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Pan Zhang

Publications and source records attributed to Pan Zhang.

At least 163 records · Page 9Linked to original sources
arXiv2019

Phase transitions and optimal algorithms for semi-supervised classifications on graphs: from belief propagation to graph convolution network

We perform theoretical and algorithmic studies for the problem of clustering and semi-supervised classification on graphs with both pairwise relational information and single-point feature information, upon a joint stochastic block model for generating synthetic graphs with both edges and node features. Asymptotically exact analysis based on the Bayesian inference of the underlying model are conducted, using the cavity method in statistical physics. Theoretically, we identify a phase transition of the generative model, which puts fundamental limits on the ability of all possible algorithms in the clustering task of the underlying model. Algorithmically, we propose a belief propagation algorithm that is asymptotically optimal on the generative model, and can be further extended to a belief propagation graph convolution neural network (BPGCN) for semi-supervised classification on graphs. For the first time, well-controlled benchmark datasets with asymptotially exact properties and optimal solutions could be produced for the evaluation of graph convolution neural networks, and for the theoretical understanding of their strengths and weaknesses. In particular, on these synthetic benchmark networks we observe that existing graph convolution neural networks are subject to an sparsity issue and an ovefitting issue in practice, both of which are successfully overcome by our BPGCN. Moreover, when combined with classic neural network methods, BPGCN yields extraordinary classification performances on some real-world datasets that have never been achieved before.

cond-mat.stat-mech↗
arXiv2019

Self-falsifiable Hierarchical Detection of Overlapping Communities On Social Networks

No community detection algorithm can be optimal for all possible networks, thus it is important to identify whether the algorithm is suitable for a given network. We propose a multi-step algorithmic solution scheme for overlapping community detection based on an advanced label propagation process, which imitates the community formation process on social networks. Our algorithm is parameter-free and is able to reveal the hierarchical order of communities in the graph. The unique property of our solution scheme is self-falsifiability; an automatic quality check of the results is conducted after the detection, and the fitness of the algorithm for the specific network is reported. Extensive experiments show that our algorithm is self-consistent, reliable on networks of a wide range of size and different sorts, and is more robust than existing algorithms on both sparse and large-scale social networks. Results further suggest that our solution scheme may uncover features of networks' intrinsic community structures.

cs.SI↗
arXiv2019

A streaming feature-based compression method for data from instrumented infrastructure

An increasing amount of civil engineering applications are utilising data acquired from infrastructure instrumented with sensing devices. This data has an important role in monitoring the response of these structures to excitation, and evaluating structural health. In this paper we seek to monitor pedestrian-events (such as a person walking) on a footbridge using strain and acceleration data. The rate of this data acquisition and the number of sensing devices make the storage and analysis of this data a computational challenge. We introduce a streaming method to compress the sensor data, whilst preserving key patterns and features (unique to different sensor types) corresponding to pedestrian-events. Numerical demonstrations of the methodology on data obtained from strain sensors and accelerometers on the pedestrian footbridge are provided to show the trade-off between compression and accuracy during and in-between periods of pedestrian-events.

cs.LG↗
arXiv2019

Solving Statistical Mechanics Using Variational Autoregressive Networks

We propose a general framework for solving statistical mechanics of systems with finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks, which support direct sampling and exact calculation of normalized probability of configurations. It computes variational free energy, estimates physical quantities such as entropy, magnetizations and correlations, and generates uncorrelated samples all at once. Training of the network employs the policy gradient approach in reinforcement learning, which unbiasedly estimates the gradient of variational parameters. We apply our approach to several classic systems, including 2D Ising models, the Hopfield model, the Sherrington-Kirkpatrick model, and the inverse Ising model, for demonstrating its advantages over existing variational mean-field methods. Our approach sheds light on solving statistical physics problems using modern deep generative neural networks.

cond-mat.stat-mech↗
arXiv2019

Tree Tensor Networks for Generative Modeling

Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of correlation in MPS restricts its representation power heavily for modeling complex data such as natural images. In this work, we push forward the effort of applying tensor networks to machine learning by employing the Tree Tensor Network (TTN) which exhibits balanced performance in expressibility and efficient training and sampling. We design the tree tensor network to utilize the 2-dimensional prior of the natural images and develop sweeping learning and sampling algorithms which can be efficiently implemented utilizing Graphical Processing Units (GPU). We apply our model to random binary patterns and the binary MNIST datasets of handwritten digits. We show that TTN is superior to MPS for generative modeling in keeping correlation of pixels in natural images, as well as giving better log-likelihood scores in standard datasets of handwritten digits. We also compare its performance with state-of-the-art generative models such as the Variational AutoEncoders, Restricted Boltzmann machines, and PixelCNN. Finally, we discuss the future development of Tensor Network States in machine learning problems.

stat.ML↗
arXiv2018

Shortcut Matrix Product States and its applications

Matrix Product States (MPS), also known as Tensor Train (TT) decomposition in mathematics, has been proposed originally for describing an (especially one-dimensional) quantum system, and recently has found applications in various applications such as compressing high-dimensional data, supervised kernel linear classifier, and unsupervised generative modeling. However, when applied to systems which are not defined on one-dimensional lattices, a serious drawback of the MPS is the exponential decay of the correlations, which limits its power in capturing long-range dependences among variables in the system. To alleviate this problem, we propose to introduce long-range interactions, which act as shortcuts, to MPS, resulting in a new model \textit{ Shortcut Matrix Product States} (SMPS). When chosen properly, the shortcuts can decrease significantly the correlation length of the MPS, while preserving the computational efficiency. We develop efficient training methods of SMPS for various tasks, establish some of their mathematical properties, and show how to find a good location to add shortcuts. Finally, using extensive numerical experiments we evaluate its performance in a variety of applications, including function fitting, partition function calculation of $2-$d Ising model, and unsupervised generative modeling of handwritten digits, to illustrate its advantages over vanilla matrix product states.

cond-mat.stat-mech↗
arXiv2018

Unsupervised Generative Modeling Using Matrix Product States

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum physics, we propose a generative model using matrix product states, which is a tensor network originally proposed for describing (particularly one-dimensional) entangled quantum states. Our model enjoys efficient learning analogous to the density matrix renormalization group method, which allows dynamically adjusting dimensions of the tensors and offers an efficient direct sampling approach for generative tasks. We apply our method to generative modeling of several standard datasets including the Bars and Stripes, random binary patterns and the MNIST handwritten digits to illustrate the abilities, features and drawbacks of our model over popular generative models such as Hopfield model, Boltzmann machines and generative adversarial networks. Our work sheds light on many interesting directions of future exploration on the development of quantum-inspired algorithms for unsupervised machine learning, which are promisingly possible to be realized on quantum devices.

cond-mat.stat-mech↗
arXiv2018

Multi-cavity ultra-stable laser towards 10-18

In this letter, we demonstrate a technique of making an ultrastable laser referenced to a multi-cavity, corresponding to a lower thermal noise limit due to the larger equivalent beam size. The multi-cavity consists of several pairs of mirrors and a common spacer. We can stabilize the laser frequencies on these cavities, and average the laser frequencies with synthesizing technique. In comparison with a single cavity system, relative frequency instability of the synthesized laser can be improved by a factor of the squire root of the cavity number (n). In addition, we perform an experiment to simulate a two-cavity system. Experimental results show that frequency instability of the synthesized laser is improved by a factor of 1.4, and discrimination of the laser frequency instability, introduced by the process of lasers synthesizing, is negligible, and can reach a floor at low level 10-18 limited by noise of currently used signal generators. This technique is comparable with other techniques; thus, it can gain a factor of the squre root of n on the frequency instability of an ultrastable laser to an unprecedented level.

physics.ins-det↗
arXiv2018

Weighted Community Detection and Data Clustering Using Message Passing

Grouping objects into clusters based on similarities or weights between them is one of the most important problems in science and engineering. In this work, by extending message passing algorithms and spectral algorithms proposed for unweighted community detection problem, we develop a non-parametric method based on statistical physics, by mapping the problem to Potts model at the critical temperature of spin glass transition and applying belief propagation to solve the marginals corresponding to the Boltzmann distribution. Our algorithm is robust to over-fitting and gives a principled way to determine whether there are significant clusters in the data and how many clusters there are. We apply our method to different clustering tasks and use extensive numerical experiments to illustrate the advantage of our method over existing algorithms. In the community detection problem in weighted and directed networks, we show that our algorithm significantly outperforms existing algorithms. In the clustering problem when the data was generated by mixture models in the sparse regime we show that our method works to the theoretical limit of detectability and gives accuracy very close to that of the optimal Bayesian inference. In the semi-supervised clustering problem, our method only needs several labels to work perfectly in classic datasets. Finally, we further develop Thouless-Anderson-Palmer equations which reduce heavily the computation complexity in dense-networks but gives almost the same performance as belief propagation.

physics.soc-ph↗
arXiv2017

Compressed Sensing by Shortest-Solution Guided Decimation

Compressed sensing is an important problem in many fields of science and engineering. It reconstructs signals by finding sparse solutions to underdetermined linear equations. In this work we propose a deterministic and non-parametric algorithm SSD (Shortest-Solution guided Decimation) to construct support of the sparse solution under the guidance of the dense least-squares solution of the recursively decimated linear equation. The most significant feature of SSD is its insensitivity to correlations in the sampling matrix. Using extensive numerical experiments we show that SSD greatly outperforms L1-norm based methods, Orthogonal Least Squares, Orthogonal Matching Pursuit, and Approximate Message Passing when the sampling matrix contains strong correlations. This nice property of correlation tolerance makes SSD a versatile and robust tool for different types of real-world signal acquisition tasks.

eess.SP↗
arXiv2017

Spectral estimation of the percolation transition in clustered networks

There have been several spectral bounds for the percolation transition in networks, using spectrum of matrices associated with the network such as the adjacency matrix and the non-backtracking matrix. However they are far from being tight when the network is sparse and displays clustering or transitivity, which is represented by existence of short loops e.g. triangles. In this work, for the bond percolation, we first propose a message passing algorithm for calculating size of percolating clusters considering effects of triangles, then relate the percolation transition to the leading eigenvalue of a matrix that we name the triangle-non-backtracking matrix, by analyzing stability of the message passing equations. We establish that our method gives a tighter lower-bound to the bond percolation transition than previous spectral bounds, and it becomes exact for an infinite network with no loops longer than 3. We evaluate numerically our methods on synthetic and real-world networks, and discuss further generalizations of our approach to include higher-order sub-structures.

physics.soc-ph↗
arXiv2016

Inequalities for Casorati curvatures of submanifolds in real space forms

By using T. Oprea's optimization methods on submanifolds, we give another proof of the inequalities relating the normalized $δ-$Casorati curvature $\hatδ_c(n-1)$ for submanifolds in real space forms. Also, inequalities relating the normalized $δ-$Casorati curvature $δ_C(n-1)$ for submanifolds in real space forms are obtained. Besides, we characterize a kind of Casorati ideal hypersurface of Euclidean 4-space. We also show that this kind of Casorati ideal hypersurface is rigid.

math.DG↗
arXiv2016

Enhanced superconductivity in hole-doped Nb$_{2}$PdS$_{5}$

We synthesized a series of Nb$_{2}$Pd$_{1-x}$Ru$_{x}$S$_{5}$ polycrystalline samples by a solid-state reaction method and systematically investigated the Ru-doping effect on superconductivity by transport and magnetic measurements. It is found that superconductivity is enhanced with Ru doping and is quite robust upon disorder. Hall coefficient measurements indicate that the charge transport is dominated by hole-type charge carriers similar to the case of Ir doping, suggesting multi-band superconductivity. Upon Ru or Ir doping, \emph H$_{c2}$/$\emph T_c$ exhibits a significant enhancement, exceeding the Pauli paramagnetic limit value by a factor of approximately 4. A comparison of $T_c$ and the upper critical field ($H_{c2}$) amongst the different doping elements on Pd site, reveals a significant role of spin--orbit coupling.

cond-mat.supr-con↗
arXiv2016

Robust Spectral Detection of Global Structures in the Data by Learning a Regularization

Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we propose a general method to solve the localization problem by learning a regularization matrix from the localized eigenvectors. Using matrix perturbation analysis, we demonstrate that the learned regularizations suppress down the eigenvalues associated with localized eigenvectors and enable us to recover the informative eigenvectors representing the global structure. We show applications of our method in several inference problems: community detection in networks, clustering from pairwise similarities, rank estimation and matrix completion problems. Using extensive experiments, we illustrate that our method solves the localization problem and works down to the theoretical detectability limits in different kinds of synthetic data. This is in contrast with existing spectral algorithms based on data matrix, non-backtracking matrix, Laplacians and those with rank-one regularizations, which perform poorly in the sparse case with noise.

stat.ML↗
arXiv2016

Data quality for the inverse Ising problem

There are many methods proposed for inferring parameters of the Ising model from given data, that is a set of configurations generated according to the model itself. However little attention has been paid until now to the data, e.g. how the data is generated, whether the inference error using one set of data could be smaller than using another set of data, etc. In this paper we address the data quality problem in the kinetic inverse Ising problem. We quantify the quality of data using effective rank of the correlation matrix, and show that data gathered in a out of-equilibrium regime has a better quality than data gathered in equilibrium for coupling reconstruction. We also propose a matrix-perturbation based method for tuning the quality of given data and for removing bad-quality (i.e. redundant) configurations from data.

cond-mat.stat-mech↗
arXiv2016

Fast and simple decycling and dismantling of networks

Decycling and dismantling of complex networks are underlying many important applications in network science. Recently these two closely related problems were tackled by several heuristic algorithms, simple and considerably sub-optimal, on the one hand, and time-consuming message-passing ones that evaluate single-node marginal probabilities, on the other hand. In this paper we propose a simple and extremely fast algorithm, CoreHD, which recursively removes nodes of the highest degree from the $2$-core of the network. CoreHD performs much better than all existing simple algorithms. When applied on real-world networks, it achieves equally good solutions as those obtained by the state-of-art iterative message-passing algorithms at greatly reduced computational cost, suggesting that CoreHD should be the algorithm of choice for many practical purposes.

physics.soc-ph↗