For example, one can simply use the splits of the edges on phylogenetic trees, and assign parameters for each split inSr. Let π be a permutation ofS and Sc, that isπ(S) is a rearrangement ofS and π(Sc) is a rearrangementofSc.

Whiletheoretical results havebeen obtained for their heavy-tailedness, the full characterization of the prior predictive distribution (i.e. its density, CDF andmoments), remained unknownpriortothiswork.

The first subset (in red) is utilized to evaluate a traditional accuracy-basedlossfunction `a,suchasthecrossentropy. This benchmark is based on a loss function designed to incentivize the trained model to produce the smallest possible conformal prediction sets with the desired coverage (e.g., 90% ifα = 0.1). The hybrid training procedure is similar to Algorithm 1, in the sense that it relies on analogous soft-sorting, soft-ranking, and soft-indexing algorithms toevaluate adifferentiable approximation Wi oftheconformity scoreWi in(8). Above, the second equality follows directly from the fact thatS(x,U;π,t), defined in (A2), is by construction increasing in t, and therefore Y / S(x,U;π,1 α) if and only if min{t [0,1]:Y S(x,U;π,t)}>1 α. The proof consists of showing that`a and`u are separately minimized by ˆπ = π,although only approximately inthelatter case.

In particular, they tend to be overconfident.

After each action, the agent observes the realizations of all the variables.

Specifically, we adopt normalized masked average pooling (NMAP) to extract latent intra-saliency categories from the SISMs and semantic features as intra cues. Then we employ a correlation fusion module (CFM) to obtain inter cues by exploiting correlations between the intra cues and single-image features. To improve Co-SOD performance, we propose a category-independent rearranged self-correlation feature(RSCF)strategy.