Enhancing Diagnostic Precision in Gastric Bleeding through Automated Lesion Segmentation: A Deep DuS-KFCM Approach

Timely and precise classification and segmentation of gastric bleeding in endoscopic imagery are pivotal for the rapid diagnosis and intervention of gastric complications, which is critical in life-saving medical procedures. Traditional methods grapple with the challenge posed by the indistinguishable intensity values of bleeding tissues adjacent to other gastric structures. Our study seeks to revolutionize this domain by introducing a novel deep learning model, the Dual Spatial Kernelized Constrained Fuzzy C-Means (Deep DuS-KFCM) clustering algorithm. This Hybrid Neuro-Fuzzy system synergizes Neural Networks with Fuzzy Logic to offer a highly precise and efficient identification of bleeding regions. Implementing a two-fold coarse-to-fine strategy for segmentation, this model initially employs the Spatial Kernelized Fuzzy C-Means (SKFCM) algorithm enhanced with spatial intensity profiles and subsequently harnesses the state-of-the-art DeepLabv3+ with ResNet50 architecture to refine the segmentation output. Through extensive experiments across mainstream gastric bleeding and red spots datasets, our Deep DuS-KFCM model demonstrated unprecedented accuracy rates of 87.95%, coupled with a specificity of 96.33%, outperforming contemporary segmentation methods. The findings underscore the model's robustness against noise and its outstanding segmentation capabilities, particularly for identifying subtle bleeding symptoms, thereby presenting a significant leap forward in medical image processing.

Asymptotic Time-Uniform Inference for Parameters in Averaged Stochastic Approximation

We study time-uniform statistical inference for parameters in stochastic approximation (SA), which encompasses a bunch of applications in optimization and machine learning. To that end, we analyze the almost-sure convergence rates of the averaged iterates to a scaled sum of Gaussians in both linear and nonlinear SA problems. We then construct three types of asymptotic confidence sequences that are valid uniformly across all times with coverage guarantees, in an asymptotic sense that the starting time is sufficiently large. These coverage guarantees remain valid if the unknown covariance matrix is replaced by its plug-in estimator, and we conduct experiments to validate our methodology.

Federated Control in Markov Decision Processes

We study problems of federated control in Markov Decision Processes. To solve an MDP with large state space, multiple learning agents are introduced to collaboratively learn its optimal policy without communication of locally collected experience. In our settings, these agents have limited capabilities, which means they are restricted within different regions of the overall state space during the training process. In face of the difference among restricted regions, we firstly introduce concepts of leakage probabilities to understand how such heterogeneity affects the learning process, and then propose a novel communication protocol that we call Federated-Q protocol (FedQ), which periodically aggregates agents' knowledge of their restricted regions and accordingly modifies their learning problems for further training. In terms of theoretical analysis, we justify the correctness of FedQ as a communication protocol, then give a general result on sample complexity of derived algorithms FedQ-X with the RL oracle , and finally conduct a thorough study on the sample complexity of FedQ-SynQ. Specifically, FedQ-X has been shown to enjoy linear speedup in terms of sample complexity when workload is uniformly distributed among agents. Moreover, we carry out experiments in various environments to justify the efficiency of our methods.

Near Minimax-Optimal Distributional Temporal Difference Algorithms and The Freedman Inequality in Hilbert Spaces

Distributional reinforcement learning (DRL) has achieved empirical success in various domains. One of the core tasks in the field of DRL is distributional policy evaluation, which involves estimating the return distribution $\eta^\pi$ for a given policy $\pi$. The distributional temporal difference (TD) algorithm has been accordingly proposed, which is an extension of the temporal difference algorithm in the classic RL literature. In the tabular case, \citet{rowland2018analysis} and \citet{rowland2023analysis} proved the asymptotic convergence of two instances of distributional TD, namely categorical temporal difference algorithm (CTD) and quantile temporal difference algorithm (QTD), respectively. In this paper, we go a step further and analyze the finite-sample performance of distributional TD. To facilitate theoretical analysis, we propose a non-parametric distributional TD algorithm (NTD). For a $\gamma$-discounted infinite-horizon tabular Markov decision process, we show that for NTD we need $\tilde{O}\left(\frac{1}{\varepsilon^{2p}(1-\gamma)^{2p+1}}\right)$ iterations to achieve an $\varepsilon$-optimal estimator with high probability, when the estimation error is measured by the $p$-Wasserstein distance. This sample complexity bound is minimax optimal (up to logarithmic factors) in the case of the $1$-Wasserstein distance. To achieve this, we establish a novel Freedman's inequality in Hilbert spaces, which would be of independent interest. In addition, we revisit CTD, showing that the same non-asymptotic convergence bounds hold for CTD in the case of the $p$-Wasserstein distance.

Finite-Time Decoupled Convergence in Nonlinear Two-Time-Scale Stochastic Approximation

In two-time-scale stochastic approximation (SA), two iterates are updated at varying speeds using different step sizes, with each update influencing the other. Previous studies in linear two-time-scale SA have found that the convergence rates of the mean-square errors for these updates are dependent solely on their respective step sizes, leading to what is referred to as decoupled convergence. However, the possibility of achieving this decoupled convergence in nonlinear SA remains less understood. Our research explores the potential for finite-time decoupled convergence in nonlinear two-time-scale SA. We find that under a weaker Lipschitz condition, traditional analyses are insufficient for achieving decoupled convergence. This finding is further numerically supported by a counterexample. But by introducing an additional condition of nested local linearity, we show that decoupled convergence is still feasible, contingent on the appropriate choice of step sizes associated with smoothness parameters. Our analysis depends on a refined characterization of the matrix cross term between the two iterates and utilizes fourth-order moments to control higher-order approximation errors induced by the local linearity assumption.

Purify++: Improving Diffusion-Purification with Advanced Diffusion Models and Control of Randomness

Adversarial attacks can mislead neural network classifiers. The defense against adversarial attacks is important for AI safety. Adversarial purification is a family of approaches that defend adversarial attacks with suitable pre-processing. Diffusion models have been shown to be effective for adversarial purification. Despite their success, many aspects of diffusion purification still remain unexplored. In this paper, we investigate and improve upon three limiting designs of diffusion purification: the use of an improved diffusion model, advanced numerical simulation techniques, and optimal control of randomness. Based on our findings, we propose Purify++, a new diffusion purification algorithm that is now the state-of-the-art purification method against several adversarial attacks. Our work presents a systematic exploration of the limits of diffusion purification methods.

Estimation and Inference in Distributional Reinforcement Learning

In this paper, we study distributional reinforcement learning from the perspective of statistical efficiency. We investigate distributional policy evaluation, aiming to estimate the complete distribution of the random return (denoted $\eta^\pi$) attained by a given policy $\pi$. We use the certainty-equivalence method to construct our estimator $\hat\eta^\pi$, given a generative model is available. We show that in this circumstance we need a dataset of size $\widetilde O\left(\frac{|\mathcal{S}||\mathcal{A}|}{\epsilon^{2p}(1-\gamma)^{2p+2}}\right)$ to guarantee a $p$-Wasserstein metric between $\hat\eta^\pi$ and $\eta^\pi$ is less than $\epsilon$ with high probability. This implies the distributional policy evaluation problem can be solved with sample efficiency. Also, we show that under different mild assumptions a dataset of size $\widetilde O\left(\frac{|\mathcal{S}||\mathcal{A}|}{\epsilon^{2}(1-\gamma)^{4}}\right)$ suffices to ensure the Kolmogorov metric and total variation metric between $\hat\eta^\pi$ and $\eta^\pi$ is below $\epsilon$ with high probability. Furthermore, we investigate the asymptotic behavior of $\hat\eta^\pi$. We demonstrate that the ``empirical process'' $\sqrt{n}(\hat\eta^\pi-\eta^\pi)$ converges weakly to a Gaussian process in the space of bounded functionals on Lipschitz function class $\ell^\infty(\mathcal{F}_{W_1})$, also in the space of bounded functionals on indicator function class $\ell^\infty(\mathcal{F}_{\mathrm{KS}})$ and bounded measurable function class $\ell^\infty(\mathcal{F}_{\mathrm{TV}})$ when some mild conditions hold. Our findings give rise to a unified approach to statistical inference of a wide class of statistical functionals of $\eta^\pi$.

Constructing Synthetic Treatment Groups without the Mean Exchangeability Assumption

The purpose of this work is to transport the information from multiple randomized controlled trials to the target population where we only have the control group data. Previous works rely critically on the mean exchangeability assumption. However, as pointed out by many current studies, the mean exchangeability assumption might be violated. Motivated by the synthetic control method, we construct a synthetic treatment group for the target population by a weighted mixture of treatment groups of source populations. We estimate the weights by minimizing the conditional maximum mean discrepancy between the weighted control groups of source populations and the target population. We establish the asymptotic normality of the synthetic treatment group estimator based on the sieve semiparametric theory. Our method can serve as a novel complementary approach when the mean exchangeability assumption is violated. Experiments are conducted on synthetic and real-world datasets to demonstrate the effectiveness of our methods.

Enhancing Adversarial Robustness via Score-Based Optimization

Adversarial attacks have the potential to mislead deep neural network classifiers by introducing slight perturbations. Developing algorithms that can mitigate the effects of these attacks is crucial for ensuring the safe use of artificial intelligence. Recent studies have suggested that score-based diffusion models are effective in adversarial defenses. However, existing diffusion-based defenses rely on the sequential simulation of the reversed stochastic differential equations of diffusion models, which are computationally inefficient and yield suboptimal results. In this paper, we introduce a novel adversarial defense scheme named ScoreOpt, which optimizes adversarial samples at test-time, towards original clean data in the direction guided by score-based priors. We conduct comprehensive experiments on multiple datasets, including CIFAR10, CIFAR100 and ImageNet. Our experimental results demonstrate that our approach outperforms existing adversarial defenses in terms of both robustness performance and inference speed.

Training Energy-Based Models with Diffusion Contrastive Divergences

Energy-Based Models (EBMs) have been widely used for generative modeling. Contrastive Divergence (CD), a prevailing training objective for EBMs, requires sampling from the EBM with Markov Chain Monte Carlo methods (MCMCs), which leads to an irreconcilable trade-off between the computational burden and the validity of the CD. Running MCMCs till convergence is computationally intensive. On the other hand, short-run MCMC brings in an extra non-negligible parameter gradient term that is difficult to handle. In this paper, we provide a general interpretation of CD, viewing it as a special instance of our proposed Diffusion Contrastive Divergence (DCD) family. By replacing the Langevin dynamic used in CD with other EBM-parameter-free diffusion processes, we propose a more efficient divergence. We show that the proposed DCDs are both more computationally efficient than the CD and are not limited to a non-negligible gradient term. We conduct intensive experiments, including both synthesis data modeling and high-dimensional image denoising and generation, to show the advantages of the proposed DCDs. On the synthetic data learning and image denoising experiments, our proposed DCD outperforms CD by a large margin. In image generation experiments, the proposed DCD is capable of training an energy-based model for generating the Celab-A $32\times 32$ dataset, which is comparable to existing EBMs.