Jun Han

Jun Han, Hui Zhang, Zhengru Zhang

In this paper, we focus on the numerical simulation of phase separation about macromolecule microsphere composite (MMC) hydrogel. The model equation is based on Time-Dependent Ginzburg-Landau (TDGL) equation with reticular free energy. We have put forward two $L^2$ stable schemes to simulate simplified TDGL equation. In numerical experiments, we observe that simulating the whole process of phase separation requires a considerably long time. We also notice that the total free energy changes significantly in initial time and varies slightly in the following time. Based on these properties, we introduce an adaptive strategy based on one of stable scheme mentioned. It is found that the introduction of the time adaptivity cannot only resolve the dynamical changes of the solution accurately but also can significantly save CPU time for the long time simulation.

Zhaoqiang Liu, Subhroshekhar Ghosh, Jun Han et al.

In 1-bit compressive sensing, each measurement is quantized to a single bit, namely the sign of a linear function of an unknown vector, and the goal is to accurately recover the vector. While it is most popular to assume a standard Gaussian sensing matrix for 1-bit compressive sensing, using structured sensing matrices such as partial Gaussian circulant matrices is of significant practical importance due to their faster matrix operations. In this paper, we provide recovery guarantees for a correlation-based optimization algorithm for robust 1-bit compressive sensing with randomly signed partial Gaussian circulant matrices and generative models. Under suitable assumptions, we match guarantees that were previously only known to hold for i.i.d.~Gaussian matrices that require significantly more computation. We make use of a practical iterative algorithm, and perform numerical experiments on image datasets to corroborate our theoretical results.

Hao Zheng, Jun Han, Hongxiao Wang et al.

A large labeled dataset is a key to the success of supervised deep learning, but for medical image segmentation, it is highly challenging to obtain sufficient annotated images for model training. In many scenarios, unannotated images are abundant and easy to acquire. Self-supervised learning (SSL) has shown great potentials in exploiting raw data information and representation learning. In this paper, we propose Hierarchical Self-Supervised Learning (HSSL), a new self-supervised framework that boosts medical image segmentation by making good use of unannotated data. Unlike the current literature on task-specific self-supervised pretraining followed by supervised fine-tuning, we utilize SSL to learn task-agnostic knowledge from heterogeneous data for various medical image segmentation tasks. Specifically, we first aggregate a dataset from several medical challenges, then pre-train the network in a self-supervised manner, and finally fine-tune on labeled data. We develop a new loss function by combining contrastive loss and classification loss and pretrain an encoder-decoder architecture for segmentation tasks. Our extensive experiments show that multi-domain joint pre-training benefits downstream segmentation tasks and outperforms single-domain pre-training significantly. Compared to learning from scratch, our new method yields better performance on various tasks (e.g., +0.69% to +18.60% in Dice scores with 5% of annotated data). With limited amounts of training data, our method can substantially bridge the performance gap w.r.t. denser annotations (e.g., 10% vs.~100% of annotated data).

Jun Han, Martin Renqiang Min, Ligong Han et al.

Learning disentangled representations leads to interpretable models and facilitates data generation with style transfer, which has been extensively studied on static data such as images in an unsupervised learning framework. However, only a few works have explored unsupervised disentangled sequential representation learning due to challenges of generating sequential data. In this paper, we propose recurrent Wasserstein Autoencoder (R-WAE), a new framework for generative modeling of sequential data. R-WAE disentangles the representation of an input sequence into static and dynamic factors (i.e., time-invariant and time-varying parts). Our theoretical analysis shows that, R-WAE minimizes an upper bound of a penalized form of the Wasserstein distance between model distribution and sequential data distribution, and simultaneously maximizes the mutual information between input data and different disentangled latent factors, respectively. This is superior to (recurrent) VAE which does not explicitly enforce mutual information maximization between input data and disentangled latent representations. When the number of actions in sequential data is available as weak supervision information, R-WAE is extended to learn a categorical latent representation of actions to improve its disentanglement. Experiments on a variety of datasets show that our models outperform other baselines with the same settings in terms of disentanglement and unconditional video generation both quantitatively and qualitatively.

Jun Han

Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the expectation of interested functions w.r.t. a target distribution. When it comes to high dimensional probability models and large datasets, efficient approximate inference becomes critically important. In this thesis, we propose a new framework for approximate inference, which combines the advantages of these three frameworks and overcomes their limitations. Our proposed four algorithms are motivated by the recent computational progress of Stein's method. Our proposed algorithms are applied to continuous and discrete distributions under the setting when the gradient information of the target distribution is available or unavailable. Theoretical analysis is provided to prove the convergence of our proposed algorithms. Our adaptive IS algorithm iteratively improves the importance proposal by functionally decreasing the KL divergence between the updated proposal and the target. When the gradient of the target is unavailable, our proposed sampling algorithm leverages the gradient of a surrogate model and corrects induced bias with importance weights, which significantly outperforms other gradient-free sampling algorithms. In addition, our theoretical results enable us to perform the goodness-of-fit test on discrete distributions. At the end of the thesis, we propose an importance-weighted method to efficiently aggregate local models in distributed learning with one-shot communication. Results on simulated and real datasets indicate the statistical efficiency and wide applicability of our algorithm.

Jun Han, Fan Ding, Xianglong Liu et al.

Gradient-based approximate inference methods, such as Stein variational gradient descent (SVGD), provide simple and general-purpose inference engines for differentiable continuous distributions. However, existing forms of SVGD cannot be directly applied to discrete distributions. In this work, we fill this gap by proposing a simple yet general framework that transforms discrete distributions to equivalent piecewise continuous distributions, on which the gradient-free SVGD is applied to perform efficient approximate inference. The empirical results show that our method outperforms traditional algorithms such as Gibbs sampling and discontinuous Hamiltonian Monte Carlo on various challenging benchmarks of discrete graphical models. We demonstrate that our method provides a promising tool for learning ensembles of binarized neural network (BNN), outperforming other widely used ensemble methods on learning binarized AlexNet on CIFAR-10 dataset. In addition, such transform can be straightforwardly employed in gradient-free kernelized Stein discrepancy to perform goodness-of-fit (GOF) test on discrete distributions. Our proposed method outperforms existing GOF test methods for intractable discrete distributions.

Jun Han, Salvator Lombardo, Christopher Schroers et al.

The usage of deep generative models for image compression has led to impressive performance gains over classical codecs while neural video compression is still in its infancy. Here, we propose an end-to-end, deep generative modeling approach to compress temporal sequences with a focus on video. Our approach builds upon variational autoencoder (VAE) models for sequential data and combines them with recent work on neural image compression. The approach jointly learns to transform the original sequence into a lower-dimensional representation as well as to discretize and entropy code this representation according to predictions of the sequential VAE. Rate-distortion evaluations on small videos from public data sets with varying complexity and diversity show that our model yields competitive results when trained on generic video content. Extreme compression performance is achieved when training the model on specialized content.

Jun Han, Qiang Liu

Stein variational gradient decent (SVGD) has been shown to be a powerful approximate inference algorithm for complex distributions. However, the standard SVGD requires calculating the gradient of the target density and cannot be applied when the gradient is unavailable. In this work, we develop a gradient-free variant of SVGD (GF-SVGD), which replaces the true gradient with a surrogate gradient, and corrects the induced bias by re-weighting the gradients in a proper form. We show that our GF-SVGD can be viewed as the standard SVGD with a special choice of kernel, and hence directly inherits the theoretical properties of SVGD. We shed insights on the empirical choice of the surrogate gradient and propose an annealed GF-SVGD that leverages the idea of simulated annealing to improve the performance on high dimensional complex distributions. Empirical studies show that our method consistently outperforms a number of recent advanced gradient-free MCMC methods.

Jun Han, Qiang Liu

We propose a novel adaptive importance sampling algorithm which incorporates Stein variational gradient decent algorithm (SVGD) with importance sampling (IS). Our algorithm leverages the nonparametric transforms in SVGD to iteratively decrease the KL divergence between our importance proposal and the target distribution. The advantages of this algorithm are twofold: first, our algorithm turns SVGD into a standard IS algorithm, allowing us to use standard diagnostic and analytic tools of IS to evaluate and interpret the results; second, we do not restrict the choice of our importance proposal to predefined distribution families like traditional (adaptive) IS methods. Empirical experiments demonstrate that our algorithm performs well on evaluating partition functions of restricted Boltzmann machines and testing likelihood of variational auto-encoders.

Jun Han, Qiang Liu

In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A simple method is to linearly average the parameters of the local models, which, however, tends to be degenerate or not applicable on non-convex models, or models with different parameter dimensions. One more practical strategy is to generate bootstrap samples from the local models, and then learn a joint model based on the combined bootstrap set. Unfortunately, the bootstrap procedure introduces additional noise and can significantly deteriorate the performance. In this work, we propose two variance reduction methods to correct the bootstrap noise, including a weighted M-estimator that is both statistically efficient and practically powerful. Both theoretical and empirical analysis is provided to demonstrate our methods.