arXiv subjects

Ji Zhu

Publications and source records attributed to Ji Zhu.

At least 55 records · Page 3Linked to original sources

arXiv2022

Adaptive Algorithm for Quantum Amplitude Estimation

Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on Grover's algorithm. The key ingredient is the introduction of an adjustment factor, which adjusts the amplitude of good states such that the amplitude after the adjustment, and the original amplitude, can be estimated without ambiguity in the subsequent step. We show with numerical studies that the proposed algorithm uses a similar number of quantum queries to achieve the same level of precision $ε$ compared to state-of-the-art algorithms, but the classical part, i.e., the non-quantum part, has substantially lower computational complexity. We rigorously prove that the number of oracle queries achieves $O(1/ε)$, i.e., a quadratic speedup over classical Monte Carlo sampling, and the computational complexity of the classical part achieves $O(\log(1/ε))$, both up to a double-logarithmic factor.

quant-ph↗

arXiv2021

SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks

In this paper, we propose a flexible model for survival analysis using neural networks along with scalable optimization algorithms. One key technical challenge for directly applying maximum likelihood estimation (MLE) to censored data is that evaluating the objective function and its gradients with respect to model parameters requires the calculation of integrals. To address this challenge, we recognize that the MLE for censored data can be viewed as a differential-equation constrained optimization problem, a novel perspective. Following this connection, we model the distribution of event time through an ordinary differential equation and utilize efficient ODE solvers and adjoint sensitivity analysis to numerically evaluate the likelihood and the gradients. Using this approach, we are able to 1) provide a broad family of continuous-time survival distributions without strong structural assumptions, 2) obtain powerful feature representations using neural networks, and 3) allow efficient estimation of the model in large-scale applications using stochastic gradient descent. Through both simulation studies and real-world data examples, we demonstrate the effectiveness of the proposed method in comparison to existing state-of-the-art deep learning survival analysis models. The implementation of the proposed SODEN approach has been made publicly available at https://github.com/jiaqima/SODEN.

stat.ML↗

arXiv2021

Survival Analysis via Ordinary Differential Equations

This paper introduces an Ordinary Differential Equation (ODE) notion for survival analysis. The ODE notion not only provides a unified modeling framework, but more importantly, also enables the development of a widely applicable, scalable, and easy-to-implement procedure for estimation and inference. Specifically, the ODE modeling framework unifies many existing survival models, such as the proportional hazards model, the linear transformation model, the accelerated failure time model, and the time-varying coefficient model as special cases. The generality of the proposed framework serves as the foundation of a widely applicable estimation procedure. As an illustrative example, we develop a sieve maximum likelihood estimator for a general semi-parametric class of ODE models. In comparison to existing estimation methods, the proposed procedure has advantages in terms of computational scalability and numerical stability. Moreover, to address unique theoretical challenges induced by the ODE notion, we establish a new general sieve M-theorem for bundled parameters and show that the proposed sieve estimator is consistent and asymptotically normal, and achieves the semi-parametric efficiency bound. The finite sample performance of the proposed estimator is examined in simulation studies and a real-world data example.

stat.ME↗

arXiv2021

Fast Network Community Detection with Profile-Pseudo Likelihood Methods

The stochastic block model is one of the most studied network models for community detection. It is well-known that most algorithms proposed for fitting the stochastic block model likelihood function cannot scale to large-scale networks. One prominent work that overcomes this computational challenge is Amini et al.(2013), which proposed a fast pseudo-likelihood approach for fitting stochastic block models to large sparse networks. However, this approach does not have convergence guarantee, and is not well suited for small- or medium- scale networks. In this article, we propose a novel likelihood based approach that decouples row and column labels in the likelihood function, which enables a fast alternating maximization; the new method is computationally efficient, performs well for both small and large scale networks, and has provable convergence guarantee. We show that our method provides strongly consistent estimates of the communities in a stochastic block model. As demonstrated in simulation studies, the proposed method outperforms the pseudo-likelihood approach in terms of both estimation accuracy and computation efficiency, especially for large sparse networks. We further consider extensions of our proposed method to handle networks with degree heterogeneity and bipartite properties.

stat.ME↗

arXiv2021

Latent space models for multiplex networks with shared structure

Latent space models are frequently used for modeling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well-developed for more complex network structures, which are becoming increasingly common in practice. Here we propose a new latent space model for multiplex networks: multiple, heterogeneous networks observed on a shared node set. Multiplex networks can represent a network sample with shared node labels, a network evolving over time, or a network with multiple types of edges. The key feature of our model is that it learns from data how much of the network structure is shared between layers and pools information across layers as appropriate. We establish identifiability, develop a fitting procedure using convex optimization in combination with a nuclear norm penalty, and prove a guarantee of recovery for the latent positions as long as there is sufficient separation between the shared and the individual latent subspaces. We compare the model to competing methods in the literature on simulated networks and on a multiplex network describing the worldwide trade of agricultural products.

stat.ME↗

arXiv2021

Wilks' theorems in some exponential random graph models

We are concerned here with the likelihood ratio statistics in two exponential random graph models -- the $β$-model and the Bradley-Terry model, in which the degree sequence on an undirected graph and the out-degree sequence on a weighted directed graph are the exclusively sufficient statistics in the exponential-family distributions on graphs, respectively. We prove the Wilks type of theorems for some fixed and growing dimensional hypothesis testing problems. More specifically, under two fixed dimensional null hypotheses $H_0: β_i=β_i^0$ for $i=1,\ldots, r$ and $H_0: β_1=\ldots=β_r$, we show that $2[\ell(\widehat{\boldsymbolβ}) - \ell(\widehat{\boldsymbolβ}^0)]$ converges in distribution to a Chi-square distribution with the respective degrees of freedoms, $r$ and $r-1$, as the dimension $n$ of the full parameter space goes to infinity. Here, $\ell(\boldsymbolβ)$ is the log-likelihood function on the parameter $\boldsymbolβ$, $\widehat{\boldsymbolβ}$ is the MLE under the full parameter space, and $\widehat{\boldsymbolβ}^0$ is the restricted MLE under the null parameter space. For two increasing dimensional null hypotheses $H_0: β_i = β_i^0$ for $i=1, \ldots, n$ and $H_0: β_1=\ldots=β_r$ with $r/n \ge c$, we show that the normalized log-likelihood ratio statistics, $(2[\ell(\widehat{\boldsymbolβ}) - \ell(\boldsymbolβ^0)] -n)/(2n)^{1/2}$ and $(2[\ell(\widehat{\boldsymbolβ}) - \ell(\widehat{\boldsymbolβ}^0)] -r)/(2r)^{1/2}$, both converge in distribution to the standard normal distribution. Simulation studies and an application to NBA data illustrate the theoretical results.

math.ST↗

arXiv2021

Community models for networks observed through edge nominations

Communities are a common and widely studied structure in networks, typically under the assumption that the network is fully and correctly observed. In practice, network data are often collected by querying nodes about their connections. In some settings, all edges of a sampled node will be recorded, and in others, a node may be asked to name its connections. These sampling mechanisms introduce noise and bias which can obscure the community structure and invalidate assumptions underlying standard community detection methods. We propose a general model for a class of network sampling mechanisms based on recording edges via querying nodes, designed to improve community detection for network data collected in this fashion. We model edge sampling probabilities as a function of both individual preferences and community parameters, and show community detection can be performed by spectral clustering under this general class of models. We also propose, as a special case of the general framework, a parametric model for directed networks we call the nomination stochastic block model, which allows for meaningful parameter interpretations and can be fitted by the method of moments. Both spectral clustering and the method of moments in this case are computationally efficient and come with theoretical guarantees of consistency. We evaluate the proposed model in simulation studies on both unweighted and weighted networks and apply it to a faculty hiring dataset, discovering a meaningful hierarchy of communities among US business schools.

stat.ME↗

arXiv2020

Detection of the number of principal components by extended AIC-type method

Estimating the number of principal components is one of the fundamental problems in many scientific fields such as signal processing (or the spiked covariance model). In this paper, we first demonstrate that, for fixed $p$, any penalty term of the form $k'(p-k'/2+1/2)C_n$ may lead to an asymptotically consistent estimator under the condition that $C_n\to\infty$ and $C_n/n\to0$. We also extend our results to the case $n,p\to\infty$, with $p/n\to c>0$. In this case, for $k=o(n^{\frac{1}{3}})$, we first investigate the limiting laws for the leading eigenvalues of the sample covariance matrix $S_n$ under the condition that $λ_k>1+\sqrt{c}$. At low SNR, since the AIC tends to underestimate the number of signals $k$, the AIC should be re-defined in this case. As a natural extension of the AIC for fixed $p$, we propose the extended AIC (EAIC), i.e., the AIC-type method with tuning parameter $γ=φ(c)=1/2+\sqrt{1/c}-\log(1+\sqrt{c})/c$, and demonstrate that the EAIC-type method, i.e., the AIC-type method with tuning parameter $γ>φ(c)$, can select the number of signals $k$ consistently. In the following two cases, (1) $p$ fixed, $n\to\infty$, (2) $n,p\to\infty$ with $p/n\to 0$, if the AIC is defined as the degeneration of the EAIC in the case $n,p\to\infty$ with $p/n\to c>0$, i.e., $γ=\lim_{c\rightarrow 0+0}φ(c)=1$, then we have essentially demonstrated that, to achieve the consistency of the AIC-type method in the above two cases, $γ>1$ is required. Moreover, we show that the EAIC-type method is essentially tuning-free and outperforms the well-known KN estimator proposed in Kritchman and Nadler (2008) and the BCF estimator proposed in Bai, Choi and Fujikoshi (2018). Numerical studies indicate that the proposed method works well.

stat.ME↗

arXiv2020

Network cross-validation by edge sampling

While many statistical models and methods are now available for network analysis, resampling network data remains a challenging problem. Cross-validation is a useful general tool for model selection and parameter tuning, but is not directly applicable to networks since splitting network nodes into groups requires deleting edges and destroys some of the network structure. Here we propose a new network resampling strategy based on splitting node pairs rather than nodes applicable to cross-validation for a wide range of network model selection tasks. We provide a theoretical justification for our method in a general setting and examples of how our method can be used in specific network model selection and parameter tuning tasks. Numerical results on simulated networks and on a citation network of statisticians show that this cross-validation approach works well for model selection.

stat.ME↗

arXiv2020

High-dimensional Gaussian graphical model for network-linked data

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that the observations are independent and identically distributed. At the same time, observations connected by a network are becoming increasingly common, and tend to violate these assumptions. Here we develop a Gaussian graphical model for observations connected by a network with potentially different mean vectors, varying smoothly over the network. We propose an efficient estimation algorithm and demonstrate its effectiveness on both simulated and real data, obtaining meaningful and interpretable results on a statistics coauthorship network. We also prove that our method estimates both the inverse covariance matrix and the corresponding graph structure correctly under the assumption of network â€œcohesionâ€, which refers to the empirically observed phenomenon of network neighbors sharing similar traits.

stat.ML↗

arXiv2020

Network-Assisted Estimation for Large-dimensional Factor Model with Guaranteed Convergence Rate Improvement

Network structure is growing popular for capturing the intrinsic relationship between large-scale variables. In the paper we propose to improve the estimation accuracy for large-dimensional factor model when a network structure between individuals is observed. To fully excavate the prior network information, we construct two different penalties to regularize the factor loadings and shrink the idiosyncratic errors. Closed-form solutions are provided for the penalized optimization problems. Theoretical results demonstrate that the modified estimators achieve faster convergence rates and lower asymptotic mean squared errors when the underlying network structure among individuals is correct. An interesting finding is that even if the priori network is totally misleading, the proposed estimators perform no worse than conventional state-of-art methods. Furthermore, to facilitate the practical application, we propose a data-driven approach to select the tuning parameters, which is computationally efficient. We also provide an empirical criterion to determine the number of common factors. Simulation studies and application to the S&P100 weekly return dataset convincingly illustrate the superiority and adaptivity of the new approach.

stat.ME↗

arXiv2019

Minorization-Maximization-based Steepest Ascent for Large-scale Survival Analysis with Time-Varying Effects: Application to the National Kidney Transplant Dataset

The time-varying effects model is a flexible and powerful tool for modeling the dynamic changes of covariate effects. However, in survival analysis, its computational burden increases quickly as the number of sample sizes or predictors grows. Traditional methods that perform well for moderate sample sizes and low-dimensional data do not scale to massive data. Analysis of national kidney transplant data with a massive sample size and large number of predictors defy any existing statistical methods and software. In view of these difficulties, we propose a Minorization-Maximization-based steepest ascent procedure for estimating the time-varying effects. Leveraging the block structure formed by the basis expansions, the proposed procedure iteratively updates the optimal block-wise direction along which the approximate increase in the log-partial likelihood is maximized. The resulting estimates ensure the ascent property and serve as refinements of the previous step. The performance of the proposed method is examined by simulations and applications to the analysis of national kidney transplant data.

stat.CO↗

arXiv2019

MSP: A Multi-step Screening Procedure for Sparse Recovery

We propose a Multi-step Screening Procedure (MSP) for the recovery of sparse linear models in high-dimensional data. This method is based on a repeated small penalty strategy that quickly converges to an estimate within a few iterations. Specifically, in each iteration, an adaptive lasso regression with a small penalty is fit within the reduced feature space obtained from the previous step, rendering its computational complexity roughly comparable with the Lasso. MSP is shown to select the true model under complex correlation structures among the predictors and response, even when the irrepresentable condition fails. Further, under suitable regularity conditions, MSP achieves the optimal minimax rate $(q \log n /n)^{1/2}$ for the upper bound of $l_2$-norm error. Numerical comparisons show that the method works effectively both in model selection and estimation, and the MSP fitted model is stable over a range of small tuning parameter values, eliminating the need to choose the tuning parameter by cross-validation. We also apply MSP to financial data and show that MSP is successful in asset allocation selection.

stat.ME↗

arXiv2019

A Flexible Generative Framework for Graph-based Semi-supervised Learning

We consider a family of problems that are concerned about making predictions for the majority of unlabeled, graph-structured data samples based on a small proportion of labeled samples. Relational information among the data samples, often encoded in the graph/network structure, is shown to be helpful for these semi-supervised learning tasks. However, conventional graph-based regularization methods and recent graph neural networks do not fully leverage the interrelations between the features, the graph, and the labels. In this work, we propose a flexible generative framework for graph-based semi-supervised learning, which approaches the joint distribution of the node features, labels, and the graph structure. Borrowing insights from random graph models in network science literature, this joint distribution can be instantiated using various distribution families. For the inference of missing labels, we exploit recent advances of scalable variational inference techniques to approximate the Bayesian posterior. We conduct thorough experiments on benchmark datasets for graph-based semi-supervised learning. Results show that the proposed methods outperform the state-of-the-art models in most settings.

cs.LG↗

arXiv2019

Using Maximum Entry-Wise Deviation to Test the Goodness-of-Fit for Stochastic Block Models

The stochastic block model is widely used for detecting community structures in network data. How to test the goodness-of-fit of the model is one of the fundamental problems and has gained growing interests in recent years. In this article, we propose a novel goodness-of-fit test based on the maximum entry of the centered and re-scaled adjacency matrix for the stochastic block model. One noticeable advantage of the proposed test is that the number of communities can be allowed to grow linearly with the number of nodes ignoring a logarithmic factor. We prove that the null distribution of the test statistic converges in distribution to a Gumbel distribution, and we show that both the number of communities and the membership vector can be tested via the proposed method. Further, we show that the proposed test has asymptotic power guarantee against a class of alternatives. We also demonstrate that the proposed method can be extended to the degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.

stat.ME↗

arXiv2019

Online Multi-Object Tracking with Dual Matching Attention Networks

In this paper, we propose an online Multi-Object Tracking (MOT) approach which integrates the merits of single object tracking and data association methods in a unified framework to handle noisy detections and frequent interactions between targets. Specifically, for applying single object tracking in MOT, we introduce a cost-sensitive tracking loss based on the state-of-the-art visual tracker, which encourages the model to focus on hard negative distractors during online learning. For data association, we propose Dual Matching Attention Networks (DMAN) with both spatial and temporal attention mechanisms. The spatial attention module generates dual attention maps which enable the network to focus on the matching patterns of the input image pair, while the temporal attention module adaptively allocates different levels of attention to different samples in the tracklet to suppress noisy observations. Experimental results on the MOT benchmark datasets show that the proposed algorithm performs favorably against both online and offline trackers in terms of identity-preserving metrics.

cs.CV↗

arXiv2018

Prediction models for network-linked data

Prediction algorithms typically assume the training data are independent samples, but in many modern applications samples come from individuals connected by a network. For example, in adolescent health studies of risk-taking behaviors, information on the subjects' social network is often available and plays an important role through network cohesion, the empirically observed phenomenon of friends behaving similarly. Taking cohesion into account in prediction models should allow us to improve their performance. Here we propose a network-based penalty on individual node effects to encourage similarity between predictions for linked nodes, and show that incorporating it into prediction leads to improvement over traditional models both theoretically and empirically when network cohesion is present. The penalty can be used with many loss-based prediction methods, such as regression, generalized linear models, and Cox's proportional hazard model. Applications to predicting levels of recreational activity and marijuana usage among teenagers from the AddHealth study based on both demographic covariates and friendship networks are discussed in detail and show that our approach to taking friendships into account can significantly improve predictions of behavior while providing interpretable estimates of covariate effects.

stat.ME↗

arXiv2018

Covariance-Insured Screening

Modern bio-technologies have produced a vast amount of high-throughput data with the number of predictors far greater than the sample size. In order to identify more novel biomarkers and understand biological mechanisms, it is vital to detect signals weakly associated with outcomes among ultrahigh-dimensional predictors. However, existing screening methods, which typically ignore correlation information, are likely to miss these weak signals. By incorporating the inter-feature dependence, we propose a covariance-insured screening methodology to identify predictors that are jointly informative but only marginally weakly associated with outcomes. The validity of the method is examined via extensive simulations and real data studies for selecting potential genetic factors related to the onset of cancer.

stat.ML↗