On the fast convergence of random perturbations of the gradient flow

We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the perturbed gradient flow converges to the neighborhood of local minimizers in $O(\ln (\varepsilon^{-1}))$ time on the average, where $\varepsilon$ is the scale of the random perturbation. Under a change of time scale, this indicates that for the diffusion process that approximates the stochastic gradient method, it takes (up to logarithmic factor) only a linear time of inverse stepsize to evade from all saddle points. This can be regarded as a manifestation of fast convergence of the discrete-time stochastic gradient method, the latter being used heavily in modern statistical machine learning.Comment: Revise and Resubmit at Asymptotic Analysi

Weakly-supervised Caricature Face Parsing through Domain Adaptation

A caricature is an artistic form of a person's picture in which certain striking characteristics are abstracted or exaggerated in order to create a humor or sarcasm effect. For numerous caricature related applications such as attribute recognition and caricature editing, face parsing is an essential pre-processing step that provides a complete facial structure understanding. However, current state-of-the-art face parsing methods require large amounts of labeled data on the pixel-level and such process for caricature is tedious and labor-intensive. For real photos, there are numerous labeled datasets for face parsing. Thus, we formulate caricature face parsing as a domain adaptation problem, where real photos play the role of the source domain, adapting to the target caricatures. Specifically, we first leverage a spatial transformer based network to enable shape domain shifts. A feed-forward style transfer network is then utilized to capture texture-level domain gaps. With these two steps, we synthesize face caricatures from real photos, and thus we can use parsing ground truths of the original photos to learn the parsing model. Experimental results on the synthetic and real caricatures demonstrate the effectiveness of the proposed domain adaptation algorithm. Code is available at: https://github.com/ZJULearning/CariFaceParsing .Comment: Accepted in ICIP 2019, code and model are available at https://github.com/ZJULearning/CariFaceParsin

Short-Term Traffic Forecasting Using High-Resolution Traffic Data

This paper develops a data-driven toolkit for traffic forecasting using high-resolution (a.k.a. event-based) traffic data. This is the raw data obtained from fixed sensors in urban roads. Time series of such raw data exhibit heavy fluctuations from one time step to the next (typically on the order of 0.1-1 second). Short-term forecasts (10-30 seconds into the future) of traffic conditions are critical for traffic operations applications (e.g., adaptive signal control). But traffic forecasting tools in the literature deal predominantly with 3-5 minute aggregated data, where the typical signal cycle is on the order of 2 minutes. This renders such forecasts useless at the operations level. To this end, we model the traffic forecasting problem as a matrix completion problem, where the forecasting inputs are mapped to a higher dimensional space using kernels. The formulation allows us to capture both nonlinear dependencies between forecasting inputs and outputs but also allows us to capture dependencies among the inputs. These dependencies correspond to correlations between different locations in the network. We further employ adaptive boosting to enhance the training accuracy and capture historical patterns in the data. The performance of the proposed methods is verified using high-resolution data obtained from a real-world traffic network in Abu Dhabi, UAE. Our experimental results show that the proposed method outperforms other state-of-the-art algorithms

Joint Control of Manufacturing and Onsite Microgrid System Via Novel Neural-Network Integrated Reinforcement Learning Algorithms

Microgrid is a promising technology of distributed energy supply system, which consists of storage devices, generation capacities including renewable sources, and controllable loads. It has been widely investigated and applied for residential and commercial end-use customers as well as critical facilities. In this paper, we propose a joint state-based dynamic control model on microgrids and manufacturing systems where optimal controls for both sides are implemented to coordinate the energy demand and supply so that the overall production cost can be minimized considering the constraint of production target. Markov Decision Process (MDP) is used to formulate the decision-making procedure. The main computing challenge to solve the formulated MDP lies in the co-existence of both discrete and continuous parts of the high-dimensional state/action space that are intertwined with constraints. A novel reinforcement learning algorithm that leverages both Temporal Difference (TD) and Deterministic Policy Gradient (DPG) algorithms is proposed to address the computation challenge. Experiments for a manufacturing system with an onsite microgrid system with renewable sources have been implemented to justify the effectiveness of the proposed method

Spectral co-Clustering in Rank-deficient Multi-layer Stochastic co-Block Models

Modern network analysis often involves multi-layer network data in which the nodes are aligned, and the edges on each layer represent one of the multiple relations among the nodes. Current literature on multi-layer network data is mostly limited to undirected relations. However, direct relations are more common and may introduce extra information. In this paper, we study the community detection (or clustering) in multi-layer directed networks. To take into account the asymmetry, we develop a novel spectral-co-clustering-based algorithm to detect co-clusters, which capture the sending patterns and receiving patterns of nodes, respectively. Specifically, we compute the eigen-decomposition of the debiased sum of Gram matrices over the layer-wise adjacency matrices, followed by the k-means, where the sum of Gram matrices is used to avoid possible cancellation of clusters caused by direct summation. We provide theoretical analysis of the algorithm under the multi-layer stochastic co-block model, where we relax the common assumption that the cluster number is coupled with the rank of the model. After a systematic analysis of the eigen-vectors of population version algorithm, we derive the misclassification rates which show that multi-layers would bring benefit to the clustering performance. The experimental results of simulated data corroborate the theoretical predictions, and the analysis of a real-world trade network dataset provides interpretable results

Underlying burning resistant mechanisms for titanium alloy

The "titanium fire" as produced during high pressure and friction is the major failure scenario for aero-engines. To alleviate this issue, Ti-V-Cr and Ti-Cu-Al series burn resistant titanium alloys have been developed. However, which burn resistant alloy exhibit better property with reasonable cost needs to be evaluated. This work unveils the burning mechanisms of these alloys and discusses whether burn resistance of Cr and V can be replaced by Cu, on which thorough exploration is lacking. Two representative burn resistant alloys are considered, including Ti14(Ti-13Cu-1Al-0.2Si) and Ti40(Ti-25V-15Cr-0.2Si)alloys. Compared with the commercial non-burn resistant titanium alloy, i.e., TC4(Ti-6Al-4V)alloy, it has been found that both Ti14 and Ti40 alloys form "protective" shields during the burning process. Specifically, for Ti14 alloy, a clear Cu-rich layer is formed at the interface between burning product zone and heat affected zone, which consumes oxygen by producing Cu-O compounds and impedes the reaction with Ti-matrix. This work has established a fundamental understanding of burning resistant mechanisms for titanium alloys. Importantly, it is found that Cu could endow titanium alloys with similar burn resistant capability as that of V or Cr, which opens a cost-effective avenue to design burn resistant titanium alloys.Comment: 6 figure

Congestion pricing by priority auction

This paper analyzes a communication network facing users with a continuous distribution of delay cost per unit time. Priority queueing is often used as a way to provide differential services for users with different delay sensitivities. Delay is a key dimension of network service quality, so priority is a valuable resource which is limited and should to be optimally allocated. We investigate the allocation of priority in queues via a simple bidding mechanism. In our mechanism, arriving users can decide not to enter the network at all or submit an announced delay sensitive value. User entering the network obtains priority over all users who make lower bids, and is charged by a payment function which is designed following an exclusion compensation principle. The payment function is proved to be incentive compatible, so the equilibrium bidding behavior leads to the implementation of "cµ-rule". Social warfare or revenue maximizing by appropriately setting the reserve payment is also analyzed

An adaptive scheduling scheme for fair bandwidth allocation

Class-based service differentiation is provided in DiffServ networks. However, this differentiation will be disordered under dynamic traffic loads due to the fixed weighted scheduling. An adaptive weighted scheduling scheme is proposed in this paper to achieve fair bandwidth allocation among different service classes. In this scheme, the number of active flows and the subscribed bandwidth are estimated based on the measurement of local queue metrics, then the scheduling weights of each service class are adjusted for the per-flow fairness of excess bandwidth allocation. This adaptive scheme can be combined with any weighted scheduling algorithm. Simulation results show that, comparing with fixed weighted scheduling, it effectively improve the fairness of excess bandwidth allocation