AMP to get insights into the statistical properties of SLOPE.

We propose a probabilistic framework for modelling and exploring the latent structure of relational data. Given feature information for the nodes in a network, the scalable deep generative relational model (SDREM) builds a deep network architecture that can approximate potential nonlinear mappings between nodes' feature information and the nodes' latent representations. Our contribution is two-fold: (1) We incorporate high-order neighbourhood structure information to generate the latent representations at each node, which vary smoothly over the network.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Please also discuss on how this can be extended to the analysis of ADMM. This paper is an extension of Tseng [20], Tseng and Yun A coordinate gradient descent method for nonsmooth separable minimization and Zhang et al. [22], which established the same result using the error-bound condition for lasso and group lasso, to the trace norm. This is a non-trivial extension but the contribution seems purely technical. The presentation of the proofs is mostly clear.

However, their data structure requires a significantly increased super-linear storage space, as well as super-linear preprocessing time.

Self-supervised learning holds great promise for improving representations when labeled data are scarce. In semi-supervised learning, recent self-supervision methods are state-of-the-art [Gidaris et al., 2018, Dosovitskiy et al., 2016, Zhai et al., 2019], and self-supervision is essential in video tasks where annotation is costly [V ondrick et al., 2016, 2018].

We note that while the subclasses used in practice (e.g., trees) may well be infinite beyond a simple Our proposed method for solving this optimization problem is presented in full in Algorithm 1. The supplemental material contains exemplary code for Algorithm 1 that uses generic scikit-learn regressors.

Meta-learning, or 'learning to learn' [ However, it can be any useful knowledge which can be learned in the meta-training stage. This setting is intuitive and theoretically sound.

The EM algorithm is one of the most popular algorithm for inference in latent data models. The original formulation of the EM algorithm does not scale to large data set, because the whole data set is required at each iteration of the algorithm. To alleviate this problem, Neal and Hinton [1998] have proposed an incremental version of the EM (iEM) in which at each iteration the conditional expectation of the latent data (E-step) is updated only for a mini-batch of observations. Another approach has been proposed by Capp e and Moulines [2009] in which the E-step is replaced by a stochastic approximation step, closely related to stochastic gradient. In this paper, we analyze incremental and stochastic version of the EM algorithm as well as the variance reduced-version of [Chen et al., 2018] in a common unifying framework. We also introduce a new version incremental version, inspired by the SAGA algorithm by Defazio et al. [2014]. We establish non-asymptotic convergence bounds for global convergence. Numerical applications are presented in this article to illustrate our findings.