Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs without requiring explicit prior knowledge. However, since existing DMD algorithms are in principle formulated based on the concatenation of scalar observables, it is not directly applicable to data with dependent structures among observables, which take, for example, the form of a sequence of graphs. In this paper, we formulate Koopman spectral analysis for NLDSs with structures among observables and propose an estimation algorithm for this problem. This method can extract and visualize the underlying low-dimensional global dynamics of NLDSs with structures among observables from data, which can be useful in understanding the underlying dynamics of such NLDSs. To this end, we first formulate the problem of estimating spectra of the Koopman operator defined in vector-valued reproducing kernel Hilbert spaces, and then develop an estimation procedure for this problem by reformulating tensor-based DMD. As a special case of our method, we propose the method named as Graph DMD, which is a numerical algorithm for Koopman spectral analysis of graph dynamical systems, using a sequence of adjacency matrices. We investigate the empirical performance of our method by using synthetic and real-world data.

Stochastic momentum methods have been widely adopted in training deep neural networks. However, their theoretical analysis of convergence of the training objective and the generalization error for prediction is still under-explored. This paper aims to bridge the gap between practice and theory by analyzing the stochastic gradient (SG) method, and the stochastic momentum methods including two famous variants, i.e., the stochastic heavy-ball (SHB) method and the stochastic variant of Nesterov's accelerated gradient (SNAG) method. We propose a framework that unifies the three variants. We then derive the convergence rates of the norm of gradient for the non-convex optimization problem, and analyze the generalization performance through the uniform stability approach. Particularly, the convergence analysis of the training objective exhibits that SHB and SNAG have no advantage over SG. However, the stability analysis shows that the momentum term can improve the stability of the learned model and hence improve the generalization performance. These theoretical insights verify the common wisdom and are also corroborated by our empirical analysis on deep learning.

For any autonomous driving vehicle, control module determines its road performance and safety, i.e. its precision and stability should stay within a carefully-designed range. Nonetheless, control algorithms require vehicle dynamics (such as longitudinal dynamics) as inputs, which, unfortunately, are obscure to calibrate in real time. As a result, to achieve reasonable performance, most, if not all, research-oriented autonomous vehicles do manual calibrations in a one-by-one fashion. Since manual calibration is not sustainable once entering into mass production stage for industrial purposes, we here introduce a machine-learning based auto-calibration system for autonomous driving vehicles. In this paper, we will show how we build a data-driven longitudinal calibration procedure using machine learning techniques. We first generated offline calibration tables from human driving data. The offline table serves as an initial guess for later uses and it only needs twenty-minutes data collection and process. We then used an online-learning algorithm to appropriately update the initial table (the offline table) based on real-time performance analysis. This longitudinal auto-calibration system has been deployed to more than one hundred Baidu Apollo self-driving vehicles (including hybrid family vehicles and electronic delivery-only vehicles) since April 2018. By August 27, 2018, it had been tested for more than two thousands hours, ten thousands kilometers (6,213 miles) and yet proven to be effective.

Rather than programming, training allows robots to achieve behaviors that generalize better and are capable to respond to real-world needs. However, such training requires a big amount of experimentation which is not always feasible for a physical robot. In this work, we present robot_gym, a framework to accelerate robot training through simulation in the cloud that makes use of roboticists' tools, simplifying the development and deployment processes on real robots. We unveil that, for simple tasks, simple 3DoF robots require more than 140 attempts to learn. For more complex, 6DoF robots, the number of attempts increases to more than 900 for the same task. We demonstrate that our framework, for simple tasks, accelerates the robot training time by more than 33% while maintaining similar levels of accuracy and repeatability.

It has been argued that it is much easier to convey logical statements using rules rather than OWL (or description logic (DL)) axioms. Based on recent theoretical developments on transformations between rules and DLs, we have developed ROWLTab, a Protege plugin that allows users to enter OWL axioms by way of rules; the plugin then automatically converts these rules into OWL 2 DL axioms if possible, and prompts the user in case such a conversion is not possible without weakening the semantics of the rule. In this paper, we present ROWLTab, together with a user evaluation of its effectiveness compared to entering axioms using the standard Protege interface. Our evaluation shows that modeling with ROWLTab is much quicker than the standard interface, while at the same time, also less prone to errors for hard modeling tasks.

Embeddings of tree-like graphs in hyperbolic space were recently shown to surpass their Euclidean counterparts in performance by a large margin. Inspired by these results, we present an algorithm for learning word embeddings in hyperbolic space from free text. An objective function based on the hyperbolic distance is derived and included in the skip-gram architecture from word2vec. The hyperbolic word embeddings are then evaluated on word similarity and analogy benchmarks. The results demonstrate the potential of hyperbolic word embeddings, particularly in low dimensions, though without clear superiority over their Euclidean counterparts. We further discuss problems in the formulation of the analogy task resulting from the curvature of hyperbolic space.

Multi-hop reasoning is an effective approach for query answering (QA) over incomplete knowledge graphs (KGs). The problem can be formulated in a reinforcement learning (RL) setup, where a policy-based agent sequentially extends its inference path until it reaches a target. However, in an incomplete KG environment, the agent receives low-quality rewards corrupted by false negatives in the training data, which harms generalization at test time. Furthermore, since no golden action sequence is used for training, the agent can be misled by spurious search trajectories that incidentally lead to the correct answer. We propose two modeling advances to address both issues: (1) we reduce the impact of false negative supervision by adopting a pretrained one-hop embedding model to estimate the reward of unobserved facts; (2) we counter the sensitivity to spurious paths of on-policy RL by forcing the agent to explore a diverse set of paths using randomly generated edge masks. Our approach significantly improves over existing path-based KGQA models on several benchmark datasets and is comparable or better than embedding-based models.

We introduce a new virtual environment for simulating a card game known as "Big 2". This is a four-player game of imperfect information with a relatively complicated action space (being allowed to play 1,2,3,4 or 5 card combinations from an initial starting hand of 13 cards). As such it poses a challenge for many current reinforcement learning methods. We then use the recently proposed "Proximal Policy Optimization" algorithm to train a deep neural network to play the game, purely learning via self-play, and find that it is able to reach a level which outperforms amateur human players after only a relatively short amount of training time and without needing to search a tree of future game states.

Hybrid Bayesian networks have received an increasing attention during the last years. The difference with respect to standard Bayesian networks is that they can host discrete and continuous variables simultaneously, which extends the applicability of the Bayesian network framework in general. However, this extra feature also comes at a cost: inference in these types of models is computationally more challenging and the underlying models and updating procedures may not even support closed-form solutions. In this paper we provide an overview of the main trends and principled approaches for performing inference in hybrid Bayesian networks. The methods covered in the paper are organized and discussed according to their methodological basis. We consider how the methods have been extended and adapted to also include (hybrid) dynamic Bayesian networks, and we end with an overview of established software systems supporting inference in these types of models.

A Justice Ministry statement said Wednesday that after an almost yearlong investigation the State Attorney's office summoned top Aeronautics Ltd. officials, including its chief executive, for a hearing pending indictment.