Zuheng Xu

Xin Ding, Yongwei Wang, Zuheng Xu

Continuous Conditional Generative Adversarial Networks (CcGANs) enable generative modeling conditional on continuous scalar variables (termed regression labels). However, they can produce subpar fake images due to limited training data. Although Negative Data Augmentation (NDA) effectively enhances unconditional and class-conditional GANs by introducing anomalies into real training images, guiding the GANs away from low-quality outputs, its impact on CcGANs is limited, as it fails to replicate negative samples that may occur during the CcGAN sampling. We present a novel NDA approach called Dual-NDA specifically tailored for CcGANs to address this problem. Dual-NDA employs two types of negative samples: visually unrealistic images generated from a pre-trained CcGAN and label-inconsistent images created by manipulating real images' labels. Leveraging these negative samples, we introduce a novel discriminator objective alongside a modified CcGAN training algorithm. Empirical analysis on UTKFace and Steering Angle reveals that Dual-NDA consistently enhances the visual fidelity and label consistency of fake images generated by CcGANs, exhibiting a substantial performance gain over the vanilla NDA. Moreover, by applying Dual-NDA, CcGANs demonstrate a remarkable advancement beyond the capabilities of state-of-the-art conditional GANs and diffusion models, establishing a new pinnacle of performance. Our codes can be found at https://github.com/UBCDingXin/Dual-NDA.

Naitong Chen, Zuheng Xu, Trevor Campbell

A Bayesian coreset is a small, weighted subset of data that replaces the full dataset during Bayesian inference, with the goal of reducing computational cost. Although past work has shown empirically that there often exists a coreset with low inferential error, efficiently constructing such a coreset remains a challenge. Current methods tend to be slow, require a secondary inference step after coreset construction, and do not provide bounds on the data marginal evidence. In this work, we introduce a new method -- sparse Hamiltonian flows -- that addresses all three of these challenges. The method involves first subsampling the data uniformly, and then optimizing a Hamiltonian flow parametrized by coreset weights and including periodic momentum quasi-refreshment steps. Theoretical results show that the method enables an exponential compression of the dataset in a representative model, and that the quasi-refreshment steps reduce the KL divergence to the target. Real and synthetic experiments demonstrate that sparse Hamiltonian flows provide accurate posterior approximations with significantly reduced runtime compared with competing dynamical-system-based inference methods.

Zuheng Xu, Naitong Chen, Trevor Campbell

This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling, density evaluation, and unbiased ELBO estimation. We then show that MixFlows have MCMC-like convergence guarantees when the flow map is ergodic and measure-preserving, and provide bounds on the accumulation of error for practical implementations where the flow map is approximated. Finally, we develop an implementation of MixFlows based on uncorrected discretized Hamiltonian dynamics combined with deterministic momentum refreshment. Simulated and real data experiments show that MixFlows can provide more reliable posterior approximations than several black-box normalizing flows, as well as samples of comparable quality to those obtained from state-of-the-art MCMC methods.

Zuheng Xu, Trevor Campbell

In this paper, we investigate the impact of numerical instability on the reliability of sampling, density evaluation, and evidence lower bound (ELBO) estimation in variational flows. We first empirically demonstrate that common flows can exhibit a catastrophic accumulation of error: the numerical flow map deviates significantly from the exact map -- which affects sampling -- and the numerical inverse flow map does not accurately recover the initial input -- which affects density and ELBO computations. Surprisingly though, we find that results produced by flows are often accurate enough for applications despite the presence of serious numerical instability. In this work, we treat variational flows as dynamical systems, and leverage shadowing theory to elucidate this behavior via theoretical guarantees on the error of sampling, density evaluation, and ELBO estimation. Finally, we develop and empirically test a diagnostic procedure that can be used to validate results produced by numerically unstable flows in practice.

Johnny Xi, Jana Osea, Zuheng Xu et al.

Multimodal representation learning techniques typically rely on paired samples to learn common representations, but paired samples are challenging to collect in fields such as biology where measurement devices often destroy the samples. This paper presents an approach to address the challenge of aligning unpaired samples across disparate modalities in multimodal representation learning. We draw an analogy between potential outcomes in causal inference and potential views in multimodal observations, which allows us to use Rubin's framework to estimate a common space in which to match samples. Our approach assumes we collect samples that are experimentally perturbed by treatments, and uses this to estimate a propensity score from each modality, which encapsulates all shared information between a latent state and treatment and can be used to define a distance between samples. We experiment with two alignment techniques that leverage this distance -- shared nearest neighbours (SNN) and optimal transport (OT) matching -- and find that OT matching results in significant improvements over state-of-the-art alignment approaches in both a synthetic multi-modal setting and in real-world data from NeurIPS Multimodal Single-Cell Integration Challenge.

Kyurae Kim, Zuheng Xu, Jacob R. Gardner et al.

The performance of sequential Monte Carlo (SMC) samplers heavily depends on the tuning of the Markov kernels used in the path proposal. For SMC samplers with unadjusted Markov kernels, standard tuning objectives, such as the Metropolis-Hastings acceptance rate or the expected-squared jump distance, are no longer applicable. While stochastic gradient-based end-to-end optimization has been explored for tuning SMC samplers, they often incur excessive training costs, even for tuning just the kernel step sizes. In this work, we propose a general adaptation framework for tuning the Markov kernels in SMC samplers by minimizing the incremental Kullback-Leibler (KL) divergence between the proposal and target paths. For step size tuning, we provide a gradient- and tuning-free algorithm that is generally applicable for kernels such as Langevin Monte Carlo (LMC). We further demonstrate the utility of our approach by providing a tailored scheme for tuning kinetic LMC used in SMC samplers. Our implementations are able to obtain a full schedule of tuned parameters at the cost of a few vanilla SMC runs, which is a fraction of gradient-based approaches.

Amin Adibi, Xu Cao, Zongliang Ji et al.

The fourth Machine Learning for Health (ML4H) symposium was held in person on December 15th and 16th, 2024, in the traditional, ancestral, and unceded territories of the Musqueam, Squamish, and Tsleil-Waututh Nations in Vancouver, British Columbia, Canada. The symposium included research roundtable sessions to foster discussions between participants and senior researchers on timely and relevant topics for the ML4H community. The organization of the research roundtables at the conference involved 13 senior and 27 junior chairs across 13 tables. Each roundtable session included an invited senior chair (with substantial experience in the field), junior chairs (responsible for facilitating the discussion), and attendees from diverse backgrounds with an interest in the session's topic.

Zuheng Xu, Trevor Campbell

Gaussian variational inference and the Laplace approximation are popular alternatives to Markov chain Monte Carlo that formulate Bayesian posterior inference as an optimization problem, enabling the use of simple and scalable stochastic optimization algorithms. However, a key limitation of both methods is that the solution to the optimization problem is typically not tractable to compute; even in simple settings the problem is nonconvex. Thus, recently developed statistical guarantees -- which all involve the (data) asymptotic properties of the global optimum -- are not reliably obtained in practice. In this work, we provide two major contributions: a theoretical analysis of the asymptotic convexity properties of variational inference with a Gaussian family and the maximum a posteriori (MAP) problem required by the Laplace approximation; and two algorithms -- consistent Laplace approximation (CLA) and consistent stochastic variational inference (CSVI) -- that exploit these properties to find the optimal approximation in the asymptotic regime. Both CLA and CSVI involve a tractable initialization procedure that finds the local basin of the optimum, and CSVI further includes a scaled gradient descent algorithm that provably stays locally confined to that basin. Experiments on nonconvex synthetic and real-data examples show that compared with standard variational and Laplace approximations, both CSVI and CLA improve the likelihood of obtaining the global optimum of their respective optimization problems.

Xin Ding, Yongwei Wang, Zuheng Xu et al.

Knowledge distillation (KD) has been actively studied for image classification tasks in deep learning, aiming to improve the performance of a student based on the knowledge from a teacher. However, applying KD in image regression with a scalar response variable has been rarely studied, and there exists no KD method applicable to both classification and regression tasks yet. Moreover, existing KD methods often require a practitioner to carefully select or adjust the teacher and student architectures, making these methods less flexible in practice. To address the above problems in a unified way, we propose a comprehensive KD framework based on cGANs, termed cGAN-KD. Fundamentally different from existing KD methods, cGAN-KD distills and transfers knowledge from a teacher model to a student model via cGAN-generated samples. This novel mechanism makes cGAN-KD suitable for both classification and regression tasks, compatible with other KD methods, and insensitive to the teacher and student architectures. An error bound for a student model trained in the cGAN-KD framework is derived in this work, providing a theory for why cGAN-KD is effective as well as guiding the practical implementation of cGAN-KD. Extensive experiments on CIFAR-100 and ImageNet-100 show that we can combine state of the art KD methods with the cGAN-KD framework to yield a new state of the art. Moreover, experiments on Steering Angle and UTKFace demonstrate the effectiveness of cGAN-KD in image regression tasks, where existing KD methods are inapplicable.

Xin Ding, Yongwei Wang, Zuheng Xu et al.

This work proposes the continuous conditional generative adversarial network (CcGAN), the first generative model for image generation conditional on continuous, scalar conditions (termed regression labels). Existing conditional GANs (cGANs) are mainly designed for categorical conditions (eg, class labels); conditioning on regression labels is mathematically distinct and raises two fundamental problems:(P1) Since there may be very few (even zero) real images for some regression labels, minimizing existing empirical versions of cGAN losses (aka empirical cGAN losses) often fails in practice;(P2) Since regression labels are scalar and infinitely many, conventional label input methods are not applicable. The proposed CcGAN solves the above problems, respectively, by (S1) reformulating existing empirical cGAN losses to be appropriate for the continuous scenario; and (S2) proposing a naive label input (NLI) method and an improved label input (ILI) method to incorporate regression labels into the generator and the discriminator. The reformulation in (S1) leads to two novel empirical discriminator losses, termed the hard vicinal discriminator loss (HVDL) and the soft vicinal discriminator loss (SVDL) respectively, and a novel empirical generator loss. The error bounds of a discriminator trained with HVDL and SVDL are derived under mild assumptions in this work. Two new benchmark datasets (RC-49 and Cell-200) and a novel evaluation metric (Sliding Fréchet Inception Distance) are also proposed for this continuous scenario. Our experiments on the Circular 2-D Gaussians, RC-49, UTKFace, Cell-200, and Steering Angle datasets show that CcGAN is able to generate diverse, high-quality samples from the image distribution conditional on a given regression label. Moreover, in these experiments, CcGAN substantially outperforms cGAN both visually and quantitatively.