6 problems

Arlot–Massart slope heuristics conjecture. In a quite general framework, if a penalty satisfies

Complexity-grouping conjecture. This grouping of the models is sufficient to take into account the richness of $\mathcal{M}_n$ for the optimal calibration of the penalty.

General-use conjecture. Even if the factor $2$ arising from the closeness of $\mathbb{E}[p_1]$ and $\mathbb{E}[p_2]$ may not be universally valid, Algorithm can be used in settings…

Minimal-penalty conjecture. The minimal amount of penalty required for the model-selection procedure to work is $p_2(m)$.

General-framework slope heuristics conjecture. Even if the factor $2$ arising from the closeness of $\mathbb{E}[p_1]$ and $\mathbb{E}[p_2]$ is not universally valid, the calibratio…

Slope heuristics conjecture. The restriction to piecewise constant-function models is mainly technical, and the slope heuristics should remain valid at least in the general least-s…