arXiv subjects

Kun Chen

Publications and source records attributed to Kun Chen.

At least 163 records · Page 9Linked to original sources

arXiv2018

Boosted Sparse and Low-Rank Tensor Regression

We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both parsimonious and highly interpretable, as it implies that the outcome is related to the features through a few distinct pathways, each of which may only involve subsets of feature dimensions. We take a divide-and-conquer strategy to simplify the task into a set of sparse unit-rank tensor regression problems. To make the computation efficient and scalable, for the unit-rank tensor regression, we propose a stagewise estimation procedure to efficiently trace out its entire solution path. We show that as the step size goes to zero, the stagewise solution paths converge exactly to those of the corresponding regularized regression. The superior performance of our approach is demonstrated on various real-world and synthetic examples.

cs.LG↗

arXiv2018

Even-Odd effect of an Spin-S impurity coupled to a quantum critical system

We discuss an even-odd effect for an impurity with an $N$-fold degenerate internal states immersed in a two-dimensional superfluid--Mott-insulator quantum critical bath, which is described by an spin-$S$ XY Bose-Kondo impurity model with $N=2S+1$. Using a dimensional- and momentum-cut off regularized renormalization group and unbiased large-scale Monte Carlo numerical simulations, we establish the phase diagram for the $S=1$ impurity with all the relevant terms included. We show that the $S=1$ impurity with 3-fold degeneracy is fully screened by the critical bath, in qualitative contrast to the spin-1/2 case where the impurity is only partially screened. We then argue that all impurities with odd 2$S$ share the same universal physics as the spin-1/2 case, and all impurities with even 2$S$ are as the spin-1 case. We validate our conjecture with unbiased Monte Carlo simulations up to $S=2$. A physical consequence of this even-odd effect is that two $N=2$ degenerate impurities in the critical bath form a bound state at a sufficiently low temperature, which can be realized using ultracold atoms in an optical lattice.

cond-mat.quant-gas↗

arXiv2018

Quantized Magnetic Flux and the Magneto-halon Effect in a Critical Superconductor

Employing the standard worldline-vortex mapping, we conclude that at the critical temperature, superconductors demonstrate the magneto-halon effect with respect to the quantized net magnetic flux generated by a solenoid inserted into the system. The effect is a direct counterpart of the recently revealed halon effect in terms of the quantized particle charge of a static impurity in the two-dimensional U(1) quantum-critical environment. The flux-loop model (a.k.a. frozen lattice superconductor) with a quasi-solenoid perturbation proves to be the model of choice for qualitative and quantitative description of both the halon and the magneto-halon effects.

cond-mat.supr-con↗

arXiv2018

Integrative Multi-View Reduced-Rank Regression: Bridging Group-Sparse and Low-Rank Models

Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high dimensionality. It is likely that only a few views are relevant to prediction, and the predictors within each relevant view contribute to the prediction collectively rather than sparsely. We cast this new problem under the familiar multivariate regression framework and propose an integrative reduced-rank regression (iRRR), where each view has its own low-rank coefficient matrix. As such, latent features are extracted from each view in a supervised fashion. For model estimation, we develop a convex composite nuclear norm penalization approach, which admits an efficient algorithm via alternating direction method of multipliers. Extensions to non-Gaussian and incomplete data are discussed. Theoretically, we derive non-asymptotic oracle bounds of iRRR under a restricted eigenvalue condition. Our results recover oracle bounds of several special cases of iRRR including Lasso, group Lasso and nuclear norm penalized regression. Therefore, iRRR seamlessly bridges group-sparse and low-rank methods and can achieve substantially faster convergence rate under realistic settings of multi-view learning. Simulation studies and an application in the Longitudinal Studies of Aging further showcase the efficacy of the proposed methods.

stat.ME↗

arXiv2018

The halon: a quasiparticle featuring critical charge fractionalization

The halon is a special critical state of an impurity in a quantum-critical environment. The hallmark of the halon physics is that a well-defined integer charge gets fractionalized into two parts: a microscopic core with half-integer charge and a critically large halo carrying a complementary charge of $\pm 1/2$. The halon phenomenon emerges when the impurity--environment interaction is fine-tuned to the vicinity of a boundary quantum critical point (BQCP), at which the energies of two quasiparticle states with adjacent integer charges approach each other. The universality class of such BQCP is captured by a model of pseudo-spin-$1/2$ impurity coupled to the quantum-critical environment, in such a way that the rotational symmetry in the pseudo-spin $xy$-plane is respected, with a small local "magnetic" field along the pseudo-spin $z$-axis playing the role of control parameter driving the system away from the BQCP. On the approach to BQCP, the half-integer projection of the pseudo-spin on its $z$-axis gets delocalized into a halo of critically divergent radius, capturing the essence of the phenomenon of charge fractionalization. With large-scale Monte Carlo simulations, we confirm the existence of halons---and quantify their universal features---in O(2) and O(3) quantum critical systems.

cond-mat.quant-gas↗

arXiv2018

Beyond the Click-Through Rate: Web Link Selection with Multi-level Feedback

The web link selection problem is to select a small subset of web links from a large web link pool, and to place the selected links on a web page that can only accommodate a limited number of links, e.g., advertisements, recommendations, or news feeds. Despite the long concerned click-through rate which reflects the attractiveness of the link itself, the revenue can only be obtained from user actions after clicks, e.g., purchasing after being directed to the product pages by recommendation links. Thus, the web links have an intrinsic \emph{multi-level feedback structure}. With this observation, we consider the context-free web link selection problem, where the objective is to maximize revenue while ensuring that the attractiveness is no less than a preset threshold. The key challenge of the problem is that each link's multi-level feedbacks are stochastic, and unobservable unless the link is selected. We model this problem with a constrained stochastic multi-armed bandit formulation, and design an efficient link selection algorithm, called Constrained Upper Confidence Bound algorithm (\textbf{Con-UCB}), and prove $O(\sqrt{T\ln T})$ bounds on both the regret and the violation of the attractiveness constraint. We conduct extensive experiments on three real-world datasets, and show that \textbf{Con-UCB} outperforms state-of-the-art context-free bandit algorithms concerning the multi-level feedback structure.

cs.LG↗

arXiv2018

Trapping Collapse

Weak potential wells (or traps) in one and two dimensions, and the potential wells slightly deeper than the critical ones in three dimensions, feature shallow bound states with localization length much larger than the well radii. We address a simple fundamental question of how many repulsively interacting bosons can be localized by such traps. We find that under rather generic conditions, for both weakly and strongly repulsive particles, in two and three dimensions--but not in one-dimension!--the potential well can trap infinitely many bosons. For example, even hard-core repulsive interactions do not prevent this "trapping collapse" phenomenon from taking place. For the weakly interacting/dilute regime, the effect can be revealed by the mean-field argument, while in the case of strong correlations the evidence comes from path-integral simulations. We also discuss the possibility of having a transition between the infinite and finite number of trapped particles when strong repulsive inter-particle correlations are increased.

cond-mat.quant-gas↗

arXiv2018

Timely-Throughput Optimal Scheduling with Prediction

Motivated by the increasing importance of providing delay-guaranteed services in general computing and communication systems, and the recent wide adoption of learning and prediction in network control, in this work, we consider a general stochastic single-server multi-user system and investigate the fundamental benefit of predictive scheduling in improving timely-throughput, being the rate of packets that are delivered to destinations before their deadlines. By adopting an error rate-based prediction model, we first derive a Markov decision process (MDP) solution to optimize the timely-throughput objective subject to an average resource consumption constraint. Based on a packet-level decomposition of the MDP, we explicitly characterize the optimal scheduling policy and rigorously quantify the timely-throughput improvement due to predictive-service, which scales as $Θ(p\left[C_{1}\frac{(a-a_{\max}q)}{p-q}ρ^τ+C_{2}(1-\frac{1}{p})\right](1-ρ^{D}))$, where $a, a_{\max}, ρ\in(0, 1), C_1>0, C_2\ge0$ are constants, $p$ is the true-positive rate in prediction, $q$ is the false-negative rate, $τ$ is the packet deadline and $D$ is the prediction window size. We also conduct extensive simulations to validate our theoretical findings. Our results provide novel insights into how prediction and system parameters impact performance and provide useful guidelines for designing predictive low-latency control algorithms.

cs.NI↗

arXiv2017

Multi-level Feedback Web Links Selection Problem: Learning and Optimization

Selecting the right web links for a website is important because appropriate links not only can provide high attractiveness but can also increase the website's revenue. In this work, we first show that web links have an intrinsic \emph{multi-level feedback structure}. For example, consider a $2$-level feedback web link: the $1$st level feedback provides the Click-Through Rate (CTR) and the $2$nd level feedback provides the potential revenue, which collectively produce the compound $2$-level revenue. We consider the context-free links selection problem of selecting links for a homepage so as to maximize the total compound $2$-level revenue while keeping the total $1$st level feedback above a preset threshold. We further generalize the problem to links with $n~(n\ge2)$-level feedback structure. The key challenge is that the links' multi-level feedback structures are unobservable unless the links are selected on the homepage. To our best knowledge, we are the first to model the links selection problem as a constrained multi-armed bandit problem and design an effective links selection algorithm by learning the links' multi-level structure with provable \emph{sub-linear} regret and violation bounds. We uncover the multi-level feedback structures of web links in two real-world datasets. We also conduct extensive experiments on the datasets to compare our proposed \textbf{LExp} algorithm with two state-of-the-art context-free bandit algorithms and show that \textbf{LExp} algorithm is the most effective in links selection while satisfying the constraint.

cs.LG↗

arXiv2017

Dyck Words, Lattice Paths, and Abelian Borders

We use results on Dyck words and lattice paths to derive a formula for the exact number of binary words of a given length with a given minimal abelian border length, tightening a bound on that number from Christodoulakis et al. (Discrete Applied Mathematics, 2014). We also extend to any number of distinct abelian borders a result of Rampersad et al. (Developments in Language Theory, 2013) on the exact number of binary words of a given length with no abelian borders. Furthermore, we generalize these results to partial words.

cs.FL↗

arXiv2017

Robust Reduced Rank Regression

In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used reduced-rank methods are sensitive to data corruption, as the low-rank dependence structure between response variables and predictors is easily distorted by outliers. We propose a robust reduced-rank regression approach for joint modeling and outlier detection. The problem is formulated as a regularized multivariate regression with a sparse mean-shift parametrization, which generalizes and unifies some popular robust multivariate methods. An efficient thresholding-based iterative procedure is developed for optimization. We show that the algorithm is guaranteed to converge, and the coordinatewise minimum point produced is statistically accurate under regularity conditions. Our theoretical investigations focus on nonasymptotic robust analysis, which demonstrates that joint rank reduction and outlier detection leads to improved prediction accuracy. In particular, we show that redescending $ψ$-functions can essentially attain the minimax optimal error rate, and in some less challenging problems convex regularization guarantees the same low error rate. The performance of the proposed method is examined by simulation studies and real data examples.

math.ST↗

arXiv2017

SOFAR: large-scale association network learning

Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsity and orthogonality have been two largely incompatible goals. To accommodate both features, in this paper we suggest the method of sparse orthogonal factor regression (SOFAR) via the sparse singular value decomposition with orthogonality constrained optimization to learn the underlying association networks, with broad applications to both unsupervised and supervised learning tasks such as biclustering with sparse singular value decomposition, sparse principal component analysis, sparse factor analysis, and spare vector autoregression analysis. Exploiting the framework of convexity-assisted nonconvex optimization, we derive nonasymptotic error bounds for the suggested procedure characterizing the theoretical advantages. The statistical guarantees are powered by an efficient SOFAR algorithm with convergence property. Both computational and theoretical advantages of our procedure are demonstrated with several simulation and real data examples.

stat.ME↗

arXiv2017

Phase-controlled dual-comb coherent anti-Stokes Raman spectroscopic imaging

Coherent Raman microscopy provide label-free imaging by interrogating the intrinsic vibration of biomolecules. Nevertheless, trade-off between high chemical-specificity and high imaging-speed currently exists in transition from spectroscopy to spectroscopic imaging when capturing dynamics in complex living systems. Here, we present a novel concept in dual-comb scheme to substantially beat this trade-off and facilitate high-resolution broadband coherent anti-Stokes Raman spectroscopic imaging based on down-converted, automatically varying delay-time in spectral focusing excitation. A rapid measurement of vibrational microspectroscopy on sub-microsecond scale over a spectral span ~700 cm-1 with solid signal-to-noise ratio provides access to well-resolved molecular signatures within the fingerprint region. We demonstrate this high-performance spectroscopic imaging of spatially inhomogeneous distributions of chemical substances as well as the carotenoids accumulation in plant cells. This technique offers an unprecedented route for broadband CARS imaging with hundreds of kHz frame rate using available 1-GHz oscillators.

physics.optics↗

arXiv2016

Trapping Centers at the Superfluid-Mott-insulator Criticality: Transition between Charge-quantized States

Under the conditions of superfluid-Mott-insulator criticality in two dimensions, the trapping centers--i.e., local potential wells and bumps--are generically characterized by an integer charge corresponding to the number of trapped particles (if positive) or holes (if negative). Varying the strength of the center leads to a transition between two competing ground states with charges differing by $\pm 1$. The hallmark of the transition scenario is a splitting of the number density distortion, $δn(r)$, into a half-integer core and a large halo carrying the complementary charge of $\pm 1/2$. The sign of the halo changes across the transition and the radius of the halo, $r_0$, diverges on the approach to the critical strength of the center, $V = V_c$, by the law $r_0 \propto |V-V_c|^{-\tildeν}$, with $\tildeν \approx 2.33(5)$.

cond-mat.quant-gas↗

arXiv2016

Hybrid Recommender System Based on Personal Behavior Mining

Recommender systems are mostly well known for their applications in e-commerce sites and are mostly static models. Classical personalized recommender algorithm includes item-based collaborative filtering method applied in Amazon, matrix factorization based collaborative filtering algorithm from Netflix, etc. In this article, we hope to combine traditional model with behavior pattern extraction method. We use desensitized mobile transaction record provided by T-mall, Alibaba to build a hybrid dynamic recommender system. The sequential pattern mining aims to find frequent sequential pattern in sequence database and is applied in this hybrid model to predict customers' payment behavior thus contributing to the accuracy of the model.

cs.IR↗

arXiv2016

Age-of-Information in the Presence of Error

We consider the peak age-of-information (PAoI) in an M/M/1 queueing system with packet delivery error, i.e., update packets can get lost during transmissions to their destination. We focus on two types of policies, one is to adopt Last-Come-First-Served (LCFS) scheduling, and the other is to utilize retransmissions, i.e., keep transmitting the most recent packet. Both policies can effectively avoid the queueing delay of a busy channel and ensure a small PAoI. Exact PAoI expressions under both policies with different error probabilities are derived, including First-Come-First-Served (FCFS), LCFS with preemptive priority, LCFS with non-preemptive priority, Retransmission with preemptive priority, and Retransmission with non-preemptive priority. Numerical results obtained from analysis and simulation are presented to validate our results.

cs.PF↗

arXiv2016

Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice

We study the low-temperature physics of the $SU(2)$-symmetric spin-$1/2$ Heisenberg antiferromagnet on a pyrochlore lattice and find fingerprint evidence for the thermal spin-ice state in this frustrated quantum magnet. Our conclusions are based on the results of bold diagrammatic Monte Carlo simulations, with good convergence of the skeleton series down to the temperature $T/J=1/6$. The identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for the static structure factor between the quantum Heisenberg, classical Heisenberg, and Ising models at all accessible temperatures, and the characteristic bowtie pattern with pinch points observed at $T/J=1/6$. The dynamic structure factor at real frequencies (obtained by the analytic continuation of numerical data) is consistent with diffusive spinon dynamics at the pinch points.

cond-mat.str-el↗

arXiv2016

Background-free coherent anti-stokes Raman spectroscopy and microscopy by dual-soliton pulse generation

We propose an all-fiber-generated dual-soliton pulses based scheme for the background-free detection of coherent anti-Stokes Raman spectroscopy under the spectral focusing mechanism. Due to the strong birefringence and high nonlinearity of a polarization-maintaining photonic crystal fiber (PM-PCF), two redshifted soliton pulses can be simultaneously generated relying on high-order dispersion and nonlinear effects along two eigenpolarization axes in the anomalous dispersion regime, while allowing feasible tunability of the frequency distance and temporal interval between them. This proposed scheme, termed as DS-CARS, exploits a unique combination of slight frequency-shift and advisable temporal walk-off of this two soliton pulses to achieve robust and efficient suppression of nonresonant background with compact all-fiber coherent excitation source. Capability of the DS-CARS is experimentally demonstrated by the background-free CARS spectroscopy and unambiguous CARS microscopy of polymer beads in the fingerprint region.

physics.optics↗