Under any Multiclass Classification (MCC) setting defined by a collection of labeled point-cloud specified by a feature-set, we extract only stochastic partial orderings from all possible triplets of point-cloud without explicitly measuring the three cloud-to-cloud distances. We demonstrate that such a collective of partial ordering can efficiently compute a label embedding tree geometry on the Label-space. This tree in turn gives rise to a predictive graph, or a network with precisely weighted linkages. Such two multiscale geometries are taken as the coarse scale information content of MCC. They indeed jointly shed lights on explainable knowledge on why and how labeling comes about and facilitates error-free prediction with potential multiple candidate labels supported by data. For revealing within-label heterogeneity, we further undergo labeling naturally found clusters within each point-cloud, and likewise derive multiscale geometry as its fine-scale information content contained in data. This fine-scale endeavor shows that our computational proposal is indeed scalable to a MCC setting having a large label-space. Overall the computed multiscale collective of data-driven patterns and knowledge will serve as a basis for constructing visible and explainable subject matter intelligence regarding the system of interest.

Recurrent Neural Networks (RNNs) have been widely used in sequence analysis and modeling. However, when processing high-dimensional data, RNNs typically require very large model sizes, thereby bringing a series of deployment challenges. Although the state-of-the-art tensor decomposition approaches can provide good model compression performance, these existing methods are still suffering some inherent limitations, such as restricted representation capability and insufficient model complexity reduction. To overcome these limitations, in this paper we propose to develop compact RNN models using Hierarchical Tucker (HT) decomposition. HT decomposition brings strong hierarchical structure to the decomposed RNN models, which is very useful and important for enhancing the representation capability. Meanwhile, HT decomposition provides higher storage and computational cost reduction than the existing tensor decomposition approaches for RNN compression. Our experimental results show that, compared with the state-of-the-art compressed RNN models, such as TT-LSTM, TR-LSTM and BT-LSTM, our proposed HT-based LSTM (HT-LSTM), consistently achieves simultaneous and significant increases in both compression ratio and test accuracy on different datasets.

State-of-the-art machine learning frameworks support a wide variety of design features to enable a flexible machine learning programming interface and to ease the programmability burden on machine learning developers. Identifying and using a performance-optimal setting in feature-rich frameworks, however, involves a non-trivial amount of performance characterization and domain-specific knowledge. This paper takes a deep dive into analyzing the performance impact of key design features and the role of parallelism. The observations and insights distill into a simple set of guidelines that one can use to achieve much higher training and inference speedup. The evaluation results show that our proposed performance tuning guidelines outperform both the Intel and TensorFlow recommended settings by 1.29x and 1.34x, respectively, across a diverse set of real-world deep learning models.

Unmanned aerial vehicles (UAVs) are envisioned to complement the 5G communication infrastructure in future smart cities. Hot spots easily appear in road intersections, where effective communication among vehicles is challenging. UAVs may serve as relays with the advantages of low price, easy deployment, line-of-sight links, and flexible mobility. In this paper, we study a UAV-assisted vehicular network where the UAV jointly adjusts its transmission power and bandwidth allocation under 3D flight to maximize the total throughput. First, we formulate a Markov Decision Process (MDP) problem by modeling the mobility of vehicles and the state transitions caused by the UAV's 3D flight. Secondly, we solve the target problem using a deep reinforcement learning method, namely, the deep deterministic policy gradient, and propose three solutions with different control objectives. Thirdly, in a simplified model with small state and action spaces, we verify the optimality of proposed algorithms. Comparing with two baseline schemes, we demonstrate the effectiveness of proposed algorithms in a realistic model.

Mobile edge computing (MEC) emerges recently as a promising solution to relieve resource-limited mobile devices from computation-intensive tasks, which enables devices to offload workloads to nearby MEC servers and improve the quality of computation experience. Nevertheless, by considering an MEC system consisting of multiple mobile users with stochastic task arrivals and wireless channels in this paper, the design of computation offloading policies is challenging to minimize the long-term average computation cost in terms of power consumption and buffering delay. A deep reinforcement learning (DRL) based decentralized dynamic computation offloading strategy is investigated to build a scalable MEC system with limited feedback. Specifically, a continuous action space based DRL approach named deep deterministic policy gradient (DDPG) is adopted to learn efficient computation offloading policies independently at each mobile user. Thus, powers of both local execution and task offloading can be adaptively allocated by the learned policies from each user's local observation of the MEC system. Numerical results are illustrated to demonstrate that efficient policies can be learned at each user, and performance of the proposed DDPG based decentralized strategy outperforms the conventional deep Q-network (DQN) based discrete power control strategy and some other greedy strategies with reduced computation cost. Besides, the power-delay tradeoff is also analyzed for both the DDPG based and DQN based strategies.

Early detection of cyber-attacks is crucial for a safe and reliable operation of the smart grid. In the literature, outlier detection schemes making sample-by-sample decisions and online detection schemes requiring perfect attack models have been proposed. In this paper, we formulate the online attack/anomaly detection problem as a partially observable Markov decision process (POMDP) problem and propose a universal robust online detection algorithm using the framework of model-free reinforcement learning (RL) for POMDPs. Numerical studies illustrate the effectiveness of the proposed RL-based algorithm in timely and accurate detection of cyber-attacks targeting the smart grid.

Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of nuclear norms of matricizations of a tensor has been shown to be very efficient in recovering a low-Tucker-rank sampled tensor. In this paper, we propose to recover a low-TT-rank sampled tensor by minimizing a weighted sum of nuclear norms of unfoldings of the tensor. We provide numerical results to show that our proposed method requires significantly less number of samples to recover to the original tensor in comparison with simply minimizing the sum of nuclear norms since the structure of the unfoldings in the TT tensor model is fundamentally different from that of matricizations in the Tucker tensor model.

Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we aim to approximate the unknown rank based on the location of sampled entries and some given completion. We consider a number of data models, including single-view matrix, multi-view matrix, CP tensor, tensor-train tensor and Tucker tensor. For each of these data models, we provide an upper bound on the rank when an arbitrary low-rank completion is given. We characterize these bounds both deterministically, i.e., with probability one given that the sampling pattern satisfies certain combinatorial properties, and probabilistically, i.e., with high probability given that the sampling probability is above some threshold. Moreover, for both single-view matrix and CP tensor, we are able to show that the obtained upper bound is exactly equal to the unknown rank if the lowest-rank completion is given. Furthermore, we provide numerical experiments for the case of single-view matrix, where we use nuclear norm minimization to find a low-rank completion of the sampled data and we observe that in most of the cases the proposed upper bound on the rank is equal to the true rank.

We consider the problem of low canonical polyadic (CP) rank tensor completion. A completion is a tensor whose entries agree with the observed entries and its rank matches the given CP rank. We analyze the manifold structure corresponding to the tensors with the given rank and define a set of polynomials based on the sampling pattern and CP decomposition. Then, we show that finite completability of the sampled tensor is equivalent to having a certain number of algebraically independent polynomials among the defined polynomials. Our proposed approach results in characterizing the maximum number of algebraically independent polynomials in terms of a simple geometric structure of the sampling pattern, and therefore we obtain the deterministic necessary and sufficient condition on the sampling pattern for finite completability of the sampled tensor. Moreover, assuming that the entries of the tensor are sampled independently with probability $p$ and using the mentioned deterministic analysis, we propose a combinatorial method to derive a lower bound on the sampling probability $p$, or equivalently, the number of sampled entries that guarantees finite completability with high probability. We also show that the existing result for the matrix completion problem can be used to obtain a loose lower bound on the sampling probability $p$. In addition, we obtain deterministic and probabilistic conditions for unique completability. It is seen that the number of samples required for finite or unique completability obtained by the proposed analysis on the CP manifold is orders-of-magnitude lower than that is obtained by the existing analysis on the Grassmannian manifold.

In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the deterministic necessary and sufficient conditions on the locations of the samples to ensure finite completability. Specifically, we propose an algebraic geometric analysis on the TT manifold that can incorporate the whole rank vector simultaneously in contrast to the existing approach based on the Grassmannian manifold that can only incorporate one rank component. Our proposed technique characterizes the algebraic independence of a set of polynomials defined based on the sampling pattern and the TT decomposition, which is instrumental to obtaining the deterministic condition on the sampling pattern for finite completability. In addition, based on the proposed analysis, assuming that the entries of the tensor are sampled independently with probability $p$, we derive a lower bound on the sampling probability $p$, or equivalently, the number of sampled entries that ensures finite completability with high probability. Moreover, we also provide the deterministic and probabilistic conditions for unique completability.