# Low Rank Forecasting

arXiv: https://arxiv.org/abs/2101.12414 · HTML: https://mlsanity.com/paper/2101.12414/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 157 references that are in the map.
- First posted on arXiv 29 Jan 2021.

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Generalized Low Rank Models](https://mlsanity.com/paper/1410.0342/) (2014)
- [Non-convex Robust PCA](https://mlsanity.com/paper/1410.7660/) (2014)
- [Forecasting Economics and Financial Time Series: ARIMA vs. LSTM](https://mlsanity.com/paper/1803.06386/) (2018)
- [Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization](https://mlsanity.com/paper/1310.7991/) (2013)
- [Low Rank and Structured Modeling of High-dimensional Vector Autoregressions](https://mlsanity.com/paper/1812.03568/) (2018)
- [Estimating Structured Vector Autoregressive Model](https://mlsanity.com/paper/1602.06606/) (2016)
- [Fitting a Kalman Smoother to Data](https://mlsanity.com/paper/1910.08615/) (2019)
- [Structured low-rank matrix completion for forecasting in time series analysis](https://mlsanity.com/paper/1802.08242/) (2018)
- [High dimensional VAR with low rank transition](https://mlsanity.com/paper/1905.00959/) (2019)
- [Low-Rank Autoregressive Tensor Completion for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2006.10436/) (2020)
- [Forecasting Multiple Time Series with One-Sided Dynamic Principal Components](https://mlsanity.com/paper/1708.04705/) (2017)
- [Autoregressive Convolutional Recurrent Neural Network for Univariate and Multivariate Time Series Prediction](https://mlsanity.com/paper/1903.02540/) (2019)
- [Dynamic Energy Management](https://mlsanity.com/paper/1903.06230/) (2019)
- [Predictable Feature Analysis](https://mlsanity.com/paper/1311.2503/) (2013)

## Built on by (most cited first, 1 of 1)

- [DeepTensor: Low-Rank Tensor Decomposition with Deep Network Priors](https://mlsanity.com/paper/2204.03145/) (2022)

## Abstract (arXiv)

We consider the problem of forecasting multiple values of the future of a vector time series, using some past values. This problem, and related ones such as one-step-ahead prediction, have a very long history, and there are a number of well-known methods for it, including vector auto-regressive models, state-space methods, multi-task regression, and others. Our focus is on low rank forecasters, which break forecasting up into two steps: estimating a vector that can be interpreted as a latent state, given the past, and then estimating the future values of the time series, given the latent state estimate. We introduce the concept of forecast consistency, which means that the estimates of the same value made at different times are consistent. We formulate the forecasting problem in general form, and focus on linear forecasters, for which we propose a formulation that can be solved via convex optimization. We describe a number of extensions and variations, including nonlinear forecasters, data weighting, the inclusion of auxiliary data, and additional objective terms. We illustrate our methods with several examples.