arXiv subjects

Guodong Li

Publications and source records attributed to Guodong Li.

At least 55 records · Page 3Linked to original sources

arXiv2024

Tucker tensor factor models: matricization and mode-wise PCA estimation

High-dimensional, higher-order tensor data are gaining prominence in a variety of fields, including but not limited to computer vision and network analysis. Tensor factor models, induced from noisy versions of tensor decompositions or factorizations, are natural potent instruments to study a collection of tensor-variate objects that may be dependent or independent. However, it is still in the early stage of developing statistical inferential theories for the estimation of various low-rank structures, which are customary to play the role of signals of tensor factor models. In this paper, we attempt to ``decode" the estimation of a higher-order tensor factor model by leveraging tensor matricization. Specifically, we recast it into mode-wise traditional high-dimensional vector/fiber factor models, enabling the deployment of conventional principal components analysis (PCA) for estimation. Demonstrated by the Tucker tensor factor model (TuTFaM), which is induced from the noisy version of the widely-used Tucker decomposition, we summarize that estimations on signal components are essentially mode-wise PCA techniques, and the involvement of projection and iteration will enhance the signal-to-noise ratio to various extent. We establish the inferential theory of the proposed estimators, conduct rich simulation experiments, and illustrate how the proposed estimations can work in tensor reconstruction, and clustering for independent video and dependent economic datasets, respectively.

stat.ME↗

arXiv2024

Overdensity of Lyman-Break Galaxy Candidates Around Hot Dust-Obscured Galaxies

Hot dust-obscured galaxies (Hot DOGs), are a family of hyper-luminous, heavily obscured quasars. A number of studies have shown that these objects reside in significantly overdense regions of the Universe based on the identification of companions at optical through far-IR wavelengths. Here we present further characterization of their environments by studying the surface density of Lyman break galaxy (LBG) candidates in the vicinity of three Hot DOGs. For two of them, WISE J041010.60-091305.2 at z=3.631 and WISE J083153.25+014010.8 at z=3.912, we identify the candidate LBG companions using deep observations obtained with Baade/IMACS. For the third, WISE J224607.56-052634.9 at z=4.601, we re-analyse previously published data obtained with Gemini-S/GMOS-S. We optimise the LBG photometric selection criteria at the redshift of each target using the COSMOS2020 catalog. When comparing the density of LBG candidates found in the vicinity of these Hot DOGs with that in the COSMOS2020 catalog, we find overdensities of $δ=1.83\pm 0.08$ ($δ' = 7.49\pm 0.68$), $δ=4.67\pm 0.21$ ($δ' = 29.17\pm 2.21$), and $δ= 2.36\pm 0.25$ ($δ' = 11.60\pm 1.96$) around W0410-0913, W0831+0140, and W2246-0526, respectively, without (with) contamination correction. Additionally, we find that the overdensities are centrally concentrated around each Hot DOG. Our analysis also reveals that the overdensity of the fields surrounding W0410-0913 and W0831+0140 declines steeply beyond physical scales of $\sim$2 Mpc. If these overdensities evolve to clusters by z=0, these results suggest that the Hot DOG may correspond to the early formation stages of the brightest cluster galaxy. We were unable to determine if this is also the case for W2246-0526 due to the smaller field of view of the GMOS-S observations. Our results imply that Hot DOGs may be excellent tracers of protoclusters.

astro-ph.GA↗

arXiv2024

FAST H I 21 cm study of blueberry galaxies

Green Peas (GPs) and blueberry galaxies (BBs) are thought to be local analogs ($z<$0.1) of high redshift Ly$α$ emitters. H I study of these can help us understand the star formation in the primordial Universe. In this Letter, we present the results of H I 21 cm study of 28 high specific star formation rate (sSFR $\gtrsim$10$^{-8}$ yr$^{-1}$) BBs at $z\lesssim$0.05 with the Five-hundred-meter Aperture Spherical radio Telescope. We report significant H I detection towards two BBs namely J1026+0426 and J1132+0809, and discuss possible H I contribution from neighboring galaxies. The median 3$σ$ upper limit of $\sim$2.0$\times$10$^{8}$ M$_{\odot}$ was obtained on H I mass for galaxies with nondetections. We find BBs tend to have lower H I-to-stellar mass ratio or gas fraction ($f_{\rm HI}$) than expected from $f_{\rm HI}$-sSFR and $f_{\rm HI}$-$M_{\ast}$ relations for main-sequence galaxies. The BBs also have a median 3$σ$ upper limit on H I gas depletion time scale ($τ_{\rm HI}$) $\sim$0.5 Gyr, about 1 order of magnitude lower than $τ_{\rm HI}$ for local main-sequence galaxies. We find a significantly low H I detection rate of 2/28 (7.1$^{+9.4}_{-4.6}$ \%) towards these galaxies, which is similar to previous H I studies of low redshift GPs of high ionization parameter indicator, O32 $\equiv$O[{\sc iii}]$λ$5007/O[{\sc ii}]$λ$3727 ratios $\gtrsim$10.

astro-ph.GA↗

arXiv2024

Robust estimation for high-dimensional time series with heavy tails

We study in this paper the problem of least absolute deviation (LAD) regression for high-dimensional heavy-tailed time series which have finite $α$-th moment with $α\in (1,2]$. To handle the heavy-tailed dependent data, we propose a Catoni type truncated minimization problem framework and obtain an $\mathcal{O}\big( \big( (d_1+d_2) (d_1\land d_2) \log^2 n / n \big)^{(α- 1)/α} \big)$ order excess risk, where $d_1$ and $d_2$ are the dimensionality and $n$ is the number of samples. We apply our result to study the LAD regression on high-dimensional heavy-tailed vector autoregressive (VAR) process. Simulations for the VAR($p$) model show that our new estimator with truncation are essential because the risk of the classical LAD has a tendency to blow up. We further apply our estimation to the real data and find that ours fits the data better than the classical LAD.

math.ST↗

arXiv2024

Black Hole Mass and Eddington Ratio Distribution of Hot Dust-Obscured Galaxies

Hot Dust-Obscured Galaxies (Hot DOGs) are a rare population of hyper-luminous infrared galaxies discovered by the WISE mission. Despite the significant obscuration of the AGN by dust in these systems, pronounced broad and blue-shifted emission lines are often observed. Previous work has shown that 8 Hot DOGs, referred to as Blue-excess Hot DOGs (BHDs), present a blue excess consistent with type 1 quasar emission in their UV-optical SEDs, which has been shown to originate from the light of the obscured central engine scattered into the line of sight. We present an analysis of the rest-frame optical emission characteristics for 172 Hot DOGs through UV-MIR SED modeling and spectroscopic details, with a particular focus on the identification of BHDs. We find that while the optical emission observed in Hot DOGs is in most cases dominated by a young stellar population, 26% of Hot DOGs show a significant enough blue excess emission to be classified as BHDs. Based on their broad CIV and MgII lines, we find that the $M_{\rm BH}$ in BHDs range from $10^{8.7}$ to $10^{10} \ M_{\odot}$. When using the same emission lines in regular Hot DOGs, we find the $M_{\rm BH}$ estimates cover the entire range found for BHDs while also extending to somewhat lower values. This agreement may imply that the broad lines in regular Hot DOGs also originate from scattered light from the central engine, just as in BHDs, although a more detailed study would be needed to rule out an outflow-driven nature. Similar to $z\sim 6$ quasars, we find that Hot DOGs sit above the local relation between stellar and black hole mass, suggesting either that AGN feedback has not yet significantly suppressed the stellar mass growth in the host galaxies, or that they will be outliers of the relation when reaching $z$=0.

astro-ph.GA↗

arXiv2024

DGCformer: Deep Graph Clustering Transformer for Multivariate Time Series Forecasting

Multivariate time series forecasting tasks are usually conducted in a channel-dependent (CD) way since it can incorporate more variable-relevant information. However, it may also involve a lot of irrelevant variables, and this even leads to worse performance than the channel-independent (CI) strategy. This paper combines the strengths of both strategies and proposes the Deep Graph Clustering Transformer (DGCformer) for multivariate time series forecasting. Specifically, it first groups these relevant variables by a graph convolutional network integrated with an autoencoder, and a former-latter masked self-attention mechanism is then considered with the CD strategy being applied to each group of variables while the CI one for different groups. Extensive experimental results on eight datasets demonstrate the superiority of our method against state-of-the-art models, and our code will be publicly available upon acceptance.

cs.LG↗

arXiv2024

An efficient tensor regression for high-dimensional data

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater than four or five. However, for the simplest tensor autoregression in handling time series data, its coefficient tensor already has the order of six. This paper revises a newly proposed tensor train (TT) decomposition and then applies it to tensor regression such that a nice statistical interpretation can be obtained. The new tensor regression can well match the data with hierarchical structures, and it even can lead to a better interpretation for the data with factorial structures, which are supposed to be better fitted by models with Tucker decomposition. More importantly, the new tensor regression can be easily applied to the case with higher order tensors since TT decomposition can compress the coefficient tensors much more efficiently. The methodology is also extended to tensor autoregression for time series data, and nonasymptotic properties are derived for the ordinary least squares estimations of both tensor regression and autoregression. A new algorithm is introduced to search for estimators, and its theoretical justification is also discussed. Theoretical and computational properties of the proposed methodology are verified by simulation studies, and the advantages over existing methods are illustrated by two real examples.

stat.ME↗

arXiv2024

PGformer: Proxy-Bridged Game Transformer for Multi-Person Highly Interactive Extreme Motion Prediction

Multi-person motion prediction is a challenging task, especially for real-world scenarios of highly interacted persons. Most previous works have been devoted to studying the case of weak interactions (e.g., walking together), in which typically forecasting each human pose in isolation can still achieve good performances. This paper focuses on collaborative motion prediction for multiple persons with extreme motions and attempts to explore the relationships between the highly interactive persons' pose trajectories. Specifically, a novel cross-query attention (XQA) module is proposed to bilaterally learn the cross-dependencies between the two pose sequences tailored for this situation. A proxy unit is additionally introduced to bridge the involved persons, which cooperates with our proposed XQA module and subtly controls the bidirectional spatial information flows. These designs are then integrated into a Transformer-based architecture and the resulting model is called Proxy-bridged Game Transformer (PGformer) for multi-person interactive motion prediction. Its effectiveness has been evaluated on the challenging ExPI dataset, which involves highly interactive actions. Our PGformer consistently outperforms the state-of-the-art methods in both short- and long-term predictions by a large margin. Besides, our approach can also be compatible with the weakly interacted CMU-Mocap and MuPoTS-3D datasets and extended to the case of more than 2 individuals with encouraging results.

cs.CV↗

arXiv2024

A benchmark for extreme conditions of the multiphase interstellar medium in the most luminous hot dust-obscured galaxy at z = 4.6

WISE J224607.6-052634.9 (W2246-0526) is a hot dust-obscured galaxy at $z$ = 4.601, and the most luminous obscured quasar known to date. W2246-0526 harbors a heavily obscured supermassive black hole that is most likely accreting above the Eddington limit. We present observations with the Atacama Large Millimeter/submillimeter Array (ALMA) in seven bands, including band 10, of the brightest far-infrared (FIR) fine-structure emission lines of this galaxy: [OI]$_{63μm}$, [OIII]$_{88μm}$, [NII]$_{122μm}$, [OI]$_{145μm}$, [CII]$_{158μm}$, [NII]$_{205μm}$, [CI]$_{370μm}$, and [CI]$_{609μm}$. A comparison of the data to a large grid of Cloudy radiative transfer models reveals that a high hydrogen density ($n_{H}\sim3\times10^3$ cm$^{-3}$) and extinction ($A_{V}\sim300$ mag), together with extreme ionization ($log(U)=-0.5$) and a high X-ray to UV ratio ($α_{ox}\geq-0.8$) are required to reproduce the observed nuclear line ratios. The values of $α_{ox}$ and $U$ are among the largest found in the literature and imply the existence of an X-ray-dominated region (XDR). In fact, this component explains the a priori very surprising non-detection of the [OIII]$_{88μm}$ emission line, which is actually suppressed, instead of boosted, in XDR environments. Interestingly, the best-fitted model implies higher X-ray emission and lower CO content than what is detected observationally, suggesting the presence of a molecular gas component that should be further obscuring the X-ray emission over larger spatial scales than the central region that is being modeled. These results highlight the need for multiline infrared observations to characterize the multiphase gas in high redshift quasars and, in particular, W2246-0526 serves as an extreme benchmark for comparisons of interstellar medium conditions with other quasar populations at cosmic noon and beyond.

astro-ph.GA↗

arXiv2023

Discovery and Timing of Millisecond Pulsars in the Globular Cluster M5 (NGC 5904) with FAST and Arecibo

We report on a comprehensive multi-wavelength study of the pulsars in the globular cluster (GC) M5, including the discovery of M5G, a new compact non-eclipsing "black widow" pulsar. Thanks to the analysis of 34 years of radio data taken with the FAST and Arecibo telescopes, we obtained new phase-connected timing solutions for four pulsars in the clusters and improved those of the other three known pulsars. These have resulted in, among other things: a) much improved proper motions for five pulsars, with transverse velocities that are smaller than their respective escape velocities; b) 3-sigma and 1.5-sigma detections of Shapiro delays in M5F and M5D, respectively; c) greatly improved measurement of the periastron advance in M5B, whose value of 0.01361(6) implies that M5B is still likely to be a heavy neutron star. The binary pulsars M5D, E and F are confirmed to be in low-eccentricity binary systems, the low-mass companions of which are newly identified to be He white dwarfs using Hubble Space Telescope data. Four pulsars are also found to be associated with X-ray sources. Similarly to the eclipsing pulsar M5C, M5G shows little or no non-thermal X-ray emission, indicative of weak synchrotron radiation produced by intra-binary shocks. All the seven pulsars known in M5 have short spin periods and five are in binary systems with low orbital eccentricities. These characteristics differ from the overall GC pulsar population, but confirm the expectations for the pulsar population in a cluster with a small rate of stellar encounters per binary system.

astro-ph.HE↗

arXiv2023

MSR Codes with Linear Field Size and Smallest Sub-packetization for Any Number of Helper Nodes

The sub-packetization $\ell$ and the field size $q$ are of paramount importance in the MSR array code constructions. For optimal-access MSR codes, Balaji et al. proved that $\ell\geq s^{\left\lceil n/s \right\rceil}$, where $s = d-k+1$. Rawat et al. showed that this lower bound is attainable for all admissible values of $d$ when the field size is exponential in $n$. After that, tremendous efforts have been devoted to reducing the field size. However, till now, reduction to linear field size is only available for $d\in\{k+1,k+2,k+3\}$ and $d=n-1$. In this paper, we construct the first class of explicit optimal-access MSR codes with the smallest sub-packetization $\ell = s^{\left\lceil n/s \right\rceil}$ for all $d$ between $k+1$ and $n-1$, resolving an open problem in the survey (Ramkumar et al., Foundations and Trends in Communications and Information Theory: Vol. 19: No. 4). We further propose another class of explicit MSR code constructions (not optimal-access) with even smaller sub-packetization $s^{\left\lceil n/(s+1)\right\rceil }$ for all admissible values of $d$, making significant progress on another open problem in the survey. Previously, MSR codes with $\ell=s^{\left\lceil n/(s+1)\right\rceil }$ and $q=O(n)$ were only known for $d=k+1$ and $d=n-1$. The key insight that enables a linear field size in our construction is to reduce $\binom{n}{r}$ global constraints of non-vanishing determinants to $O_s(n)$ local ones, which is achieved by carefully designing the parity check matrices.

cs.IT↗

arXiv2023

The Initial Mass Function Based on the Full-sky 20-pc Census of $\sim$3,600 Stars and Brown Dwarfs

A complete accounting of nearby objects -- from the highest-mass white dwarf progenitors down to low-mass brown dwarfs -- is now possible, thanks to an almost complete set of trigonometric parallax determinations from Gaia, ground-based surveys, and Spitzer follow-up. We create a census of objects within a Sun-centered sphere of 20-pc radius and check published literature to decompose each binary or higher-order system into its separate components. The result is a volume-limited census of $\sim$3,600 individual star formation products useful in measuring the initial mass function across the stellar ($<8 M_\odot$) and substellar ($\gtrsim 5 M_{Jup}$) regimes. Comparing our resulting initial mass function to previous measurements shows good agreement above 0.8$M_\odot$ and a divergence at lower masses. Our 20-pc space densities are best fit with a quadripartite power law, $ξ(M) = dN/dM \propto M^{-α}$ with long-established values of $α= 2.3$ at high masses ($0.55 < M < 8.00 M_\odot$) and $α= 1.3$ at intermediate masses ($0.22 < M < 0.55 M_\odot$), but at lower masses we find $α= 0.25$ for $0.05 < M <0.22 M_\odot$ and $α= 0.6$ for $0.01 < M < 0.05 M_\odot$. This implies that the rate of production as a function of decreasing mass diminishes in the low-mass star/high-mass brown dwarf regime before increasing again in the low-mass brown dwarf regime. Correcting for completeness, we find a star to brown dwarf number ratio of, currently, 4:1, and an average mass per object of 0.41 $M_\odot$.

astro-ph.SR↗

arXiv2023

Supervised Factor Modeling for High-Dimensional Linear Time Series

Motivated by Tucker tensor decomposition, this paper imposes low-rank structures to the column and row spaces of coefficient matrices in a multivariate infinite-order vector autoregression (VAR), which leads to a supervised factor model with two factor modelings being conducted to responses and predictors simultaneously. Interestingly, the stationarity condition implies an intrinsic weak group sparsity mechanism of infinite-order VAR, and hence a rank-constrained group Lasso estimation is considered for high-dimensional linear time series. Its non-asymptotic properties are discussed thoughtfully by balancing the estimation, approximation and truncation errors. Moreover, an alternating gradient descent algorithm with thresholding is designed to search for high-dimensional estimates, and its theoretical justifications, including statistical and convergence analysis, are also provided. Theoretical and computational properties of the proposed methodology are verified by simulation experiments, and the advantages over existing methods are demonstrated by two real examples.

stat.ME↗

arXiv2023

Discovery of a Low-Redshift Hot Dust-Obscured Galaxy

We report the discovery of the hyperluminous, highly obscured AGN WISE J190445.04+485308.9 (W1904+4853 hereafter, $L_{bol} = 1.1 \times 10^{13} \ L_{\odot}$) at z=0.415. Its well-sampled spectral energy distribution (SED) is dominated by infrared dust emission, though broad emission lines are detected in the optical spectra. These features suggest that W1904+4853 contains an actively accreting supermassive black hole hidden in its dusty cocoon, resembling the observed properties of Hot Dust-Obscured Galaxies (Hot DOGs), a population previously only identified at z>1.0. Using the broad component of the MgII emission line, we estimate a black hole mass of $log \ (M_{BH}/M_{\odot}) = 8.4 \pm 0.4$. The corresponding Eddington ratio of 1.4 implies that the central black hole accretion is at the theoretical limit of isotropic accretion. The rest-frame UV-optical SED also indicates that the host galaxy of W1904+4853 harbors strong star formation activity at the rate of $6-84 \ M_{\odot} \ \rm{yr^{-1}}$ with an independent estimate of SFR up to $\sim 45 \ M_{\odot} \ \rm{yr^{-1}}$ using the [O II] emission line. With an estimated stellar mass of $3 \times 10^{10} \ M_{\odot}$, the host galaxy appears to be a starburst system with respect to the main sequence of the star-forming galaxies at the same redshift. Although blueshifted and asymmetric [O III] emission provides evidence of an outflow, we estimate it to be an order of magnitude smaller than the star formation rate, indicating that the current obscured AGN activity at the center has not yet produced significant feedback on the host galaxy star formation activity. W1904+4853 supports the interpretation that Hot DOGs are a rare transitional phase of AGN accretion in galaxy evolution, a phase that can persist into the present-day Universe.

astro-ph.GA↗

arXiv2023

Quantile autoregressive conditional heteroscedasticity

This paper proposes a novel conditional heteroscedastic time series model by applying the framework of quantile regression processes to the ARCH(\infty) form of the GARCH model. This model can provide varying structures for conditional quantiles of the time series across different quantile levels, while including the commonly used GARCH model as a special case. The strict stationarity of the model is discussed. For robustness against heavy-tailed distributions, a self-weighted quantile regression (QR) estimator is proposed. While QR performs satisfactorily at intermediate quantile levels, its accuracy deteriorates at high quantile levels due to data scarcity. As a remedy, a self-weighted composite quantile regression (CQR) estimator is further introduced and, based on an approximate GARCH model with a flexible Tukey-lambda distribution for the innovations, we can extrapolate the high quantile levels by borrowing information from intermediate ones. Asymptotic properties for the proposed estimators are established. Simulation experiments are carried out to access the finite sample performance of the proposed methods, and an empirical example is presented to illustrate the usefulness of the new model.

stat.ME↗

arXiv2023

ABS+ Polar Codes: Exploiting More Linear Transforms on Adjacent Bits

ABS polar codes were recently proposed to speed up polarization by swapping certain pairs of adjacent bits after each layer of polar transform. In this paper, we observe that applying the Arikan transform $(U_i, U_{i+1}) \mapsto (U_{i}+U_{i+1}, U_{i+1})$ on certain pairs of adjacent bits after each polar transform layer leads to even faster polarization. In light of this, we propose ABS+ polar codes which incorporate the Arikan transform in addition to the swapping transform in ABS polar codes. In order to efficiently construct and decode ABS+ polar codes, we derive a new recursive relation between the joint distributions of adjacent bits through different layers of polar transforms. Simulation results over a wide range of parameters show that the CRC-aided SCL decoder of ABS+ polar codes improves upon that of ABS polar codes by 0.1dB--0.25dB while maintaining the same decoding time. Moreover, ABS+ polar codes improve upon standard polar codes by 0.2dB--0.45dB when they both use the CRC-aided SCL decoder with list size $32$. The implementations of all the algorithms in this paper are available at https://github.com/PlumJelly/ABS-Polar

cs.IT↗

arXiv2023

H I content of selected mid-infrared bright, starburst blue compact dwarf galaxies

We report measurements of H I content in 11 nearby, actively star-forming, blue compact dwarf galaxies (BCDs) from 21 cm observations with the Arecibo telescope. These BCDs, selected by their red (W2[4.6 $μ$m]$-$W3[12 $μ$m]$>$3.8 mag) and bright mid-infrared (MIR) emission (W4[22 $μ$m]$<$ 7.6 mag), have high specific star formation rates (median sSFR $\sim$10$^{-7.8}$ yr$^{-1}$), similar to high redshift galaxies. H I emission was detected in six sources. We analyze our new detections in the context of previous H I observations of 218 dwarf irregulars (dIs) and BCDs in the literature. The $M_{\rm HI}$-$M_{\ast}$ relation resulting from our observations confirms the dominating fraction of H I gas among baryons in galaxies with lower stellar masses. This Arecibo BCD sample has significantly lower median H I depletion timescales ($τ_{\rm HI}\sim$ 0.3 Gyr) than other dIs/BCDs ($\sim$ 6.3 Gyr) in the literature. The majority of the sources (10/11) in the Arecibo sample are very red in W1[3.4 $μ$m]$-$W2[4.6 $μ$m] colour ($>$ 0.8 mag) implying the presence of warm dust. We investigate the relation of $τ_{\rm HI}$ with stellar mass ($M_{\ast}$) and sSFR. We find that $τ_{\rm HI}$ is significantly anti-correlated with $M_{\ast}$ for higher sSFR ($>$10$^{-8.5}$ yr$^{-1}$) and with sSFR for higher stellar mass ($>10^{7.5}\,{\rm M}_{\odot}$) dwarf galaxies. The high sSFR for the BCDs in the Arecibo observed sample is mainly due to their high atomic gas star formation efficiency (SFE) or low $τ_{\rm HI}$. The low $τ_{\rm HI}$ or high SFE in these sources is possibly due to runaway star formation in compact and dense super star clusters.

astro-ph.GA↗

arXiv2023

High-Dimensional Low-Rank Tensor Autoregressive Time Series Modeling

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper provides a new modeling framework to accomplish this task via autoregression (AR). By considering a low-rank Tucker decomposition for the transition tensor, the proposed tensor AR can flexibly capture the underlying low-dimensional tensor dynamics, providing both substantial dimension reduction and meaningful multi-dimensional dynamic factor interpretations. For this model, we first study several nuclear-norm-regularized estimation methods and derive their non-asymptotic properties under the approximate low-rank setting. In particular, by leveraging the special balanced structure of the transition tensor, a novel convex regularization approach based on the sum of nuclear norms of square matricizations is proposed to efficiently encourage low-rankness of the coefficient tensor. To further improve the estimation efficiency under exact low-rankness, a non-convex estimator is proposed with a gradient descent algorithm, and its computational and statistical convergence guarantees are established. Simulation studies and an empirical analysis of tensor-valued time series data from multi-category import-export networks demonstrate the advantages of the proposed approach.

stat.ME↗