8 problems

Calibration conjecture. The calibration result under consideration should also hold for general symmetric distributions, including heavy-tailed distributions.

Let $b_t$ be an arbitrary ordered vector of base forecasts, and let $\theta_t$ and $\tilde{\theta}_t$ denote the MultiQT iterates in the general setting. Bounded projection distanc…

Incompatibility conjecture. Probabilism and calibration are fundamentally incompatible: there is no construction of a data-dependent probability distribution quantifying uncertaint…

Let a model be recalibrated using the same training data on which the model was trained, and let the resulting calibration be evaluated by an expected calibration error or related…

Let $\mathcal{D}$ be a natural distribution over examples, let $n$ be the number of samples, let $\mathcal{F}$ be a family of interpolating models, and let $\varepsilon\geq0$. A pa…

Consider a Venn predictor producing outputs $f_1(X),\ldots,f_L(X)$ from a sample of size $n$, and let $\alpha\in(0,1)$. Venn predictor individual-output calibration conjecture. The…

Let $(f_1,f_2,\ldots,f_L)$ be a multiprobabilistic predictor, with each $f_i$ mapping $\mathcal{X}$ to the probability simplex $\Delta_{L-1}$. Define … and … Here…

Let $f$ be a prediction function and let a parametric post-hoc calibration method produce a calibrated output from $f$, with the output depending continuously on $f$. Continuous pa…