Human emotions unfold over time, and more affective computing research has to prioritize capturing this crucial component of real-world affect. Modeling dynamic emotional stimuli requires solving the twin challenges of time-series modeling and of collecting high-quality time-series datasets. We begin by assessing the state-of-the-art in time-series emotion recognition, and we review contemporary time-series approaches in affective computing, including discriminative and generative models. We then introduce the first version of the Stanford Emotional Narratives Dataset (SENDv1): a set of rich, multimodal videos of self-paced, unscripted emotional narratives, annotated for emotional valence over time. The complex narratives and naturalistic expressions in this dataset provide a challenging test for contemporary time-series emotion recognition models. We demonstrate several baseline and state-of-the-art modeling approaches on the SEND, including a Long Short-Term Memory model and a multimodal Variational Recurrent Neural Network, which perform comparably to the human-benchmark. We end by discussing the implications for future research in time-series affective computing.

Granger causality is a widely-used criterion for analyzing interactions in large-scale networks. As most physical interactions are inherently nonlinear, we consider the problem of inferring the existence of pairwise Granger causality between nonlinearly interacting stochastic processes from their time series measurements. Our proposed approach relies on modeling the embedded nonlinearities in the measurements using a component-wise time series prediction model based on Statistical Recurrent Units (SRUs). We make a case that the network topology of Granger causal relations is directly inferrable from a structured sparse estimate of the internal parameters of the SRU networks trained to predict the processes$'$ time series measurements. We propose a variant of SRU, called economy-SRU, which, by design has considerably fewer trainable parameters, and therefore less prone to overfitting. The economy-SRU computes a low-dimensional sketch of its high-dimensional hidden state in the form of random projections to generate the feedback for its recurrent processing. Additionally, the internal weight parameters of the economy-SRU are strategically regularized in a group-wise manner to facilitate the proposed network in extracting meaningful predictive features that are highly time-localized to mimic real-world causal events. Extensive experiments are carried out to demonstrate that the proposed economy-SRU based time series prediction model outperforms the MLP, LSTM and attention-gated CNN-based time series models considered previously for inferring Granger causality.

Deep neural networks suffer from performance decay when there is domain shift between the labeled source domain and unlabeled target domain, which motivates the research on domain adaptation (DA). Conventional DA methods usually assume that the labeled data is sampled from a single source distribution. However, in practice, labeled data may be collected from multiple sources, while naive application of the single-source DA algorithms may lead to suboptimal solutions. In this paper, we propose a novel multi-source distilling domain adaptation (MDDA) network, which not only considers the different distances among multiple sources and the target, but also investigates the different similarities of the source samples to the target ones. Specifically, the proposed MDDA includes four stages: (1) pre-train the source classifiers separately using the training data from each source; (2) adversarially map the target into the feature space of each source respectively by minimizing the empirical Wasserstein distance between source and target; (3) select the source training samples that are closer to the target to fine-tune the source classifiers; and (4) classify each encoded target feature by corresponding source classifier, and aggregate different predictions using respective domain weight, which corresponds to the discrepancy between each source and target. Extensive experiments are conducted on public DA benchmarks, and the results demonstrate that the proposed MDDA significantly outperforms the state-of-the-art approaches. Our source code is released at: https://github.com/daoyuan98/MDDA.

$K$-NN classifier is one of the most famous classification algorithms, whose performance is crucially dependent on the distance metric. When we consider the distance metric as a parameter of $K$-NN, learning an appropriate distance metric for $K$-NN can be seen as minimizing the empirical risk of $K$-NN. In this paper, we design a new type of continuous decision function of the $K$-NN classification rule which can be used to construct the continuous empirical risk function of $K$-NN. By minimizing this continuous empirical risk function, we obtain a novel distance metric learning algorithm named as adaptive nearest neighbor (ANN). We have proved that the current algorithms such as the large margin nearest neighbor (LMNN), neighbourhood components analysis (NCA) and the pairwise constraint methods are special cases of the proposed ANN by setting the parameter different values. Compared with the LMNN, NCA, and pairwise constraint methods, our method has a broader searching space which may contain better solutions. At last, extensive experiments on various data sets are conducted to demonstrate the effectiveness and efficiency of the proposed method.

In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a more convenient manner. Since the weighted Laplacian strategy inherits the virtues of spectral methods, graph algorithms designed using weighted Laplacian will necessarily possess more robust theoretical guarantees for algorithmic performances, comparing with those existing algorithms that are heuristically proposed. In order to illustrate its powerful utility both in theory and in practice, we also present two effective applications of our weighted Laplacian method to multilevel graph partitioning and balanced minimum cut problem, respectively. By means of variational methods and theory of partial differential equations (PDEs), we have established the equivalence relations among the weighted cut problem, balanced minimum cut problem and the initial clustering problem that arises in the middle stage of graph partitioning algorithms under a multilevel structure. These equivalence relations can indeed provide solid theoretical support for algorithms based on our proposed weighted Laplacian strategy. Moreover, from the perspective of the application to the balanced minimum cut problem, weighted Laplacian can make it possible for research of numerical solutions of PDEs to be a powerful tool for the algorithmic study of graph problems. Experimental results also indicate that the algorithm embedded with our strategy indeed outperforms other existing graph algorithms, especially in terms of accuracy, thus verifying the efficacy of the proposed weighted Laplacian.

Margaret Trautner Department of Mathematics Sai Ravela † Department of Earth, Atmospheric, and Planetary Sciences Earth Signals and Systems Group, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (Dated: November 26, 2019) Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Modeled as recurrent networks embedding a continuous neural differential equation, they achieve fully neural temporal output. Using the polynomial class of dynamical systems, we demonstrate equivalence of neural and numerical integration. I. INTRODUCTION Neural dynamical systems are dynamical systems described at least in part by neural networks. Our interest in the subject emerges in the context of Systems Dynamics and Optimization [21] (SDO), which is central to many applications such as storm prediction [19], climate-risk based decision support [22], or autonomous observatories [25]. The SDO cycle conceptually involves a forward path dynamically parameterizing, reducing, calibrating, initializing and simulating numerical models, and quantifying their uncertainties. SDO further involves a return path for adaptive observation, inversion and estimation.

The correspondence between residual networks and dynamical systems motivates researchers to unravel the physics of ResNets with well-developed tools in numeral methods of ODE systems. The Runge-Kutta-Fehlberg method is an adaptive time stepping that renders a good trade-off between the stability and efficiency. Can we also have an adaptive time stepping for ResNets to ensure both stability and performance? In this study, we analyze the effects of time stepping on the Euler method and ResNets. We establish a stability condition for ResNets with step sizes and weight parameters, and point out the effects of step sizes on the stability and performance. Inspired by our analyses, we develop an adaptive time stepping controller that is dependent on the parameters of the current step, and aware of previous steps. The controller is jointly optimized with the network training so that variable step sizes and evolution time can be adaptively adjusted. We conduct experiments on ImageNet and CIFAR to demonstrate the effectiveness. It is shown that our proposed method is able to improve both stability and accuracy without introducing additional overhead in inference phase.

Abstract-- As one type of efficient unsupervised learning methods, clustering algorithms have been widely used in data mining and knowledge discovery with noticeable advantages. However, clustering algorithms based on density peak have limited clustering effect on data with varying density distribution (VDD), equilibrium distribution (ED), and multiple domain-density maximums (MDDM), leading to the problems of sparse cluster loss and cluster fragmentation. T o address these problems, we propose a Domain-Adaptive Density Clustering (DADC) algorithm, which consists of three steps: domain-adaptive density measurement, cluster center self-identification, and cluster self-ensemble. For data with VDD features, clusters in sparse regions are often neglected by using uniform density peak thresholds, which results in the loss of sparse clusters. We treat each data point and its KNN neighborhood as a subgroup to better reflect its density distribution in a domain view. In addition, for data with ED or MDDM features, a large number of density peaks with similar values can be identified, which results in cluster fragmentation. We propose a cluster center self-identification and cluster self-ensemble method to automatically extract the initial cluster centers and merge the fragmented clusters. Experimental results demonstrate that compared with other comparative algorithms, the proposed DADC algorithm can obtain more reasonable clustering results on data with VDD, ED and MDDM features. Benefitting from a few parameter requirement and non-iterative nature, DADC achieves low computational complexity and is suitable for large-scale data clustering. Numerous clustering algorithms have been proposed, including the partitioning-based, hierarchical-based, density-based, grid-based, model-based, and density-peak-based methods [3-6]. Among them, density-based methods (e.g., DBSCAN, CLIQUE, and OPTICS) can effectively discover clusters of arbitrary shape using the density connectivity of clusters, and do not require a predefined number of clusters [6]. In recent years, Density-Peak-based Clustering (DPC) algorithms, as a branch of density-based clustering, were introduced in [7, 8], assuming that the cluster centers are surrounded by low-density neighbors and can be detected by efficiently searching for local density peaks. Benefitting from few parameter requirements and non-iterative nature, DPC algorithms can efficiently detect clusters of arbitrarily shape from large-scale datasets with low computational complexity . However, as shown in Figure 1, DPC algorithms have limited clustering effect on data with varying density distribution (VDD), multiple domain-density maximums (MDDM), or equilibrium distribution (ED).

Because deep neural networks (DNNs) rely on a large number of parameters and computations, their implementation in energy-constrained systems is challenging. In this paper, we investigate the solution of reducing the supply voltage of the memories used in the system, which results in bit-cell faults. We explore the robustness of state-of-the-art DNN architectures towards such defects and propose a regularizer meant to mitigate their effects on accuracy. Our experiments clearly demonstrate the interest of operating the system in a faulty regime to save energy without reducing accuracy.

Multivariate time series (MTS) forecasting is widely used in various domains, such as meteorology and traffic. Due to limitations on data collection, transmission, and storage, real-world MTS data usually contains missing values, making it infeasible to apply existing MTS forecasting models such as linear regression and recurrent neural networks. Though many efforts have been devoted to this problem, most of them solely rely on local dependencies for imputing missing values, which ignores global temporal dynamics. Local dependencies/patterns would become less useful when the missing ratio is high, or the data have consecutive missing values; while exploring global patterns can alleviate such problem. Thus, jointly modeling local and global temporal dynamics is very promising for MTS forecasting with missing values. However, work in this direction is rather limited. Therefore, we study a novel problem of MTS forecasting with missing values by jointly exploring local and global temporal dynamics. We propose a new framework LGnet, which leverages memory network to explore global patterns given estimations from local perspectives. We further introduce adversarial training to enhance the modeling of global temporal distribution. Experimental results on real-world datasets show the effectiveness of LGnet for MTS forecasting with missing values and its robustness under various missing ratios. Introduction Multivariate time series (MTS) forecasting is widely used in many applications such as weather forecasting (Xingjian et al. 2015), clinical diagnosis (Che et al. 2018), sales forecasting (Wu et al. 2018; Wu et al. 2019) and traffic analysis (Y ao et al. 2019b; Y ao et al. 2018; Y ao et al. 2019a; Tang et al. 2019).