Neural Information Processing Systems http://nips.cc/

This paper considers the subspace clustering problem where the data contains irrelevant or corrupted features. We propose a method termed "robust Dantzig selector" which can successfully identify the clustering structure even with the presence of irrelevant features. The idea is simple yet powerful: we replace the inner product by its robust counterpart, which is insensitive to the irrelevant features given an upper bound of the number of irrelevant features. We establish theoretical guarantees for the algorithm to identify the correct subspace, and demonstrate the effectiveness of the algorithm via numerical simulations. To the best of our knowledge, this is the first method developed to tackle subspace clustering with irrelevant features.

This supplementary material provides implementation details, hyper-parameters settings, additional results and visualisations. Section A presents a focus on the design choices we use for IMGEP-HOLMES Section B provides implementation details for the main paper evaluation procedure - B.1: Quantitative evaluation of diversity - B.2: Quantitative evaluation of Representational Similarity - D.1: Complete RSA analysis of the hierarchy of behavioral characterizations learned Figure 6: Focus on the different design choices made for the HOLMES architecture. We summarize those components in Figure 6. The connection scheme is summarized in Figure 6. There are two main choices: when to split a node and how to redirect the patterns toward either the left or right children.

We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the dependency that is not captured by the original variational distribution, and thus the augmented variational family guarantees better approximations to the posterior. With stochastic optimization, inference on the augmented distribution is scalable. Furthermore, our strategy is generic: it can be applied to any inference procedure that currently uses the mean-field or structured approach. Copula variational inference has many advantages: it reduces bias; it is less sensitive to local optima; it is less sensitive to hyperparameters; and it helps characterize and interpret the dependency among the latent variables.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/