Typos-Suggestions.md

2.1 Classification with Adaptive Predictive Sets

Suggestion: in $ k=\inf\left{ k:\sum_{i=1}^k\hat{f}(X_{test})_{\pi_i}\geq 1-\alpha \right} $, using the same symbol $k$ both for the infimum of the sum upper bounds, and for the sum upper bounds, can be a bit confusing, so maybe consider using a different symbol?

2.2 Conformalized Quantile Regression

Suggestion: since regression is usually done on tabular data, and boosting regressors tend to do better than NNs on tabular data you may want to mention that scikit-learn offers the possibility to train a GradientBoostingRegressor with pinball loss. XGBoost usually gives better point estimates than GradientBoostingRegressor, but that library doesn't currently offer the possibility to train with pinball loss. However, they're working on it (see issue #7435).

2.3 Conformalizing Scalar Uncertainty Estimates

Typo: the caption of Figure 8 is wrong (part of it is copy-pasted from Figure 6) Suggestion: you may want to mention that Henrik Bostrom wrote a sklearn-like library crepes which offers the possibility to conformalize generic regressors using uncertainty scalars. I wasn't paid by Henrik to tell you this (I don't even know him 😀)

3.2 Checking for correct coverage

The standard deviation of $\bar{C}$

Typo: "We now we will examine the distribution of $C_j$". Typo: "Unfortunately, the distribution of $\bar{C}-$the mean of R independent beta-binomial distributions random variables$-$does not have a closed form". Typo: "If the simulated average empirical coverage does not align well with the coverage observed on the real data, there is likely a problem in the conformal implementation.".

3.2 Evaluating adaptiveness

Feature-stratified coverage metric.

Typo: "In words, this is the observed coverage for all units for which to the discrete feature takes value g" Not sure if typo: "For example, in classification we might divide the observations into units into three groups". The last part is a bit unclear to me, not sure if it's a typo or not.

5.2 Simultaneous guarantees on OOD detection and coverage

Typo: in the table at the top of page 25,, the two null hypotheses are $H_\lambda^{(1)}:R_1(\lambda)\leq\alpha_1,\ H_\lambda^{(2)}:R_2(\lambda)\leq\alpha_2$. They should be $H_\lambda^{(1)}:R_1(\lambda)>\alpha_1,\ H_\lambda^{(2)}:R_2(\lambda)>\alpha_2$

6.1 Group-balanced conformal prediction

Typo: "For example, we may we may require"

6.4 Conformal prediction under covariate shift

Typo: "[..] so diseases present during to infancy will be over-predicted." Typo: the formula for $\hat{q}(x)$ has some typo (maybe a ) is missing?), but I can't really tell, because frankly this is the part I understood the least 😅

A Theorem and Proof: Coverage Property of Conformal Prediction

Typo: equation in the middle of the page, more or less: ${Y_{test} \in \mathcal{T}(X_{test})} = {s_{n+1} \sout{>}\leq s_{\lceil(n+1)(1−α)\rceil}}.$