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Hua Liu

Publications and source records attributed to Hua Liu.

29 records · Page 2Linked to original sources
arXiv2021

Functional L-Optimality Subsampling for Massive Data

Massive data bring the big challenges of memory and computation for analysis. These challenges can be tackled by taking subsamples from the full data as a surrogate. For functional data, it is common to collect multiple measurements over their domains, which require even more memory and computation time when the sample size is large. The computation would be much more intensive when statistical inference is required through bootstrap samples. To the best of our knowledge, this article is the first attempt to study the subsampling method for the functional linear model. We propose an optimal subsampling method based on the functional L-optimality criterion. When the response is a discrete or categorical variable, we further extend our proposed functional L-optimality subsampling (FLoS) method to the functional generalized linear model. We establish the asymptotic properties of the estimators by the FLoS method. The finite sample performance of our proposed FLoS method is investigated by extensive simulation studies. The FLoS method is further demonstrated by analyzing two large-scale datasets: the global climate data and the kidney transplant data. The analysis results on these data show that the FLoS method is much better than the uniform subsampling approach and can well approximate the results based on the full data while dramatically reducing the computation time and memory.

stat.ME↗
arXiv2021

Elastic Graph Neural Networks

While many existing graph neural networks (GNNs) have been proven to perform $\ell_2$-based graph smoothing that enforces smoothness globally, in this work we aim to further enhance the local smoothness adaptivity of GNNs via $\ell_1$-based graph smoothing. As a result, we introduce a family of GNNs (Elastic GNNs) based on $\ell_1$ and $\ell_2$-based graph smoothing. In particular, we propose a novel and general message passing scheme into GNNs. This message passing algorithm is not only friendly to back-propagation training but also achieves the desired smoothing properties with a theoretical convergence guarantee. Experiments on semi-supervised learning tasks demonstrate that the proposed Elastic GNNs obtain better adaptivity on benchmark datasets and are significantly robust to graph adversarial attacks. The implementation of Elastic GNNs is available at \url{https://github.com/lxiaorui/ElasticGNN}.

cs.LG↗
arXiv2021

A Game-theoretical Approach to Analyze Film Release Time

Film release dates play an important part in box office revenues because of the facts of obvious seasonality demand in the film industry and severe competition among films shown at the same time. In this paper, we study how film studios choose release time for movies they produce to maximize their box offices. We first formalize this problem as an attraction competition game where players (film studios) consider both potential profits and competitors' choices when deciding the release time. Then we prove that there always exists a pure Nash equilibrium and give the sufficient condition of the uniqueness of the Nash equilibrium. Our model can be generalized to an extensive game and we compute the subgame-perfect equilibrium for homogeneous players. For the case that one film studio could have multiple movies to release, we prove that finding a player's best response is NP-hard and it does not guarantee the existence of a pure Nash equilibrium. Experiments are provided to support the soundness of our model. In the final state, most of film studios, accounting for 84 percent of the market, would not change their release time. The behaviors of film studios imply they are following some strategies to reach a Nash equilibrium.

cs.GT↗
arXiv2019

Omni SCADA Intrusion Detection Using Deep Learning Algorithms

We investigate deep learning based omni intrusion detection system (IDS) for supervisory control and data acquisition (SCADA) networks that are capable of detecting both temporally uncorrelated and correlated attacks. Regarding the IDSs developed in this paper, a feedforward neural network (FNN) can detect temporally uncorrelated attacks at an {F$_{1}$} of {99.967${\pm}$0.005\%} but correlated attacks as low as {58${\pm}$2\%}. In contrast, long-short term memory (LSTM) detects correlated attacks at {99.56${\pm}$0.01\%} while uncorrelated attacks at {99.3${\pm}$0.1\%}. Combining LSTM and FNN through an ensemble approach further improves the IDS performance with {F$_{1}$} of {99.68${\pm}$0.04\%} regardless the temporal correlations among the data packets.

eess.SY↗
arXiv2017

Hilbert Transformation and $r\mathrm{Spin}(n)+\mathbb{R}^n$ Group

In this paper we study symmetry properties of the Hilbert transformation of several real variables in the Clifford algebra setting. In order to describe the symmetry properties we introduce the group $r\mathrm{Spin}(n)+\mathbb{R}^n, r>0,$ which is essentially an extension of the ax+b group. The study concludes that the Hilbert transformation has certain characteristic symmetry properties in terms of $r\mathrm{Spin}(n)+\mathbb{R}^n.$ In the present paper, for $n=2$ and $3$ we obtain, explicitly, the induced spinor representations of the $r\mathrm{Spin}(n)+\mathbb{R}^n$ group. Then we decompose the natural representation of $r\mathrm{Spin}(n)+\mathbb{R}^n$ into the direct sum of some two irreducible spinor representations, by which we characterize the Hilbert transformation in $\mathbb{R}^3$ and $\mathbb{R}^2.$ Precisely, we show that a nontrivial skew operator is the Hilbert transformation if and only if it is invariant under the action of the $r\mathrm{Spin}(n)+\mathbb{R}^n, n=2,3,$ group.

math.CV↗
arXiv2017

Hilbert Transformation and Representation of ax+b Group

In this paper we study the Hilbert transformations over $L^2(\mathbb{R})$ and $L^2(\mathbb{T})$ from the viewpoint of symmetry. For a linear operator over $L^2(\mathbb{R})$ commutative with the ax+b group we show that the operator is of the form $λI+ηH, $ where $I$ and $H$ are the identity operator and Hilbert transformation respectively, and $λ,η$ are complex numbers. In the related literature this result was proved through first invoking the boundedness result of the operator, proved though a big machinery. In our setting the boundedness is a consequence of the boundedness of the Hilbert transformation. The methodology that we use is Gelfand-Naimark's representation of the ax+b group. Furthermore we prove a similar result on the unit circle. Although there does not exist a group like ax+b on the unit circle, we construct a semigroup to play the same symmetry role for the Hilbert transformations over the circle $L^2(\mathbb{T}).$

math.CV↗
arXiv2017

On Convergence Sets of Power Series with Holomorphic Coefficients

We consider convergence sets of formal power series of the form $f(z,t)=\sum_{n=0}^{\infty} f_n(z)t^n$, where $f_n(z)$ are holomorphic functions on a domain $Ω$ in $\mathbb{C}$. A subset $E$ of $Ω$ is said to be a convergence set in $Ω$ if there is a series $f(z,t)$ such that $E$ is exactly the set of points $z$ for which $f(z,t)$ converges as a power series in a single variable $t$ in some neighborhood of the origin. A $σ$-convex set is defined to be the union of a countable collection of polynomially convex compact subsets. We prove that a subset of $\mathbb{C}$ is a convergence set if and only if it is $σ$-convex.

math.CV↗
arXiv2016

Derivation of Fokker-Planck equations for stochastic dynamical systems under excitation of multiplicative non-Gaussian white noise

Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and play an important role in quantifying propagation and evolution of uncertainty. Although Fokker-Planck equations can be written explicitly for nonlinear dynamical systems excited by Gaussian white noise, they are not available in general for nonlinear dynamical systems excited by multiplicative non-Gaussian white noise. Marcus stochastic differential equations are often appropriate models in engineering and physics for stochastic dynamical systems excited by non-Gaussian white noise. In this paper, we derive explicit forms of Fokker-Planck equations for one dimensional systems modeled by Marcus stochastic differential equations under multiplicative non-Gaussian white noise. As examples to illustrate the theoretical results, the derived formula is used to obtain Fokker-Plank equations for nonlinear dynamical systems under excitation of (i) $α$-stable white noise; (ii) combined Gaussian and Poisson white noise, respectively.

math.DS↗
arXiv2012

Negative differential spin conductance in doped zigzag graphene nanoribbons

The spin dependent charge transport in zigzag graphene nanoribbons (ZGNRs) has been investigated by the nonequilibrium Green's function method combined with the density functional theory at the local spin density approximation. The current versus voltage curve shows distinguished behaviors for symmetric and asymmetric ZGNRs and the doping on the ZGNR edges can manipulate the spin transport. In special cases that a Be atom is substitutionally doped on one edge of the symmetric ZGNRs, one spin current shows negative differential resistance while the other increases monotonically with the bias. This property might be used to design spin oscillators or other devices for spintronics.

cond-mat.mes-hall↗
arXiv2011

A Packet Dropping Mechanism for Efficient Operation of M/M/1 Queues with Selfish Users

We consider a fundamental game theoretic problem concerning selfish users contributing packets to an M/M/1 queue. In this game, each user controls its own input rate so as to optimize a desired tradeoff between throughput and delay. We first show that the original game has an inefficient Nash Equilibrium (NE), with a Price of Anarchy (PoA) that scales linearly or worse in the number of users. In order to improve the outcome efficiency, we propose an easily implementable mechanism design whereby the server randomly drops packets with a probability that is a function of the total arrival rate. We show that this results in a modified M/M/1 queueing game that is an ordinal potential game with at least one NE. In particular, for a linear packet dropping function, which is similar to the Random Early Detection (RED) algorithm used in Internet Congestion Control, we prove that there is a unique NE. We also show that the simple best response dynamic converges to this unique equilibrium. Finally, for this scheme, we prove that the social welfare (expressed either as the summation of utilities of all players, or as the summation of the logarithm of utilities of all players) at the equilibrium point can be arbitrarily close to the social welfare at the global optimal point, i.e. the PoA can be made arbitrarily close to 1. We also study the impact of arrival rate estimation error on the PoA through simulations.

cs.GT↗