Fused $\ell_{1}$ Trend Filtering on Graphs
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917563571634176 |
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| author | Pastukhov, Vladimir |
| author_facet | Pastukhov, Vladimir |
| contents | This paper is dedicated to the fused trend filtering on a general graph, which is a combination of fused estimator and 1-st order trend filtering on a graph. There are two cases of fusion regularisers studied in this work: anisotropic total variation (i.e. fused lasso) and nearly-isotonic restriction. For the trend filtering part we consider general trend filtering on a given graph and Kronecker trend filter for the case of lattice data. We show how these estimators are related to each other and propose a computationally feasible numerical solution with a linear complexity per iteration with respect to the amount of edges in the graph. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_05250 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fused $\ell_{1}$ Trend Filtering on Graphs Pastukhov, Vladimir Statistics Theory This paper is dedicated to the fused trend filtering on a general graph, which is a combination of fused estimator and 1-st order trend filtering on a graph. There are two cases of fusion regularisers studied in this work: anisotropic total variation (i.e. fused lasso) and nearly-isotonic restriction. For the trend filtering part we consider general trend filtering on a given graph and Kronecker trend filter for the case of lattice data. We show how these estimators are related to each other and propose a computationally feasible numerical solution with a linear complexity per iteration with respect to the amount of edges in the graph. |
| title | Fused $\ell_{1}$ Trend Filtering on Graphs |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2401.05250 |