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Yuan Gao

Publications and source records attributed to Yuan Gao.

At least 505 records · Page 28Linked to original sources
arXiv2019

Fast Adaptation with Meta-Reinforcement Learning for Trust Modelling in Human-Robot Interaction

In socially assistive robotics, an important research area is the development of adaptation techniques and their effect on human-robot interaction. We present a meta-learning based policy gradient method for addressing the problem of adaptation in human-robot interaction and also investigate its role as a mechanism for trust modelling. By building an escape room scenario in mixed reality with a robot, we test our hypothesis that bi-directional trust can be influenced by different adaptation algorithms. We found that our proposed model increased the perceived trustworthiness of the robot and influenced the dynamics of gaining human's trust. Additionally, participants evaluated that the robot perceived them as more trustworthy during the interactions with the meta-learning based adaptation compared to the previously studied statistical adaptation model.

cs.RO↗
arXiv2019

Mathematical validation of the Peierls--Nabarro model for edge dislocations

In this paper, we perform mathematical validation of the Peierls--Nabarro (PN) models, which are multiscale models of dislocations that incorporate the detailed dislocation core structure. We focus on the static and dynamic PN models of an edge dislocation. In a PN model, the total energy includes the elastic energy in the two half-space continua and a nonlinear potential energy across the slip plane, which is always infinite. We rigorously establish the relationship between the PN model in the full space and the reduced problem on the slip plane in terms of both governing equations and energy variations. The shear displacement jump is determined only by the reduced problem on the slip plane while the displacement fields in the two half spaces are determined by linear elasticity. We establish the existence and sharp regularities of classical solutions in Hilbert space. For both the reduced problem and the full PN model, we prove that a static solution is a global minimizer in perturbed sense. We also show that there is a unique classical, global in time solution of the dynamic PN model.

math.AP↗
arXiv2019

Long time behavior of dynamic solution to Peierls--Nabarro dislocation model

In this paper we study the relaxation process of Peierls-Nabarro dislocation model, which is a gradient flow with singular nonlocal energy and double well potential describing how the materials relax to its equilibrium with the presence of a dislocation. We prove the dynamic solution to Peierls-Nabarro model will converge exponentially to a shifted steady profile which is uniquely determined.

math.AP↗
arXiv2019

Variational Properties of Matrix Functions via the Generalized Matrix-Fractional Function

We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which such functions are closed and proper as well as formulas for the ready computation of both their conjugates and subdifferentials. Special attention is given to support and indicator functions. Particular instances yield all weighted Ky Fan norms and squared gauges on $\mathbb R^{n\times m}$, and as an example we show that all variational Gram functions are representable as squares of gauges. Other instances yield weighted sums of the Frobenius and nuclear norms. The scope of applications is large and the range of variational properties and insight is fascinating and fundamental. An important byproduct of these representations is that they lay the foundation for a smoothing approach to many matrix functions on the interior of the domain of the GMF function, which opens the door to a range of unexplored optimization methods.

math.OC↗
arXiv2019

Deep Generative Learning via Variational Gradient Flow

We propose a general framework to learn deep generative models via \textbf{V}ariational \textbf{Gr}adient Fl\textbf{ow} (VGrow) on probability spaces. The evolving distribution that asymptotically converges to the target distribution is governed by a vector field, which is the negative gradient of the first variation of the $f$-divergence between them. We prove that the evolving distribution coincides with the pushforward distribution through the infinitesimal time composition of residual maps that are perturbations of the identity map along the vector field. The vector field depends on the density ratio of the pushforward distribution and the target distribution, which can be consistently learned from a binary classification problem. Connections of our proposed VGrow method with other popular methods, such as VAE, GAN and flow-based methods, have been established in this framework, gaining new insights of deep generative learning. We also evaluated several commonly used divergences, including Kullback-Leibler, Jensen-Shannon, Jeffrey divergences as well as our newly discovered `logD' divergence which serves as the objective function of the logD-trick GAN. Experimental results on benchmark datasets demonstrate that VGrow can generate high-fidelity images in a stable and efficient manner, achieving competitive performance with state-of-the-art GANs.

cs.LG↗
arXiv2019

NDDR-CNN: Layerwise Feature Fusing in Multi-Task CNNs by Neural Discriminative Dimensionality Reduction

In this paper, we propose a novel Convolutional Neural Network (CNN) structure for general-purpose multi-task learning (MTL), which enables automatic feature fusing at every layer from different tasks. This is in contrast with the most widely used MTL CNN structures which empirically or heuristically share features on some specific layers (e.g., share all the features except the last convolutional layer). The proposed layerwise feature fusing scheme is formulated by combining existing CNN components in a novel way, with clear mathematical interpretability as discriminative dimensionality reduction, which is referred to as Neural Discriminative Dimensionality Reduction (NDDR). Specifically, we first concatenate features with the same spatial resolution from different tasks according to their channel dimension. Then, we show that the discriminative dimensionality reduction can be fulfilled by 1x1 Convolution, Batch Normalization, and Weight Decay in one CNN. The use of existing CNN components ensures the end-to-end training and the extensibility of the proposed NDDR layer to various state-of-the-art CNN architectures in a "plug-and-play" manner. The detailed ablation analysis shows that the proposed NDDR layer is easy to train and also robust to different hyperparameters. Experiments on different task sets with various base network architectures demonstrate the promising performance and desirable generalizability of our proposed method. The code of our paper is available at https://github.com/ethanygao/NDDR-CNN.

cs.CV↗
arXiv2019

Wasserstein-Wasserstein Auto-Encoders

To address the challenges in learning deep generative models (e.g.,the blurriness of variational auto-encoder and the instability of training generative adversarial networks, we propose a novel deep generative model, named Wasserstein-Wasserstein auto-encoders (WWAE). We formulate WWAE as minimization of the penalized optimal transport between the target distribution and the generated distribution. By noticing that both the prior $P_Z$ and the aggregated posterior $Q_Z$ of the latent code Z can be well captured by Gaussians, the proposed WWAE utilizes the closed-form of the squared Wasserstein-2 distance for two Gaussians in the optimization process. As a result, WWAE does not suffer from the sampling burden and it is computationally efficient by leveraging the reparameterization trick. Numerical results evaluated on multiple benchmark datasets including MNIST, fashion- MNIST and CelebA show that WWAE learns better latent structures than VAEs and generates samples of better visual quality and higher FID scores than VAEs and GANs.

cs.LG↗
arXiv2019

Global Strong Solution With BV Derivatives to Singular Solid-on-Solid model With Exponential Nonlinearity

In this work, we consider the one dimensional very singular fourth-order equation for solid-on-solid model in attachment-detachment-limit regime with exponential nonlinearity $$h_t = \nabla \cdot (\frac{1}{|\nabla h|} \nabla e^{\frac{δE}{δh}}) =\nabla \cdot (\frac{1}{|\nabla h|}\nabla e^{- \nabla \cdot (\frac{\nabla h}{|\nabla h|})})$$ where total energy $E=\int |\nabla h|$ is the total variation of $h$. Using a logarithmic correction $E=\int |\nabla h|\ln|\nabla h| d x$ and gradient flow structure with a suitable defined functional, we prove the evolution variational inequality solution preserves a positive gradient $h_x$ which has upper and lower bounds but in BV space. We also obtain the global strong solution to the solid-on-solid model which allows an asymmetric singularity $h_{xx}^+$ happens.

math.AP↗
arXiv2018

Solution for Large-Scale Hierarchical Object Detection Datasets with Incomplete Annotation and Data Imbalance

This report demonstrates our solution for the Open Images 2018 Challenge. Based on our detailed analysis on the Open Images Datasets (OID), it is found that there are four typical features: large-scale, hierarchical tag system, severe annotation incompleteness and data imbalance. Considering these characteristics, an amount of strategies are employed, including SNIPER, soft sampling, class-aware sampling (CAS), hierarchical non-maximum suppression (HNMS) and so on. In virtue of these effective strategies, and further using the powerful SENet154 armed with feature pyramid module and deformable ROIalign as the backbone, our best single model could achieve a mAP of 56.9%. After a further ensemble with 9 models, the final mAP is boosted to 62.2% in the public leaderboard (ranked the 2nd place) and 58.6% in the private leaderboard (ranked the 3rd place, slightly inferior to the 1st place by only 0.04 point).

cs.CV↗
arXiv2018

High-dimensional functional time series forecasting: An application to age-specific mortality rates

We address the problem of forecasting high-dimensional functional time series through a two-fold dimension reduction procedure. The difficulty of forecasting high-dimensional functional time series lies in the curse of dimensionality. In this paper, we propose a novel method to solve this problem. Dynamic functional principal component analysis is first applied to reduce each functional time series to a vector. We then use the factor model as a further dimension reduction technique so that only a small number of latent factors are preserved. Classic time series models can be used to forecast the factors and conditional forecasts of the functions can be constructed. Asymptotic properties of the approximated functions are established, including both estimation error and forecast error. The proposed method is easy to implement especially when the dimension of the functional time series is large. We show the superiority of our approach by both simulation studies and an application to Japanese age-specific mortality rates.

stat.ME↗
arXiv2018

Energy Efficient and Fair Resource Allocation for LTE-Unlicensed Uplink Networks: A Two-sided Matching Approach with Partial Information

LTE-Unlicensed (LTE-U) has recently attracted worldwide interest to meet the explosion in cellular traffic data. By using carrier aggregation (CA), licensed and unlicensed bands are integrated to enhance transmission capacity while maintaining reliable and predictable performance. As there may exist other conventional unlicensed band users, such as Wi-Fi users, LTE-U users have to share the same unlicensed bands with them. Thus, an optimized resource allocation scheme to ensure the fairness between LTE-U users and conventional unlicensed band users is critical for the deployment of LTE-U networks. In this paper, we investigate an energy efficient resource allocation problem in LTE-U coexisting with other wireless networks, which aims at guaranteeing fairness among the users of different radio access networks (RANs). We formulate the problem as a multi-objective optimization problem and propose a semi-distributed matching framework with a partial information-based algorithm to solve it. We demonstrate our contributions with simulations in which various network densities and traffic load levels are considered.

cs.IT↗
arXiv2018

Gradient flow approach to an exponential thin film equation: global existence and latent singularity

In this work, we study a fourth order exponential equation, $u_t=Δe^{-Δu},$ derived from thin film growth on crystal surface in multiple space dimensions. We use the gradient flow method in metric space to characterize the latent singularity in global strong solution, which is intrinsic due to high degeneration. We define a suitable functional, which reveals where the singularity happens, and then prove the variational inequality solution under very weak assumptions for initial data. Moreover, the existence of global strong solution is established with regular initial data.

math.AP↗
arXiv2018

A vicinal surface model for epitaxial growth with logarithmic free energy

We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, $u_t = -u^2(u^3+αu)_{hhhh}$, gives the evolution for the surface slope $u$ as a function of the local height $h$ in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. The long time behavior of $u$ converging to a constant that only depends on the initial data is also investigated both analytically and numerically.

math.AP↗
arXiv2018

Functors of wrapped Fukaya categories from Lagrangian correspondences

We study wrapped Floer theory on product Liouville manifolds and prove that the wrapped Fukaya categories defined with respect to two different kinds of natural Hamiltonians and almost complex structures are equivalent. The implication is we can do quilted version of wrapped Floer theory, based on which we then construct functors between wrapped Fukaya categories of Liouville manifolds from certain classes of Lagrangian correspondences, by enlarging the wrapped Fukaya categories appropriately, allowing exact cylindrical Lagrangian immersions. For applications, we present a general Künneth formula, and also identify the Viterbo restriction functor with the functor associated to the completed graph of embedding of a Liouville sub-domain.

math.SG↗
arXiv2018

Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface

In this work we consider $$ w_t=[(w_{hh}+c_0)^{-3}]_{hh},\qquad w(0)=w^0, $$ which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the problem as the gradient flow of a suitably-defined convex functional in a non-reflexive space. Then by restricting it to a Hilbert space and proving the uniqueness of its sub-differential, we can apply the classical maximal monotone operator theory. The mathematical difficulty is due to the fact that $w_{hh}$ can appear as a positive Radon measure. We prove the existence of a global strong solution. In particular, the equation holds almost everywhere when $w_{hh}$ is replaced by its absolutely continuous part.

math.AP↗
arXiv2018

Spoken English Intelligibility Remediation with PocketSphinx Alignment and Feature Extraction Improves Substantially over the State of the Art

We use automatic speech recognition to assess spoken English learner pronunciation based on the authentic intelligibility of the learners' spoken responses determined from support vector machine (SVM) classifier or deep learning neural network model predictions of transcription correctness. Using numeric features produced by PocketSphinx alignment mode and many recognition passes searching for the substitution and deletion of each expected phoneme and insertion of unexpected phonemes in sequence, the SVM models achieve 82 percent agreement with the accuracy of Amazon Mechanical Turk crowdworker transcriptions, up from 75 percent reported by multiple independent researchers. Using such features with SVM classifier probability prediction models can help computer-aided pronunciation teaching (CAPT) systems provide intelligibility remediation.

cs.CL↗
arXiv2017

Multi-Glimpse LSTM with Color-Depth Feature Fusion for Human Detection

With the development of depth cameras such as Kinect and Intel Realsense, RGB-D based human detection receives continuous research attention due to its usage in a variety of applications. In this paper, we propose a new Multi-Glimpse LSTM (MG-LSTM) network, in which multi-scale contextual information is sequentially integrated to promote the human detection performance. Furthermore, we propose a feature fusion strategy based on our MG-LSTM network to better incorporate the RGB and depth information. To the best of our knowledge, this is the first attempt to utilize LSTM structure for RGB-D based human detection. Our method achieves superior performance on two publicly available datasets.

cs.CV↗