Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distribution-free binary classification: prediction sets, confidence
  intervals and calibration   We study three notions of uncertainty quantification -- calibration,
confidence intervals and prediction sets -- for binary classification in the
distribution-free setting, that is without making any distributional
assumptions on the data. With a focus towards calibration, we establish a
'tripod' of theorems that connect these three notions for score-based
classifiers. A direct implication is that distribution-free calibration is only
possible, even asymptotically, using a scoring function whose level sets
partition the feature space into at most countably many sets. Parametric
calibration schemes such as variants of Platt scaling do not satisfy this
requirement, while nonparametric schemes based on binning do. To close the
loop, we derive distribution-free confidence intervals for binned probabilities
for both fixed-width and uniform-mass binning. As a consequence of our 'tripod'
theorems, these confidence intervals for binned probabilities lead to
distribution-free calibration. We also derive extensions to settings with
streaming data and covariate shift.

30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys