# Graph Filter Transfer via Probability Density Ratio Weighting

arXiv: https://arxiv.org/abs/2210.14633 · HTML: https://mlsanity.com/paper/2210.14633/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 26 Oct 2022.

## Builds on (most cited first, 11 of 11)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Stationary Graph Processes and Spectral Estimation](https://mlsanity.com/paper/1603.04667/) (2016)
- [Autoregressive Moving Average Graph Filtering](https://mlsanity.com/paper/1602.04436/) (2016)
- [Stationary signal processing on graphs](https://mlsanity.com/paper/1601.02522/) (2016)
- [Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems](https://mlsanity.com/paper/1406.5429/) (2014)
- [Kernel-based Reconstruction of Graph Signals](https://mlsanity.com/paper/1605.07174/) (2016)
- [Graph Signal Restoration Using Nested Deep Algorithm Unrolling](https://mlsanity.com/paper/2106.15910/) (2021)
- [Grid-Graph Signal Processing (Grid-GSP): A Graph Signal Processing Framework for the Power Grid](https://mlsanity.com/paper/2103.06068/) (2021)
- [Bayesian Estimation of Graph Signals](https://mlsanity.com/paper/2103.15520/) (2021)
- [Non-Bayesian Estimation Framework for Signal Recovery on Graphs](https://mlsanity.com/paper/2005.01952/) (2020)

## Abstract (arXiv)

The problem of recovering graph signals is one of the main topics in graph signal processing. A representative approach to this problem is the graph Wiener filter, which utilizes the statistical information of the target signal computed from historical data to construct an effective estimator. However, we often encounter situations where the current graph differs from that of historical data due to topology changes, leading to performance degradation of the estimator. This paper proposes a graph filter transfer method, which learns an effective estimator from historical data under topology changes. The proposed method leverages the probability density ratio of the current and historical observations and constructs an estimator that minimizes the reconstruction error in the current graph domain. The experiment on synthetic data demonstrates that the proposed method outperforms other methods.