arXiv subjects

Zhou Fan

Publications and source records attributed to Zhou Fan.

At least 91 records · Page 5Linked to original sources

arXiv2020

TAP free energy, spin glasses, and variational inference

We consider the Sherrington-Kirkpatrick model of spin glasses with ferromagnetically biased couplings. For a specific choice of the couplings mean, the resulting Gibbs measure is equivalent to the Bayesian posterior for a high-dimensional estimation problem known as `$Z_2$ synchronization'. Statistical physics suggests to compute the expectation with respect to this Gibbs measure (the posterior mean in the synchronization problem), by minimizing the so-called Thouless-Anderson-Palmer (TAP) free energy, instead of the mean field (MF) free energy. We prove that this identification is correct, provided the ferromagnetic bias is larger than a constant (i.e. the noise level is small enough in synchronization). Namely, we prove that the scaled $\ell_2$ distance between any low energy local minimizers of the TAP free energy and the mean of the Gibbs measure vanishes in the large size limit. Our proof technique is based on upper bounding the expected number of critical points of the TAP free energy using the Kac-Rice formula.

math.PR↗

arXiv2019

Spectral Graph Matching and Regularized Quadratic Relaxations I: The Gaussian Model

Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes the total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper we propose a new spectral method, GRAph Matching by Pairwise eigen-Alignments (GRAMPA). Departing from prior spectral approaches that only compare top eigenvectors, or eigenvectors of the same order, GRAMPA first constructs a similarity matrix as a weighted sum of outer products between all pairs of eigenvectors of the two graphs, with weights given by a Cauchy kernel applied to the separation of the corresponding eigenvalues, then outputs a matching by a simple rounding procedure. The similarity matrix can also be interpreted as the solution to a regularized quadratic programming relaxation of the quadratic assignment problem. For the Gaussian Wigner model in which two complete graphs on $n$ vertices have Gaussian edge weights with correlation coefficient $1-σ^2$, we show that GRAMPA exactly recovers the correct vertex correspondence with high probability when $σ= O(\frac{1}{\log n})$. This matches the state of the art of polynomial-time algorithms, and significantly improves over existing spectral methods which require $σ$ to be polynomially small in $n$. The superiority of GRAMPA is also demonstrated on a variety of synthetic and real datasets, in terms of both statistical accuracy and computational efficiency. Universality results, including similar guarantees for dense and sparse Erdős-Rényi graphs, are deferred to the companion paper.

stat.ML↗

arXiv2019

Spectral Graph Matching and Regularized Quadratic Relaxations II: Erdős-Rényi Graphs and Universality

We analyze a new spectral graph matching algorithm, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), for recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs. Extending the exact recovery guarantees established in the companion paper for Gaussian weights, in this work, we prove the universality of these guarantees for a general correlated Wigner model. In particular, for two Erdős-Rényi graphs with edge correlation coefficient $1-σ^2$ and average degree at least $\operatorname{polylog}(n)$, we show that GRAMPA exactly recovers the latent vertex correspondence with high probability when $σ\lesssim 1/\operatorname{polylog}(n)$. Moreover, we establish a similar guarantee for a variant of GRAMPA, corresponding to a tighter quadratic programming relaxation of the quadratic assignment problem. Our analysis exploits a resolvent representation of the GRAMPA similarity matrix and local laws for the resolvents of sparse Wigner matrices.

math.PR↗

arXiv2019

Surfing: Iterative optimization over incrementally trained deep networks

We investigate a sequential optimization procedure to minimize the empirical risk functional $f_{\hatθ}(x) = \frac{1}{2}\|G_{\hatθ}(x) - y\|^2$ for certain families of deep networks $G_θ(x)$. The approach is to optimize a sequence of objective functions that use network parameters obtained during different stages of the training process. When initialized with random parameters $θ_0$, we show that the objective $f_{θ_0}(x)$ is "nice'' and easy to optimize with gradient descent. As learning is carried out, we obtain a sequence of generative networks $x \mapsto G_{θ_t}(x)$ and associated risk functions $f_{θ_t}(x)$, where $t$ indicates a stage of stochastic gradient descent during training. Since the parameters of the network do not change by very much in each step, the surface evolves slowly and can be incrementally optimized. The algorithm is formalized and analyzed for a family of expansive networks. We call the procedure {\it surfing} since it rides along the peak of the evolving (negative) empirical risk function, starting from a smooth surface at the beginning of learning and ending with a wavy nonconvex surface after learning is complete. Experiments show how surfing can be used to find the global optimum and for compressed sensing even when direct gradient descent on the final learned network fails.

stat.ML↗

arXiv2019

Hybrid Actor-Critic Reinforcement Learning in Parameterized Action Space

In this paper we propose a hybrid architecture of actor-critic algorithms for reinforcement learning in parameterized action space, which consists of multiple parallel sub-actor networks to decompose the structured action space into simpler action spaces along with a critic network to guide the training of all sub-actor networks. While this paper is mainly focused on parameterized action space, the proposed architecture, which we call hybrid actor-critic, can be extended for more general action spaces which has a hierarchical structure. We present an instance of the hybrid actor-critic architecture based on proximal policy optimization (PPO), which we refer to as hybrid proximal policy optimization (H-PPO). Our experiments test H-PPO on a collection of tasks with parameterized action space, where H-PPO demonstrates superior performance over previous methods of parameterized action reinforcement learning.

cs.LG↗

arXiv2019

Iterative Alpha Expansion for estimating gradient-sparse signals from linear measurements

We consider estimating a piecewise-constant image, or a gradient-sparse signal on a general graph, from noisy linear measurements. We propose and study an iterative algorithm to minimize a penalized least-squares objective, with a penalty given by the "l_0-norm" of the signal's discrete graph gradient. The method proceeds by approximate proximal descent, applying the alpha-expansion procedure to minimize a proximal gradient in each iteration, and using a geometric decay of the penalty parameter across iterations. Under a cut-restricted isometry property for the measurement design, we prove global recovery guarantees for the estimated signal. For standard Gaussian designs, the required number of measurements is independent of the graph structure, and improves upon worst-case guarantees for total-variation (TV) compressed sensing on the 1-D and 2-D lattice graphs by polynomial and logarithmic factors, respectively. The method empirically yields lower mean-squared recovery error compared with TV regularization in regimes of moderate undersampling and moderate to high signal-to-noise, for several examples of changepoint signals and gradient-sparse phantom images.

stat.ML↗

arXiv2018

The Ages of M31 Star Clusters: Spectral Energy Distribution Versus Color-Magnitude Diagram

It is well-known that fitting the Color Magnitude Diagrams (CMDs) to the theoretical isochrones is the main method to determine star cluster ages. However, when the CMDs are not available, the Spectral Energy Distribution (SED)-fitting technique is the only other approach, although it suffers the age-metallicity-reddening degeneracy. In this work, we gather the ages, metallicities and masses of dozens of M31 star clusters from the CMD-fitting with HST images from the literatures for comparison. We check the reliability of the SED-fitting results with different models, i.e., Bruzual \& Charlot 2003 model (BC03), Galaxy Evolutionary Synthesis Models ({\sl GALEV}) and Advanced Stellar Population Synthesis (ASPS) for the simple stellar populations (SSPs) with single stars (ss)-SSP/binary star (bs)-SSPs models. The photometry bands includes the Galaxy Evolution Explorer {\sl GALEX} FUV/NUV bands, optical/near-infrared $UBVRIJHK$ bands, as well as the Wide-field Infrared Survey Explorer ({\sl WISE}) $W1$/$W2$ bands. The comparisons show that the SED-fitting ages agree well with the CMD-fitting ages, either with the fixed metallicity or with the free metallicity for both the BC03 and the {\sl GALEV} model. However, for the ASPS models, it seems that SED-fitting results are systematic older than the CMD ages, especially for the ages log t <9.0 (yr). The fitting also shows that the {\sl GALEX} FUV/NUV-band are more important than the {\sl WISE} $W1$/$W2$ for constraining the ages, which confirms the previous findings. We also derived the masses of our sample star clusters from the BC03 and {\sl GALEV} models and it is found that the values agree well with that in the literature.

astro-ph.GA↗

arXiv2018

LEMONY--a Library of Empirical Medium-resolution spectra by Observations with the NAOC Xinglong 2.16\,m and YNAO Gaomeigu 2.4\,m telescopes

This study expands the coverage and improves the homogeneity of the distribution of MILES template stars in the parameter space, as well as extends the wavelength coverage of the template spectra to the far red beyond the Ca\,{\sc{ii}} triplet. To achieve this we have carried out a major observational campaign using the OMR long-slit spectrograph mounted on the NAOC 2.16\,m telescope and the YFOSC long-slit spectrograph mounted on the YNAO 2.4\,m telescope. The original sample is based on the MILES library, supplemented by 918 stars selected from PASTEL database. In total, 822 OMR and 1,324 YFOSC spectra, covering respectively the wavelength ranges $λλ$3800--5180 and $λλ$5150--9000, have been collected and reduced. The spectra have a mean resolution FWHM (full-width at half-maximum) of $\sim 3.3$\,Å and are wavelength- and flux-calibrated to an accuracy of $\sim 20$\,km\,s$^{-1}$ and $\sim 5$\,per\,cent, respectively. The spectra are further corrected for systematic errors in the wavelength calibration to an accuracy of $\sim 4$\,km\,s$^{-1}$ by cross-correlating with the theoretical spectra. Almost all the spectra have an average signal to noise ratio (SNR) better than 100 per pixel. Combined with the MILES spectra, there are now 1,731, 1,542, 1,324 and 1,273 stars with spectra covering respectively $λλ$3800--5180, $λλ$3800--7500, $λλ$5150--9000 and $λλ$3800--9000. This paper describes our template star selection, the observation and data reduction, and presents the reduced spectra collected hitherto.

astro-ph.SR↗

arXiv2018

Spiked covariances and principal components analysis in high-dimensional random effects models

We study principal components analyses in multivariate random and mixed effects linear models, assuming a spherical-plus-spikes structure for the covariance matrix of each random effect. We characterize the behavior of outlier sample eigenvalues and eigenvectors of MANOVA variance components estimators in such models under a high-dimensional asymptotic regime. Our results show that an aliasing phenomenon may occur in high dimensions, in which eigenvalues and eigenvectors of the MANOVA estimate for one variance component may be influenced by the other components. We propose an alternative procedure for estimating the true principal eigenvalues and eigenvectors that asymptotically corrects for this aliasing problem.

math.ST↗

arXiv2018

The SAGE Photometric Sky Survey: Technical Description

To investigate in more details of Stellar Abundance and Galactic Evolution (SAGE) and in a huge sample, we are performing a northern sky photometric survey named SAGES with the SAGE photometric system, which consists of 8 filters: Strömgren-$u$, SAGE-$v$, SDSS $g$, $r$, $i$, DDO-$51$, $Hα_{wide}$, and $Hα_{narrow}$, including three Sloan broadband filters, three intermediate-band filters and two narrow-band filters, and one newly-designed narrow-band filter. SAGES covers $\sim$12,000 square degrees of the northern sky with $δ> -5 ^{\circ}$, excluding the Galactic disk ($|b|<10^{\circ}$) and the sky area of 12 hr $<$ R.A. $<$ 18\,hr. The photometric detection limit depth at signal-to-noise ratio $5σ$ can be as deep as $V\sim$20\,mag. The SAGES will produce a depth-uniformed photometric catalogue for $\sim$500 million stars with atmospheric parameters including effective temperature $T_{\rm eff}$, surface gravity log\,g, and metallicity [Fe/H], as well as interstellar extinction to each individual target. In this work, we will briefly introduce the SAGE photometric system, the SAGE survey, and a preliminary test field of the open cluster NGC\,6791 and around.

astro-ph.IM↗

arXiv2018

Testing Area of the SAGE Survey

Sky survey is one of the most important motivations to improve the astrophysics development, especially when using new photometric bands. We are performing the SAGE (Stellar Abundance and Galactic Evolution) survey with a self-designed SAGE photometric system, which is composed of eight photometric bands. The project mainly aims to study the stellar atmospheric parameters of $\sim$0.5 billion stars in the $\sim12,000$ deg$^2$ of the northern sky, which mainly focuses on the Galactic sciences, as well as some extragalactic sciences. This work introduces the detailed data reduction process of the testing field NGC\,6791, including the data reduction of single-exposure image and stacking multi-exposure images, and properties of the final catalogue.

astro-ph.GA↗

arXiv2018

Investigating the Efficiency of the Beijing Faint Object Spectrograph and Camera (BFOSC) of the Xinglong 2.16-m Reflector

The Beijing Faint Object Spectrograph and Camera (BFOSC) is one of the most important instruments of the 2.16-m telescope of the Xinglong Observatory. Every year there are ~ 20 SCI-papers published based on the observational data of this telescope. In this work, we have systemically measured the total efficiency of the BFOSC of the 2.16-m reflector, based on the observations of two ESO flux standard stars. We have obtained the total efficiencies of the BFOSC instrument of different grisms with various slit widths in almost all ranges, and analysed the factors which effect the efficiency of telescope and spectrograph. For the astronomical observers, the result will be useful for them to select a suitable slit width, depending on their scientific goals and weather conditions during the observation; For the technicians, the result will help them systemically find out the real efficiency of telescope and spectrograph, and further to improve the total efficiency and observing capacity of the telescope technically.

astro-ph.IM↗

arXiv2018

Upgraded Photometric System of The 85-cm Telescope at Xinglong Station

The 85-cm telescope at the Xinglong station is a well-operated prime focus system with high science outputs. The telescope has been upgraded since 2014 with new corrector, filters and camera, which are provided by Beijing Normal University (BNU). The filter set is Johnson-Cousins UBVRI system. We report the test results of the new system including the bias, dark current, linearity, gain and readout noise of the CCD camera . Then we derive accurate instrumental calibration coefficients in UBVRI bands with Landolt standard stars in the photometric nights. Finally, we give the limiting magnitudes with various exposure time and signal-to-noise ratio for observers as references.

astro-ph.IM↗

arXiv2017

Transiting Exoplanet Monitoring Project (TEMP). III. On the Relocation of the Kepler-9~b Transit

The Kepler-9 system harbors three known transiting planets. The system holds significant interest for several reasons. First, the outer two planets exhibit a period ratio that is close to a 2:1 orbital commensurability, with attendant dynamical consequences. Second, both planets lie in the planetary mass "desert" that is generally associated with the rapid gas agglomeration phase of the core accretion process. Third, there exist attractive prospects for accurately measuring both the sky-projected stellar spin-orbit angles as well as the mutual orbital inclination between the planets in the system. Following the original \textit{Kepler} detection announcement in 2010, the initially reported orbital ephemerides for Kepler-9~b and c have degraded significantly, due to the limited time base-line of observations on which the discovery of the system rested. Here, we report new ground-based photometric observations and extensive dynamical modeling of the system. These efforts allow us to photometrically recover the transit of Kepler-9~b, and thereby greatly improve the predictions for upcoming transit mid-times. Accurate ephemerides of this system are important in order to confidently schedule follow-up observations of this system, for both in-transit Doppler measurements as well as for atmospheric transmission spectra taken during transit.

astro-ph.EP↗

arXiv2017

Eigenvalue distributions of variance components estimators in high-dimensional random effects models

We study the spectra of MANOVA estimators for variance component covariance matrices in multivariate random effects models. When the dimensionality of the observations is large and comparable to the number of realizations of each random effect, we show that the empirical spectra of such estimators are well-approximated by deterministic laws. The Stieltjes transforms of these laws are characterized by systems of fixed-point equations, which are numerically solvable by a simple iterative procedure. Our proof uses operator-valued free probability theory, and we establish a general asymptotic freeness result for families of rectangular orthogonally-invariant random matrices, which is of independent interest. Our work is motivated by the estimation of components of covariance between multiple phenotypic traits in quantitative genetics, and we specialize our results to common experimental designs that arise in this application.

math.ST↗

arXiv2017

Approximate $l_0$-penalized estimation of piecewise-constant signals on graphs

We study recovery of piecewise-constant signals on graphs by the estimator minimizing an $l_0$-edge-penalized objective. Although exact minimization of this objective may be computationally intractable, we show that the same statistical risk guarantees are achieved by the $α$-expansion algorithm which computes an approximate minimizer in polynomial time. We establish that for graphs with small average vertex degree, these guarantees are minimax rate-optimal over classes of edge-sparse signals. For spatially inhomogeneous graphs, we propose minimization of an edge-weighted objective where each edge is weighted by its effective resistance or another measure of its contribution to the graph's connectivity. We establish minimax optimality of the resulting estimators over corresponding edge-weighted sparsity classes. We show theoretically that these risk guarantees are not always achieved by the estimator minimizing the $l_1$/total-variation relaxation, and empirically that the $l_0$-based estimates are more accurate in high signal-to-noise settings.

stat.ME↗

arXiv2017

Empirical Bayesian analysis of simultaneous changepoints in multiple data sequences

Copy number variations in cancer cells and volatility fluctuations in stock prices are commonly manifested as changepoints occurring at the same positions across related data sequences. We introduce a Bayesian modeling framework, BASIC, that employs a changepoint prior to capture the co-occurrence tendency in data of this type. We design efficient algorithms to sample from and maximize over the BASIC changepoint posterior and develop a Monte Carlo expectation-maximization procedure to select prior hyperparameters in an empirical Bayes fashion. We use the resulting BASIC framework to analyze DNA copy number variations in the NCI-60 cancer cell lines and to identify important events that affected the price volatility of S&P 500 stocks from 2000 to 2009.

stat.ME↗

arXiv2017

Powerful CMD: A Tool for Colour-Magnitude Diagram Studies

We present a new tool for colour-magnitude diagram (CMD) studies, $Powerful~CMD$. This tool is built on the basis of the advanced stellar population synthesis (ASPS) model, in which single stars, binary stars, rotating stars, and star formation history have been taken into account. Via $Powerful~CMD$, the distance modulus, colour excess, metallicity, age, binary fraction, rotating star fraction, and star formation history of star clusters can be determined simultaneously from observed CMDs. The new tool is tested via both simulated and real star clusters. Five parameters of clusters NGC6362, NGC6652, NGC6838 and M67 are determined and compared to other works. It is shown that this tool is useful for CMD studies, in particular for those with the data of the Hubble Space Telescope (HST). Moreover, we find that the inclusion of binaries in theoretical stellar population models may lead to smaller colour excess compared to the case of single star population models.

astro-ph.GA↗