arXiv subjects

Faming Liang

Publications and source records attributed to Faming Liang.

At least 37 records · Page 2Linked to original sources

arXiv2022

A Kernel-Expanded Stochastic Neural Network

The deep neural network suffers from many fundamental issues in machine learning. For example, it often gets trapped into a local minimum in training, and its prediction uncertainty is hard to be assessed. To address these issues, we propose the so-called kernel-expanded stochastic neural network (K-StoNet) model, which incorporates support vector regression (SVR) as the first hidden layer and reformulates the neural network as a latent variable model. The former maps the input vector into an infinite dimensional feature space via a radial basis function (RBF) kernel, ensuring absence of local minima on its training loss surface. The latter breaks the high-dimensional nonconvex neural network training problem into a series of low-dimensional convex optimization problems, and enables its prediction uncertainty easily assessed. The K-StoNet can be easily trained using the imputation-regularized optimization (IRO) algorithm. Compared to traditional deep neural networks, K-StoNet possesses a theoretical guarantee to asymptotically converge to the global optimum and enables the prediction uncertainty easily assessed. The performances of the new model in training, prediction and uncertainty quantification are illustrated by simulated and real data examples.

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arXiv2021

Sparse Deep Learning: A New Framework Immune to Local Traps and Miscalibration

Deep learning has powered recent successes of artificial intelligence (AI). However, the deep neural network, as the basic model of deep learning, has suffered from issues such as local traps and miscalibration. In this paper, we provide a new framework for sparse deep learning, which has the above issues addressed in a coherent way. In particular, we lay down a theoretical foundation for sparse deep learning and propose prior annealing algorithms for learning sparse neural networks. The former has successfully tamed the sparse deep neural network into the framework of statistical modeling, enabling prediction uncertainty correctly quantified. The latter can be asymptotically guaranteed to converge to the global optimum, enabling the validity of the down-stream statistical inference. Numerical result indicates the superiority of the proposed method compared to the existing ones.

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arXiv2021

A Langevinized Ensemble Kalman Filter for Large-Scale Static and Dynamic Learning

The Ensemble Kalman Filter (EnKF) has achieved great successes in data assimilation in atmospheric and oceanic sciences, but its failure in convergence to the right filtering distribution precludes its use for uncertainty quantification. We reformulate the EnKF under the framework of Langevin dynamics, which leads to a new particle filtering algorithm, the so-called Langevinized EnKF. The Langevinized EnKF inherits the forecast-analysis procedure from the EnKF and the use of mini-batch data from the stochastic gradient Langevin-type algorithms, which make it scalable with respect to both the dimension and sample size. We prove that the Langevinized EnKF converges to the right filtering distribution in Wasserstein distance under the big data scenario that the dynamic system consists of a large number of stages and has a large number of samples observed at each stage. We reformulate the Bayesian inverse problem as a dynamic state estimation problem based on the techniques of subsampling and Langevin diffusion process. We illustrate the performance of the Langevinized EnKF using a variety of examples, including the Lorenz-96 model, high-dimensional variable selection, Bayesian deep learning, and Long Short Term Memory (LSTM) network learning with dynamic data.

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arXiv2021

Non-convex Learning via Replica Exchange Stochastic Gradient MCMC

Replica exchange Monte Carlo (reMC), also known as parallel tempering, is an important technique for accelerating the convergence of the conventional Markov Chain Monte Carlo (MCMC) algorithms. However, such a method requires the evaluation of the energy function based on the full dataset and is not scalable to big data. The naïve implementation of reMC in mini-batch settings introduces large biases, which cannot be directly extended to the stochastic gradient MCMC (SGMCMC), the standard sampling method for simulating from deep neural networks (DNNs). In this paper, we propose an adaptive replica exchange SGMCMC (reSGMCMC) to automatically correct the bias and study the corresponding properties. The analysis implies an acceleration-accuracy trade-off in the numerical discretization of a Markov jump process in a stochastic environment. Empirically, we test the algorithm through extensive experiments on various setups and obtain the state-of-the-art results on CIFAR10, CIFAR100, and SVHN in both supervised learning and semi-supervised learning tasks.

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arXiv2021

Accelerating Convergence of Replica Exchange Stochastic Gradient MCMC via Variance Reduction

Replica exchange stochastic gradient Langevin dynamics (reSGLD) has shown promise in accelerating the convergence in non-convex learning; however, an excessively large correction for avoiding biases from noisy energy estimators has limited the potential of the acceleration. To address this issue, we study the variance reduction for noisy energy estimators, which promotes much more effective swaps. Theoretically, we provide a non-asymptotic analysis on the exponential acceleration for the underlying continuous-time Markov jump process; moreover, we consider a generalized Girsanov theorem which includes the change of Poisson measure to overcome the crude discretization based on the Gröwall's inequality and yields a much tighter error in the 2-Wasserstein ($\mathcal{W}_2$) distance. Numerically, we conduct extensive experiments and obtain the state-of-the-art results in optimization and uncertainty estimates for synthetic experiments and image data.

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arXiv2021

Consistent Sparse Deep Learning: Theory and Computation

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training, prediction and interpretation. We propose a frequentist-like method for learning sparse DNNs and justify its consistency under the Bayesian framework: the proposed method could learn a sparse DNN with at most $O(n/\log(n))$ connections and nice theoretical guarantees such as posterior consistency, variable selection consistency and asymptotically optimal generalization bounds. In particular, we establish posterior consistency for the sparse DNN with a mixture Gaussian prior, show that the structure of the sparse DNN can be consistently determined using a Laplace approximation-based marginal posterior inclusion probability approach, and use Bayesian evidence to elicit sparse DNNs learned by an optimization method such as stochastic gradient descent in multiple runs with different initializations. The proposed method is computationally more efficient than standard Bayesian methods for large-scale sparse DNNs. The numerical results indicate that the proposed method can perform very well for large-scale network compression and high-dimensional nonlinear variable selection, both advancing interpretable machine learning.

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arXiv2020

PURE: A Framework for Analyzing Proximity-based Contact Tracing Protocols

Many proximity-based tracing (PCT) protocols have been proposed and deployed to combat the spreading of COVID-19. In this paper, we take a systematic approach to analyze PCT protocols. We identify a list of desired properties of a contact tracing design from the four aspects of Privacy, Utility, Resiliency, and Efficiency (PURE). We also identify two main design choices for PCT protocols: what information patients report to the server, and which party performs the matching. These two choices determine most of the PURE properties and enable us to conduct a comprehensive analysis and comparison of the existing protocols.

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arXiv2020

Markov Neighborhood Regression for High-Dimensional Inference

This paper proposes an innovative method for constructing confidence intervals and assessing p-values in statistical inference for high-dimensional linear models. The proposed method has successfully broken the high-dimensional inference problem into a series of low-dimensional inference problems: For each regression coefficient $β_i$, the confidence interval and $p$-value are computed by regressing on a subset of variables selected according to the conditional independence relations between the corresponding variable $X_i$ and other variables. Since the subset of variables forms a Markov neighborhood of $X_i$ in the Markov network formed by all the variables $X_1,X_2,\ldots,X_p$, the proposed method is coined as Markov neighborhood regression. The proposed method is tested on high-dimensional linear, logistic and Cox regression. The numerical results indicate that the proposed method significantly outperforms the existing ones. Based on the Markov neighborhood regression, a method of learning causal structures for high-dimensional linear models is proposed and applied to identification of drug sensitive genes and cancer driver genes. The idea of using conditional independence relations for dimension reduction is general and potentially can be extended to other high-dimensional or big data problems as well.

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arXiv2020

Stochastic Gradient Langevin Dynamics Algorithms with Adaptive Drifts

Bayesian deep learning offers a principled way to address many issues concerning safety of artificial intelligence (AI), such as model uncertainty,model interpretability, and prediction bias. However, due to the lack of efficient Monte Carlo algorithms for sampling from the posterior of deep neural networks (DNNs), Bayesian deep learning has not yet powered our AI system. We propose a class of adaptive stochastic gradient Markov chain Monte Carlo (SGMCMC) algorithms, where the drift function is biased to enhance escape from saddle points and the bias is adaptively adjusted according to the gradient of past samples. We establish the convergence of the proposed algorithms under mild conditions, and demonstrate via numerical examples that the proposed algorithms can significantly outperform the existing SGMCMC algorithms, such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian Monte Carlo (SGHMC) and preconditioned SGLD, in both simulation and optimization tasks.

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arXiv2020

Stochastic Approximation Hamiltonian Monte Carlo

Recently, the Hamilton Monte Carlo (HMC) has become widespread as one of the more reliable approaches to efficient sample generation processes. However, HMC is difficult to sample in a multimodal posterior distribution because the HMC chain cannot cross energy barrier between modes due to the energy conservation property. In this paper, we propose a Stochastic Approximate Hamilton Monte Carlo (SAHMC) algorithm for generating samples from multimodal density under the Hamiltonian Monte Carlo (HMC) framework. SAHMC can adaptively lower the energy barrier to move the Hamiltonian trajectory more frequently and more easily between modes. Our simulation studies show that the potential for SAHMC to explore a multimodal target distribution more efficiently than HMC based implementations.

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arXiv2020

An Adaptive Empirical Bayesian Method for Sparse Deep Learning

We propose a novel adaptive empirical Bayesian method for sparse deep learning, where the sparsity is ensured via a class of self-adaptive spike-and-slab priors. The proposed method works by alternatively sampling from an adaptive hierarchical posterior distribution using stochastic gradient Markov Chain Monte Carlo (MCMC) and smoothly optimizing the hyperparameters using stochastic approximation (SA). We further prove the convergence of the proposed method to the asymptotically correct distribution under mild conditions. Empirical applications of the proposed method lead to the state-of-the-art performance on MNIST and Fashion MNIST with shallow convolutional neural networks and the state-of-the-art compression performance on CIFAR10 with Residual Networks. The proposed method also improves resistance to adversarial attacks.

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arXiv2020

Extended Stochastic Gradient MCMC for Large-Scale Bayesian Variable Selection

Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed dimension and the log-posterior density is differentiable with respect to the parameters. This paper proposes an extended stochastic gradient MCMC lgoriathm which, by introducing appropriate latent variables, can be applied to more general large-scale Bayesian computing problems, such as those involving dimension jumping and missing data. Numerical studies show that the proposed algorithm is highly scalable and much more efficient than traditional MCMC algorithms. The proposed algorithms have much alleviated the pain of Bayesian methods in big data computing.

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arXiv2018

Fast Bayesian Integrative Learning of Multiple Gene Regulatory Networks for Type 1 Diabetes

Motivated by the need to study the molecular mechanism underlying Type 1 Diabetes (T1D) with the gene expression data collected from both the patients and healthy controls at multiple time points, we propose an innovative method for jointly estimating multiple dependent Gaussian graphical models. Compared to the existing methods, the proposed method has a few significant advantages. First, it includes a meta-analysis procedure to explicitly integrate information across distinct conditions. In contrast, the existing methods often integrate information through prior distributions or penalty function, which is usually less efficient. Second, instead of working on original data, the Bayesian step of the proposed method works on edge-wise scores, through which the proposed method avoids to invert high-dimensional covariance matrices and thus can perform very fast. The edge-wise score forms an equivalent measure of the partial correlation coefficient and thus provides a good summary for the graph structure information contained in the data under each condition. Third, the proposed method can provide an overall uncertainty measure for the edges detected in multiple graphical models, while the existing methods only produce a point estimate or are feasible for very small size problems. We prove consistency of the proposed method under mild conditions and illustrate its performance using simulated and real data examples. The numerical results indicate the superiority of the proposed method over the existing ones in both estimation accuracy and computational efficiency. Extension of the proposed method to joint estimation of multiple mixed graphical models is straightforward.

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arXiv2018

Learning Gene Regulatory Networks with High-Dimensional Heterogeneous Data

The Gaussian graphical model is a widely used tool for learning gene regulatory networks with high-dimensional gene expression data. Most existing methods for Gaussian graphical models assume that the data are homogeneous, i.e., all samples are drawn from a single Gaussian distribution. However, for many real problems, the data are heterogeneous, which may contain some subgroups or come from different resources. This paper proposes to model the heterogeneous data using a mixture Gaussian graphical model, and apply the imputation-consistency algorithm, combining with the $ψ$-learning algorithm, to estimate the parameters of the mixture model and cluster the samples to different subgroups. An integrated Gaussian graphical network is learned across the subgroups along with the iterations of the imputation-consistency algorithm. The proposed method is compared with an existing method for learning mixture Gaussian graphical models as well as a few other methods developed for homogeneous data, such as graphical Lasso, nodewise regression and $ψ$-learning. The numerical results indicate superiority of the proposed method in all aspects of parameter estimation, cluster identification and network construction. The numerical results also indicate generality of the proposed method: it can be applied to homogeneous data without significant harms.

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arXiv2018

A Bayesian Mark Interaction Model for Analysis of Tumor Pathology Images

With the advance of imaging technology, digital pathology imaging of tumor tissue slides is becoming a routine clinical procedure for cancer diagnosis. This process produces massive imaging data that capture histological details in high resolution. Recent developments in deep-learning methods have enabled us to identify and classify individual cells from digital pathology images at large scale. The randomly distributed cells can be considered from a marked point process, where each point is defined by its position and cell type. Reliable statistical approaches to model such marked spatial point patterns can provide new insight into tumor progression and shed light on the biological mechanisms of cancer. In this paper, we consider the problem of modeling spatial correlations among three commonly seen cells (i.e. lymphocyte, stromal, and tumor) observed in tumor pathology images. A novel marking model of marked point processes, with interpretable underlying parameters (some of which are clinically meaningful), is proposed in a Bayesian framework. We use Markov chain Monte Carlo (MCMC) sampling techniques, combined with the double Metropolis-Hastings (DMH) algorithm, to sample from the posterior distribution with an intractable normalizing constant. On the benchmark datasets, we demonstrate how this model-based analysis can lead to sharper inferences than ordinary exploratory analyses. Lastly, we conduct a case study on the pathology images of 188 lung cancer patients from the National Lung Screening Trial. The results show that the spatial correlation between tumor and stromal cells predicts patient prognosis. This statistical methodology not only presents a new model for characterizing spatial correlations in a multi-type spatial point pattern, but also provides a new perspective for understanding the role of cell-cell interactions in cancer progression.

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arXiv2018

An Imputation-Consistency Algorithm for High-Dimensional Missing Data Problems and Beyond

Missing data are frequently encountered in high-dimensional problems, but they are usually difficult to deal with using standard algorithms, such as the expectation-maximization (EM) algorithm and its variants. To tackle this difficulty, some problem-specific algorithms have been developed in the literature, but there still lacks a general algorithm. This work is to fill the gap: we propose a general algorithm for high-dimensional missing data problems. The proposed algorithm works by iterating between an imputation step and a consistency step. At the imputation step, the missing data are imputed conditional on the observed data and the current estimate of parameters; and at the consistency step, a consistent estimate is found for the minimizer of a Kullback-Leibler divergence defined on the pseudo-complete data. For high dimensional problems, the consistent estimate can be found under sparsity constraints. The consistency of the averaged estimate for the true parameter can be established under quite general conditions. The proposed algorithm is illustrated using high-dimensional Gaussian graphical models, high-dimensional variable selection, and a random coefficient model.

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arXiv2015

Parallel and Interacting Stochastic Approximation Annealing algorithms for global optimisation

We present the parallel and interacting stochastic approximation annealing (PISAA) algorithm, a stochastic simulation procedure for global optimisation, that extends and improves the stochastic approximation annealing (SAA) by using population Monte Carlo ideas. The standard SAA algorithm guarantees convergence to the global minimum when a square-root cooling schedule is used; however the efficiency of its performance depends crucially on its self-adjusting mechanism. Because its mechanism is based on information obtained from only a single chain, SAA may present slow convergence in complex optimisation problems. The proposed algorithm involves simulating a population of SAA chains that interact each other in a manner that ensures significant improvement of the self-adjusting mechanism and better exploration of the sampling space. Central to the proposed algorithm are the ideas of (i) recycling information from the whole population of Markov chains to design a more accurate/stable self-adjusting mechanism and (ii) incorporating more advanced proposals, such as crossover operations, for the exploration of the sampling space. PISAA presents a significantly improved performance in terms of convergence. PISAA can be implemented in parallel computing environments if available. We demonstrate the good performance of the proposed algorithm on challenging applications including Bayesian network learning and protein folding. Our numerical comparisons suggest that PISAA outperforms the simulated annealing, stochastic approximation annealing, and annealing evolutionary stochastic approximation Monte Carlo especially in high dimensional or rugged scenarios.

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arXiv2013

Weak Convergence Rates of Population versus Single-Chain Stochastic Approximation MCMC Algorithms

In this paper, we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation MCMC algorithms. Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than O(1/t), where t indexes the number of iterations. This is of interest for practical applications.

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