16 problems

Consider a generic orthogonally invariant generalized linear model and the spectrally initialized Bayes-GVAMP estimator. Bayes-GVAMP optimality conjecture. Bayes-GVAMP is optimal a…

Data-independent-prior extension conjecture. With additional effort, the Laplace approximation and the model-selection consistency results for excluding supersets and avoiding fals…

Hard-phase conjecture. There is no efficient algorithm that achieves better performance than GAMP in the hard phase.

Consider the generalized linear model with orthogonally invariant design, and let $\widehat{\beta}_{\mathrm{B}}=\mathbb{E}[\beta_*\mid X,y]$ be the posterior mean estimator. Let…

Maillard et al.'s threshold conjecture. This condition is conjectured to be the computationally optimal weak recovery threshold: if it is violated, no polynomial-time algorithm sho…

Let $\mathcal{B}$ be a class of candidate parameter vectors in a generalized linear model, and let $\theta_{\widehat\beta}$ be an estimator constructed from the candidates. A sharp…

Let $\mathbf{X}$ have an unknown distribution, and suppose a Gaussian identification strategy is transferred to a broader class of designs through a universality argument. Let…

Consider the proportional-asymptotic Gaussian-design setting in which the covariate covariance matrix $\bm{\Sigma}$ is unknown and is estimated from the data. No-sample-splitting c…

Let $\widehat{m}_{\mathbf{X} Y, 2}$ be the moment estimator used in the Gaussian-design GLM method-of-moments procedure, and let $\bm{\beta}$ denote the regression coefficient vect…

Let $J\geq0$ be the number of sample IRPLS iterations, let $c>0$ be a possibly small constant, and let $J_{0}\geq0$ depend on the distribution of the latent model. Suppose the clas…

Consider the generalized-linear-model extension with sample IRPLS estimator $\widehat{\boldsymbol{\beta}}_{\widehat{s}}^{(J)}$, where $J\geq0$ is fixed, and let…

Let generalized linear models be considered in the high-dimensional regime, with approximate message passing (AMP) producing iterative estimates of the signal. Under suitable model…

Generalized linear models may have no simple explicit expression for Fisher information. Power-analysis conjecture. The study of the asymptotic power of the proposed tests may be f…

Optimal tuning parameter conjecture. Based on simulation results, the DPD-SIS with an $\alpha$ value around $0.3$ performs the best in the case of dependent covariates.

Stability-condition conjecture. This condition delimits precisely the region where polynomial-time algorithms do not perform better than random guessing.

For a generalized linear model with weakly collinear design, let model selection use a single selected estimator and let averaging use estimators from all models with properly chos…