Bayesian predictive intervals are conditioned on the specific observed sequenceZ1:n and make statements on the next value[Yn+1 | Xn+1]. Subjective Bayesian statements on predictions are non-refutable, and are in this sense unscientific, but are optimal according to decision theoretic foundations. However,tomakesuch strong statements, the Bayesian must usually make the strict assumption of the model being well-specified. Asmentionedearlier,computingtheAOI interval is an efficient matrix-vector multiplication, whereas the LOO interval requires expensive broadcastingtoconstructthe ngrid T nISweightarray. We use the same Bayesian model as in (10), again consideringc=1,0.02.

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees.

This is the Appendix for "Self-Supervised Learning Disentangled Group Representation as Feature". Table .1 summarizes the abbreviations and the symbols used in the main paper.Abbreviation/Symbol Meaning Abbreviation SSL Self-supervised Learning SL Supervised Learning DCI Disentangle Metric for Informativeness IRS Interventional Robustness Score EXP Explicitness Score MOD Modularity Score LR Logistic Regression GBT Gradient Boosted Trees OOD Out-Of-Distributed Symbol in Theory U Semantic space X V ector space I Image space G Group G ( x) Group orbit w.r .t.G containing the sample x ϕ Image generation process U I φ Visual representation I X f Semantic representation U X m The number of decomposed subgroups Symbol in Algorithm P Partition of dataset P Learned partition through Eq. (3) P Set of partitions used in Eq. (2) N Number of training images θ "Dummy" parameter used by IRM I Image X List of abbreviations and symbols used in the paper. Section A provides the preliminary knowledge about the group theory. Section D presents the additional experimental results. 1 A Preliminaries Groups often arise as transformations of some space, such as a set, vector space, or topological space. The set of clockwise rotations w.r .t. its centroid to retain We say this group of rotations act on the triangle, which is formally defined below.

Time series forecasting has become a critical task due to its high practicality in real-world applications such as traffic, energy consumption, economics and finance,anddiseaseanalysis.