# Learning Multi-Frequency Partial Correlation Graphs

arXiv: https://arxiv.org/abs/2311.15756 · HTML: https://mlsanity.com/paper/2311.15756/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 70 references that are in the map.
- First posted on arXiv 27 Nov 2023.

## Builds on (most cited first, 16 of 16)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Graphical LASSO Based Model Selection for Time Series](https://mlsanity.com/paper/1410.1184/) (2014)
- [Learning to Discover Sparse Graphical Models](https://mlsanity.com/paper/1605.06359/) (2016)
- [Parallel and Distributed Methods for Nonconvex Optimization--Part II: Applications](https://mlsanity.com/paper/1601.04059/) (2016)
- [Graph topology inference based on sparsifying transform learning](https://mlsanity.com/paper/1806.01701/) (2018)
- [Spectral Analysis of High-dimensional Time Series](https://mlsanity.com/paper/1810.11223/) (2018)
- [Parallel and Distributed Successive Convex Approximation Methods for Big-Data Optimization](https://mlsanity.com/paper/1805.06963/) (2018)
- [Methods for Recovering Conditional Independence Graphs: A Survey](https://mlsanity.com/paper/2211.06829/) (2022)
- [Parallel Successive Convex Approximation for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/1406.3665/) (2014)
- [Optimization Methods for Sparse Pseudo-Likelihood Graphical Model Selection](https://mlsanity.com/paper/1409.3768/) (2014)
- [On Sparse High-Dimensional Graphical Model Learning For Dependent Time Series](https://mlsanity.com/paper/2111.07897/) (2021)
- [Frequency Domain Statistical Inference for High-Dimensional Time Series](https://mlsanity.com/paper/2206.02250/) (2022)
- [Large Spectral Density Matrix Estimation by Thresholding](https://mlsanity.com/paper/1812.00532/) (2018)
- [Learning partial correlation graphs and graphical models by covariance queries](https://mlsanity.com/paper/1906.09501/) (2019)
- [Learning Multiscale Non-stationary Causal Structures](https://mlsanity.com/paper/2208.14989/) (2022)

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

- [Wavelet Mixture of Experts for Time Series Forecasting](https://mlsanity.com/paper/2508.08825/) (2025)

## Abstract (arXiv)

Despite the large research effort devoted to learning dependencies between time series, the state of the art still faces a major limitation: existing methods learn partial correlations but fail to discriminate across distinct frequency bands. Motivated by many applications in which this differentiation is pivotal, we overcome this limitation by learning a block-sparse, frequency-dependent, partial correlation graph, in which layers correspond to different frequency bands, and partial correlations can occur over just a few layers. To this aim, we formulate and solve two nonconvex learning problems: the first has a closed-form solution and is suitable when there is prior knowledge about the number of partial correlations; the second hinges on an iterative solution based on successive convex approximation, and is effective for the general case where no prior knowledge is available. Numerical results on synthetic data show that the proposed methods outperform the current state of the art. Finally, the analysis of financial time series confirms that partial correlations exist only within a few frequency bands, underscoring how our methods enable the gaining of valuable insights that would be undetected without discriminating along the frequency domain.