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Micro-expressions (MEs) are involuntary facial movements revealing people's hidden feelings in high-stake situations and have practical importance in medical treatment, national security, interrogations and many human-computer interaction systems. Early methods for MER mainly based on traditional appearance and geometry features. Recently, with the success of deep learning (DL) in various fields, neural networks have received increasing interests in MER. Different from macro-expressions, MEs are spontaneous, subtle, and rapid facial movements, leading to difficult data collection, thus have small-scale datasets. DL based MER becomes challenging due to above ME characters. To date, various DL approaches have been proposed to solve the ME issues and improve MER performance. In this survey, we provide a comprehensive review of deep micro-expression recognition (MER), including datasets, deep MER pipeline, and the bench-marking of most influential methods. This survey defines a new taxonomy for the field, encompassing all aspects of MER based on DL. For each aspect, the basic approaches and advanced developments are summarized and discussed. In addition, we conclude the remaining challenges and and potential directions for the design of robust deep MER systems. To the best of our knowledge, this is the first survey of deep MER methods, and this survey can serve as a reference point for future MER research.

The properties of flat minima in the empirical risk landscape of neural networks have been debated for some time. Increasing evidence suggests they possess better generalization capabilities with respect to sharp ones. First, we discuss Gaussian mixture classification models and show analytically that there exist Bayes optimal pointwise estimators which correspond to minimizers belonging to wide flat regions. These estimators can be found by applying maximum flatness algorithms either directly on the classifier (which is norm independent) or on the differentiable loss function used in learning. Next, we extend the analysis to the deep learning scenario by extensive numerical validations. Using two algorithms, Entropy-SGD and Replicated-SGD, that explicitly include in the optimization objective a non-local flatness measure known as local entropy, we consistently improve the generalization error for common architectures (e.g. ResNet, EfficientNet). An easy to compute flatness measure shows a clear correlation with test accuracy.

This paper investigates Nash equilibrium (NE) seeking problems for noncooperative games over multi-players networks with finite bandwidth communication. A distributed quantized algorithm is presented, which consists of local gradient play, distributed decision estimating, and adaptive quantization. Exponential convergence of the algorithm is established, and a relationship between the convergence rate and the bandwidth is quantitatively analyzed. Finally, a simulation of an energy consumption game is presented to validate the proposed results.

We give an overview of theoretical and practical aspects of finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of n points in the plane. Both problems are known to be NP-hard and were the subject of the 2019 Computational Geometry Challenge, which presented the quest of finding good solutions to more than 200 instances, ranging from n = 10 all the way to n = 1, 000, 000.

We present a flexible public transit network design model which optimizes a social access objective while guaranteeing that the system's costs and transit times remain within a preset margin of their current levels. The purpose of the model is to find a set of minor, immediate modifications to an existing bus network that can give more communities access to the chosen services while having a minimal impact on the current network's operator costs and user costs. Design decisions consist of reallocation of existing resources in order to adjust line frequencies and capacities. We present a hybrid tabu search/simulated annealing algorithm for the solution of this optimization-based model. As a case study we apply the model to the problem of improving equity of access to primary health care facilities in the Chicago metropolitan area. The results of the model suggest that it is possible to achieve better primary care access equity through reassignment of existing buses and implementation of express runs, while leaving overall service levels relatively unaffected.

The recovery of sparse data is at the core of many applications in machine learning and signal processing. While such problems can be tackled using $\ell_1$-regularization as in the LASSO estimator and in the Basis Pursuit approach, specialized algorithms are typically required to solve the corresponding high-dimensional non-smooth optimization for large instances. Iteratively Reweighted Least Squares (IRLS) is a widely used algorithm for this purpose due its excellent numerical performance. However, while existing theory is able to guarantee convergence of this algorithm to the minimizer, it does not provide a global convergence rate. In this paper, we prove that a variant of IRLS converges with a global linear rate to a sparse solution, i.e., with a linear error decrease occurring immediately from any initialization, if the measurements fulfill the usual null space property assumption. We support our theory by numerical experiments showing that our linear rate captures the correct dimension dependence. We anticipate that our theoretical findings will lead to new insights for many other use cases of the IRLS algorithm, such as in low-rank matrix recovery.

We studied power splitting-based simultaneous wireless information and power transfer (PS-SWIPT) in multiple access channels (MAC), considering the decoding cost and non-linear energy harvesting (EH) constraints at the receiving nodes to study practical limitations of an EH communication system. Under these restrictions, we formulated and analyzed the achievable rate and maximum departure regions in two well-studied scenarios, i.e., a classical PS-SWIPT MAC and a PS-SWIPT MAC with user cooperation. In the classical PS-SWIPT MAC setting, closed-form expressions for the optimal values of the PS factors are derived for two fundamental decoding schemes: simultaneous decoding and successive interference cancellation. In the PS-SWIPT MAC with user cooperation, the joint optimal power allocation for users as well as the optimal PS factor are derived. This reveals that one decoding scheme outperforms the other in the classical PS-SWIPT MAC, depending on the function type of the decoding cost. Finally, it is shown that the cooperation between users can potentially boost the performance of a PS-SWIPT MAC under decoding cost and non-linear EH constraints. Moreover, effects of the decoding cost functions, non-linear EH model and channel quality between the users are studied, and performance characteristics of the system are discussed.

Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive capacity and effective model complexity. We review the existing studies on those two categories along four important factors, including model framework, model size, optimization process and data complexity. We also discuss the applications of deep learning model complexity including understanding model generalization capability, model optimization, and model selection and design. We conclude by proposing several interesting future directions.

We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.