# From bilinear regression to inductive matrix completion: a quasi-Bayesian analysis

arXiv: https://arxiv.org/abs/2210.15290 · HTML: https://mlsanity.com/paper/2210.15290/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2022.

## Built on by (most cited first, 7 of 7)

- [Concentration properties of fractional posterior in 1-bit matrix completion](https://mlsanity.com/paper/2404.08969/) (2024)
- [Optimal sparse phase retrieval via a quasi-Bayesian approach](https://mlsanity.com/paper/2504.09509/) (2025)
- [PAC-Bayes Bounds for Multivariate Linear Regression and Linear Autoencoders](https://mlsanity.com/paper/2512.12905/) (2025)
- [Bayesian Pliable Lasso with Horseshoe Prior for Interaction Effects in GLMs with Missing Responses](https://mlsanity.com/paper/2509.07501/) (2025)
- [High-dimensional prediction for count response via sparse exponential weights](https://mlsanity.com/paper/2410.15381/) (2024)
- [Kullback-Leibler excess risk bounds for exponential weighted aggregation in Generalized linear models](https://mlsanity.com/paper/2504.10171/) (2025)
- [Robust low-rank estimation with multiple binary responses using pairwise AUC loss](https://mlsanity.com/paper/2601.08618/) (2026)

## Abstract (arXiv)

In this paper we study the problem of bilinear regression and we further address the case when the response matrix contains missing data that referred as the problem of inductive matrix completion. We propose a quasi-Bayesian approach first to the problem of bilinear regression where a quasi-likelihood is employed. Then, we adapt this approach to the context of inductive matrix completion. Under a low-rankness assumption and leveraging PAC-Bayes bound technique, we provide statistical properties for our proposed estimators and for the quasi-posteriors. We propose a Langevin Monte Carlo method to approximately compute the proposed estimators. Some numerical studies are conducted to demonstrated our methods.