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 Statistical Learning





The Flip Side of the Reweighted Coin: Duality of Adaptive Dropout and Regularization

Neural Information Processing Systems

In machine learning, it is often valuable for models to be parsimonious or sparse for a variety of reasons, from memory savings and computational speedups to model interpretability and general-izability.



A Omitted Proofs

Neural Information Processing Systems

Since the calculations are essentially identical to the proof of Theorem 4.2, we omit the details.





Supplement to " Efficient Clustering for Stretched Mixtures: Landscape and Optimality "

Neural Information Processing Systems

K-means (DisKmeans) in Y e et al. (2008); (ii) a discriminative clustering formulation described in Bach and Harchaoui (2008); Flammarion et al. (2017); (iii) Model-based clustering (Mclust) in Fraley and Raftery (1999); (iv) Projection Pursuit (PP) in Peña and Prieto (2001); (v) Adaptive LDA-guided K-means Clustering in Ding and Li (2007); and (vi) Minimum Density Hyperplane As suggested by Y e et al. (2008), the regularization parameter To resolve this issue, they provide an automatic tuning framework. Here we provide a comparison between CURE and DisKmeans. Density Hyperplane (MDH) in Pavlidis et al. (2016) are implemented using open-source R packages The discriminative clustering method appeared in Bach and Harchaoui (2008); Flammarion et al. The iterative algorithm is terminated when y, the predicted label, no longer changes. To illustrate how the general CURE in Section 2.3 works, we consider the clustering problem with When a is sufficiently large and b 2a, f has the following properties: 1. f B.2 Step 2: landscape analysis of the population loss To kick off the landscape analysis we investigate the population version of ˆ L See Appendix E for a proof.