R libraries) in the presence of missing data as well as high levels of noise.
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The abstract, sentence by sentence
We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to make predictions. At the core of our analysis is a representation result, which states that for a large model class, the transformed time series matrix is (approximately) low-rank. In effect, this generalizes the widely used Singular Spectrum Analysis (SSA) in time series literature, and allows us to establish a rigorous link between time series analysis and matrix estimation. The key to establishing this link is constructing a Page matrix with non-overlapping entries rather than a Hankel matrix as is commonly done in the literature (e.g., SSA). This particular matrix structure allows us to provide finite sample analysis for imputation and prediction, and prove the asymptotic consistency of our method. Another salient feature of our algorithm is that it is model agnostic with respect to both the underlying time dynamics and the noise distribution in the observations. The noise agnostic property of our approach allows us to recover the latent states when only given access to noisy and partial observations a la a Hidden Markov Model; e.g., recovering the time-varying parameter of a Poisson process without knowing that the underlying process is Poisson. Furthermore, since our forecasting algorithm requires regression with noisy features, our approach suggests a matrix estimation based method - coupled with a novel, non-standard matrix estimation error metric - to solve the error-in-variable regression problem, which could be of interest in its own right. Through synthetic and real-world datasets, we demonstrate that our algorithm outperforms standard software packages (including R libraries) in the presence of missing data as well as high levels of noise.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to make predictions. | method 0.59 | 0.89 | 0.19 | asserted 0.99 |
| s1 | At the core of our analysis is a representation result, which states that for a large model class, the transformed time series matrix is (approximately) low-rank. | contribution 0.50 | 0.83 | 0.28 | asserted 0.99 |
| s2 | In effect, this generalizes the widely used Singular Spectrum Analysis (SSA) in time series literature, and allows us to establish a rigorous link between time series analysis and matrix estimation. | interpretation 0.94 | 0.65 | 0.14 | asserted 0.96 |
| s3 | The key to establishing this link is constructing a Page matrix with non-overlapping entries rather than a Hankel matrix as is commonly done in the literature (e.g., SSA). | method 0.73 | 0.77 | 0.07 | asserted 1.00 |
| s4 | This particular matrix structure allows us to provide finite sample analysis for imputation and prediction, and prove the asymptotic consistency of our method. | contribution 0.55 | 0.93 | 0.09 | asserted 0.99 |
| s5 | Another salient feature of our algorithm is that it is model agnostic with respect to both the underlying time dynamics and the noise distribution in the observations. | contribution 0.92 | 0.82 | 0.10 | asserted 1.00 |
| s6 | The noise agnostic property of our approach allows us to recover the latent states when only given access to noisy and partial observations a la a Hidden Markov Model; e.g., recovering the time-varying parameter of a Poisson process without knowing that the underlying process is Poisson. | interpretation 0.63 | 0.70 | 0.07 | asserted 0.88 |
| s7 | Furthermore, since our forecasting algorithm requires regression with noisy features, our approach suggests a matrix estimation based method - coupled with a novel, non-standard matrix estimation error metric - to solve the error-in-variable regression problem, which could be of interest in its own right. | contribution 0.73 | 0.84 | 0.07 | hedged possibility 0.99 |
| s8 | Through synthetic and real-world datasets, we demonstrate that our algorithm outperforms standard software packages (including R libraries) in the presence of missing data as well as high levels of noise. | result 0.99 | 0.96 | 0.54 | asserted 1.00 |
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The paper
Original abstract
We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to make predictions. At the core of our analysis is a representation result, which states that for a large model class, the transformed time series matrix is (approximately) low-rank. In effect, this generalizes the widely used Singular Spectrum Analysis (SSA) in time series literature, and allows us to establish a rigorous link between time series analysis and matrix estimation. The key to establishing this link is constructing a Page matrix with non-overlapping entries rather than a Hankel matrix as is commonly done in the literature (e.g., SSA). This particular matrix structure allows us to provide finite sample analysis for imputation and prediction, and prove the asymptotic consistency of our method. Another salient feature of our algorithm is that it is model agnostic with respect to both the underlying time dynamics and the noise distribution in the observations. The noise agnostic property of our approach allows us to recover the latent states when only given access to noisy and partial observations a la a Hidden Markov Model; e.g., recovering the time-varying parameter of a Poisson process without knowing that the underlying process is Poisson. Furthermore, since our forecasting algorithm requires regression with noisy features, our approach suggests a matrix estimation based method - coupled with a novel, non-standard matrix estimation error metric - to solve the error-in-variable regression problem, which could be of interest in its own right. Through synthetic and real-world datasets, we demonstrate that our algorithm outperforms standard software packages (including R libraries) in the presence of missing data as well as high levels of noise.
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References
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4 arXiv papers cite this in 4 sentences
Papers citing it · 1 sentence without a confident label
Compares with it 1 paper
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Our approach is closer to very recent work [ref] , where the authors apply low-rank models to perform denoising, imputation and forecasting on a single time series (as opposed to multiple time series, which is our setting of interest).
Time-Series Analysis via Low-Rank Matrix Factorization Applied to Infant-Sleep Data · Introduction · 0.98
Cites it as background 2 papers
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Other non-parametric predictive models have been proposed in [ref] .
Data-Enabled Predictive Control: In the Shallows of the DeePC · Introduction · 0.85
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The approach to finding $A, B$ is based on a standard ordinary least squares (OLS) given by [equation] Another closely related area is that of online prediction in time series [ref] .
Nonparametric Finite Time LTI System Identification · Related Work · 0.96
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