### VIP内容

http://jfoulds.informationsystems.umbc.edu/papers/2021/Islam%20(2021)%20-%20Debiasing%20Career%20Recommendations%20with%20Neural%20Fair%20Collaborative%20Filtering%20(WWW).pdf

### 最新论文

We consider sparse matrix estimation where the goal is to estimate an $n\times n$ matrix from noisy observations of a small subset of its entries. We analyze the estimation error of the popularly utilized collaborative filtering algorithm for the sparse regime. Specifically, we propose a novel iterative variant of the algorithm, adapted to handle the setting of sparse observations. We establish that as long as the fraction of entries observed at random scale as $\frac{\log^{1+\kappa}(n)}{n}$ for any fixed $\kappa > 0$, the estimation error with respect to the $\max$-norm decays to $0$ as $n\to\infty$ assuming the underlying matrix of interest has constant rank $r$. Our result is robust to model mis-specification in that if the underlying matrix is approximately rank $r$, then the estimation error decays to the approximate error with respect to the $\max$-norm. In the process, we establish algorithm's ability to handle arbitrary bounded noise in the observations.

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