NeurIPS 2025 论文列表

This paper studies a bilinear matrix-valued regression model where both predictors and responses are matrices. For each observation $t$, the response \( Y_t \in \mathbb{R}^{n \times p} \) and predictor \( X_t \in \mathbb{R}^{m \times q} \) satisfy $Y_t = A^* X_t B^* + E_t,$ with \( A^* \in \mathbb{R}_+^{n \times m} \) (row-wise \(\ell_1\)-normalized), \( B^* \in \mathbb{R}^{q \times p} \), and \( E_t \) independent Gaussian noise matrices. The goal is to estimate \( A^* \) and \( B^* \) from the observed pairs \( (X_t, Y_t) \). We propose explicit, optimization-free estimators and establish non-asymptotic error bounds, including sparse settings. Simulations confirm the theoretical rates and demonstrate strong finite-sample performance. We further illustrate the practical utility of our method through an image denoising application on real data.

We introduce *Backward Conformal Prediction*, a method that guarantees conformal coverage while providing flexible control over the size of prediction sets. Unlike standard conformal prediction, which fixes the coverage level and allows the conformal set size to vary, our approach defines a rule that constrains how prediction set sizes behave based on the observed data, and adapts the coverage level accordingly. Our method builds on two key foundations: (i) recent results by Gauthier et al. [2025] on post-hoc validity using e-values, which ensure marginal coverage of the form $\mathbb{P}(Y_{\rm test} \in \hat C_n^{\tilde{\alpha}}(X_{\rm test})) \ge 1 - \mathbb{E}[\tilde{\alpha}]$ up to a first-order Taylor approximation for any data-dependent miscoverage $\tilde{\alpha}$, and (ii) a novel leave-one-out estimator $\hat{\alpha}^{\rm LOO}$ of the marginal miscoverage $\mathbb{E}[\tilde{\alpha}]$ based on the calibration set, ensuring that the theoretical guarantees remain computable in practice. This approach is particularly useful in applications where large prediction sets are impractical such as medical diagnosis. We provide theoretical results and empirical evidence supporting the validity of our method, demonstrating that it maintains computable coverage guarantees while ensuring interpretable, well-controlled prediction set sizes.