baseline systems on the three proposed tasks: state-of-mind recognition, depression assessment with AI, and cross-cultural affect sensing, respectively.

The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to estimate low-dimensional parameters at parametric square-root rate in a large Gaussian graphical model? A novel regression approach is proposed to obtain asymptotically efficient estimation of each entry of a precision matrix under a sparseness condition relative to the sample size. When the precision matrix is not sufficiently sparse, or equivalently the sample size is not sufficiently large, a lower bound is established to show that it is no longer possible to achieve the parametric rate in the estimation of each entry. This lower bound result, which provides an answer to the delicate sample size question, is established with a novel construction of a subset of sparse precision matrices in an application of Le Cam's lemma. Moreover, the proposed estimator is proven to have optimal convergence rate when the parametric rate cannot be achieved, under a minimal sample requirement.The proposed estimator is applied to test the presence of an edge in the Gaussian graphical model or to recover the support of the entire model, to obtain adaptive rate-optimal estimation of the entire precision matrix as measured by the matrix ℓq operator norm and to make inference in latent variables in the graphical model. All of this is achieved under a sparsity condition on the precision matrix and a side condition on the range of its spectrum. This significantly relaxes the commonly imposed uniform signal strength condition on the precision matrix, irrepresentability condition on the Hessian tensor operator of the covariance matrix or the ℓ1 constraint on the precision matrix. Numerical results confirm our theoretical findings. The ROC curve of the proposed algorithm, Asymptotic Normal Thresholding (ANT), for support recovery significantly outperforms that of the popular GLasso algorithm.1. Introduction. The Gaussian graphical model, a powerful tool for investigating the relationship among a large number of random variables in a complex system, is used in a wide range of scientific applications. A central question for Gaussian graphical models is how to recover the structure of an undirected Gaussian graph. Let G = (V, E) be an undirected graph representing the conditional dependence relationship between components of a random vector Z = (Z 1 , . . . , Z p ) T as follows. The vertex set V = {V 1 , . . . , V p } represents the components of Z. The edge set E consists of pairs (i, j) indicating the conditional dependence between Z i and Z j given all other components. In applications, the following question is fundamental: Is there an edge between V i and V j ? It is well known that recovering the structure of an undirected Gaussian graph G = (V, E) is equivalent to recovering the support of the population precision matrix of the data in the Gaussian graphical model. Let

Covariance matrix estimation is one of the most important problems in statistics. To accommodate the complexity of modern datasets, it is desired to have estimation procedures that not only can incorporate the structural assumptions of covariance matrices, but are also robust to outliers from arbitrary sources. In this paper, we define a new concept called matrix depth and then propose a robust covariance matrix estimator by maximizing the empirical depth function. The proposed estimator is shown to achieve minimax optimal rate under Huber's -contamination model for estimating covariance/scatter matrices with various structures including bandedness and sparsity.

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The INTERSPEECH 2018 Computational Paralinguistics Challenge addresses four different problems for the first time in a research competition under well-defined conditions: In the Atypical Affect Sub-Challenge, four basic emotions annotated in the speech of handicapped subjects have to be classified; in the Self-Assessed Affect Sub-Challenge, valence scores given by the speakers themselves are used for a three-class classification problem; in the Crying Sub-Challenge, three types of infant vocalisations have to be told apart; and in the Heart Beats Sub-Challenge, three different types of heart beats have to be determined. We describe the Sub-Challenges, their conditions, and baseline feature extraction and classifiers, which include data-learnt (supervised) feature representations by end-to-end learning, the 'usual' ComParE and BoAW features, and deep unsupervised representation learning using the AUDEEP toolkit for the first time in the challenge series.