6 problems

Let $K$ be prefix Kolmogorov complexity, let $\boldsymbol{\vartheta}_0$ be the true parameter, and let $\Delta(k)$ denote the complexity difference used in the MDL setup. Strengthe…

Let $v$ be a string, let $L^m(v)$ denote the length of its shortest grammar, and let $\boldsymbol{\operatorname{MDL}}(v)$ denote the MDL code for $v$. Let $\gamma(n):=n f_1(n)$. Sy…

The paper considers model selection using plug-in codes, which code each new outcome using a distribution indexed by the maximum-likelihood estimator based on preceding outcomes. P…

Let $\mathcal{M}$ be a sufficiently capable base model trained on a corpus containing code, mathematics, and structured data, and let $n^*$ be a PLT trie node with probability…

Shtarkov–Jeffreys finiteness conjecture. The Shtarkov integral is finite if and only if the corresponding Jeffreys integral is finite. This conjecture concerns when the original no…

Let a statistical model be a smoothly parametrized family of distributions whose parameter space is finite-dimensional. Suppose that conditional MDL is a Bayesian prediction for th…