When !(x)= !1(x1) !d(xd), multi ones, and2) reads KN(x, y)=

The split of training, validation and test sets follows the settings of the previous method[10]. The inputpointcloudconsists of2048pointsrepresented bytheirEuclidean coordinates sampled from a normalized object, and the indexes of keypoints are given. The learning rate is set to1 10 3 andhalvedevery10epochs. Wesetthetargetvarianceσ2t to4,thelossweight ofvariance regularization to1, and the loss weight of distributions regularization to0.01 to achieve the best results after tuning. Wesetthetargetvarianceσ2t to4,thelossweightofvariance regularization to1, and the loss weight of distributions regularization to0.01 to achieve the best results after tuning.

Inthiswork,wepropose sampling-argmax, adifferentiable training method that imposes implicit constraints tothe shape of the probability map by minimizing the expectation of the localization error.

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way.

Models of disease progression are instrumental forpredictingpatient outcomes and understandingdisease dynamics. Existing models provide the patient with pragmatic (supervised) predictions of risk, but do not provide the clinician with intelligible (unsupervised) representations ofdiseasepathology.

For all parameter settings, see Appendix B.2. The code of our CRCL will be released on GitHub.