We introduce a new general identifiable framework for principled disentanglement referred to as Structured Nonlinear Independent Component Analysis (SNICA). Our contribution is to extend the identifiability theory of deep generative models for a very broad class of structured models. While previous works have shown identifiability for specific classes of time-series models, our theorems extend this to more general temporal structures as well as to models with more complex structures such as spatial dependencies. In particular, we establish the major result that identifiability for this framework holds even in the presence of noise of unknown distribution. Finally, as an example of our framework's flexibility, we introduce the first nonlinear ICA model for time-series that combines the following very useful properties: it accounts for both nonstationarity and autocorrelation in a fully unsupervised setting; performs dimensionality reduction; models hidden states; and enables principled estimation and inference by variational maximum-likelihood.

Contemporary vision benchmarks predominantly consider tasks on which humans can achieve near-perfect performance. However, humans are frequently presented with visual data that they cannot classify with 100% certainty, and models trained on standard vision benchmarks achieve low performance when evaluated on this data. To address this issue, we introduce a procedure for creating datasets of ambiguous images and use it to produce SQUID-E ("Squidy"), a collection of noisy images extracted from videos. All images are annotated with ground truth values and a test set is annotated with human uncertainty judgments. We use this dataset to characterize human uncertainty in vision tasks and evaluate existing visual event classification models. Experimental results suggest that existing vision models are not sufficiently equipped to provide meaningful outputs for ambiguous images and that datasets of this nature can be used to assess and improve such models through model training and direct evaluation of model calibration. These findings motivate large-scale ambiguous dataset creation and further research focusing on noisy visual data.1

L.1 Source Dataset: ImageNet Table 13 and Table 14 describe 5-way 1-shot and 5-way 5-shot CD-FSL performance when ImageNet is used as the source dataset, respectively. Note that Table 14 is added for convenience and this is the same with Table 3 in the main paper.

A t the world's biggest car fair, which opened in Beijing on Friday, there were hundreds of manufacturers, more than 1,000 vehicles, hundreds of thousands of enthusiasts - and hardly anyone behind a wheel. China's car companies have cornered the domestic electric vehicle market, and are increasingly visible on the global stage . Now they are turning their attention to what they are betting is the future of mobility: autonomous driving. At the Beijing Auto Fair, a huge industry event that covers 380,000 square metres on the outskirts of the capital, the country's carmakers showed off a range of intelligent driving technologies. In China's cut-throat domestic market, nearly every big carmaker is investing heavily in the software and computing power needed to make "hands-free" driving a reality as they compete to offer additional perks and find new ways to generate revenue.

Note that here we used that lower triangular504 halves of matrices L and H have the same sparsity patterns, which follows from the fact that banded505 graph is a chordal graph with perfect elimination order {1,2,...,n }. Proof of Theorem 3.1 The proof follows trivially from Theorem 3.1, when b is set to 1.509 A.2 Regret bound analysis510 Proof sketch of Theorem 3.3. We decompose the regret into RT T1+T2+T3 in Lemma .1 and indi-511 vidually bound the terms. This ex-514 plicit expression is later used to bound each entry of (X 1t+1 X 1t)with O(1/ p t)in Appendix A.2.4,515 this gives a O( p T) upperbound on T2. Substituting the above identity in the Equation (19) proves the lemma.527