This study explores the classification error of Mixture Discriminant Analysis (MDA) in scenarios where the number of mixture components exceeds those present in the actual data distribution, a condition known as overspecification. We use a two-component Gaussian mixture model within each class to fit data generated from a single Gaussian, analyzing both the algorithmic convergence of the Expectation-Maximization (EM) algorithm and the statistical classification error. We demonstrate that, with suitable initialization, the EM algorithm converges exponentially fast to the Bayes risk at the population level. Further, we extend our results to finite samples, showing that the classification error converges to Bayes risk with a rate $n^{-1/2}$ under mild conditions on the initial parameter estimates and sample size. This work provides a rigorous theoretical framework for understanding the performance of overspecified MDA, which is often used empirically in complex data settings, such as image and text classification. To validate our theory, we conduct experiments on remote sensing datasets.

Small subsets of data with disproportionate influence on model outcomes can have dramatic impacts on conclusions, with a few data points sometimes overturning key findings. While recent work has developed methods to identify these most influential sets, no formal theory exists to determine when their influence reflects genuine problems rather than natural sampling variation. We address this gap by developing a principled framework for assessing the statistical significance of most influential sets. Our theoretical results characterize the extreme value distributions of maximal influence and enable rigorous hypothesis tests for excessive influence, replacing current ad-hoc sensitivity checks. We demonstrate the practical value of our approach through applications across economics, biology, and machine learning benchmarks.

Multi-modal fusion is crucial in medical data research, enabling a comprehensive understanding of diseases and improving diagnostic performance by combining diverse modalities. However, multi-modal fusion faces challenges, including capturing interactions between modalities, addressing missing modalities, handling erroneous modal information, and ensuring interpretability. Many existing researchers tend to design different solutions for these problems, often overlooking the commonalities among them. This paper proposes a novel multi-modal fusion framework that achieves adaptive adjustment over the weights of each modality by introducing the Modal-Domain Attention (MDA). It aims to facilitate the fusion of multi-modal information while allowing for the inclusion of missing modalities or intrinsic noise, thereby enhancing the representation of multi-modal data. We provide visualizations of accuracy changes and MDA weights by observing the process of modal fusion, offering a comprehensive analysis of its interpretability. Extensive experiments on various gastrointestinal disease benchmarks, the proposed MDA maintains high accuracy even in the presence of missing modalities and intrinsic noise. One thing worth mentioning is that the visualization of MDA is highly consistent with the conclusions of existing clinical studies on the dependence of different diseases on various modalities. Code and dataset will be made available.

In many practical applications, it is often difficult and expensive to obtain large-scale labeled data to train state-of-the-art deep neural networks. Therefore, transferring the learned knowledge from a separate, labeled source domain to an unlabeled or sparsely labeled target domain becomes an appealing alternative. However, direct transfer often results in significant performance decay due to domain shift. Domain adaptation (DA) aims to address this problem by aligning the distributions between the source and target domains. Multi-source domain adaptation (MDA) is a powerful and practical extension in which the labeled data may be collected from multiple sources with different distributions. In this survey, we first define various MDA strategies. Then we systematically summarize and compare modern MDA methods in the deep learning era from different perspectives, followed by commonly used datasets and a brief benchmark. Finally, we discuss future research directions for MDA that are worth investigating.

Robustness is pivotal for comprehending, designing, optimizing, and rehabilitating networks, with simulation attacks being the prevailing evaluation method. Simulation attacks are often time-consuming or even impractical, however, a more crucial yet persistently overlooked drawback is that any attack strategy merely provides a potential paradigm of disintegration. The key concern is: in the worst-case scenario or facing the most severe attacks, what is the limit of robustness, referred to as ``Worst Robustness'', for a given system? Understanding a system's worst robustness is imperative for grasping its reliability limits, accurately evaluating protective capabilities, and determining associated design and security maintenance costs. To address these challenges, we introduce the concept of Most Destruction Attack (MDA) based on the idea of knowledge stacking. MDA is employed to assess the worst robustness of networks, followed by the application of an adapted CNN algorithm for rapid worst robustness prediction. We establish the logical validity of MDA and highlight the exceptional performance of the adapted CNN algorithm in predicting the worst robustness across diverse network topologies, encompassing both model and empirical networks.

We use information-theoretic tools to derive a novel analysis of Multi-source Domain Adaptation (MDA) from the representation learning perspective. Concretely, we study joint distribution alignment for supervised MDA with few target labels and unsupervised MDA with pseudo labels, where the latter is relatively hard and less commonly studied. We further provide algorithm-dependent generalization bounds for these two settings, where the generalization is characterized by the mutual information between the parameters and the data. Then we propose a novel deep MDA algorithm, implicitly addressing the target shift through joint alignment. Finally, the mutual information bounds are extended to this algorithm providing a non-vacuous gradient-norm estimation. The proposed algorithm has comparable performance to the state-of-the-art on target-shifted MDA benchmark with improved memory efficiency.

Learning with noisy labels is a vital topic for practical deep learning as models should be robust to noisy open-world datasets in the wild. The state-of-the-art noisy label learning approach JoCoR fails when faced with a large ratio of noisy labels. Moreover, selecting small-loss samples can also cause error accumulation as once the noisy samples are mistakenly selected as small-loss samples, they are more likely to be selected again. In this paper, we try to deal with error accumulation in noisy label learning from both model and data perspectives. We introduce mean point ensemble to utilize a more robust loss function and more information from unselected samples to reduce error accumulation from the model perspective. Furthermore, as the flip images have the same semantic meaning as the original images, we select small-loss samples according to the loss values of flip images instead of the original ones to reduce error accumulation from the data perspective. Extensive experiments on CIFAR-10, CIFAR-100, and large-scale Clothing1M show that our method outperforms state-of-the-art noisy label learning methods with different levels of label noise. Our method can also be seamlessly combined with other noisy label learning methods to further improve their performance and generalize well to other tasks. The code is available in https://github.com/zyh-uaiaaaa/MDA-noisy-label-learning.

Variable importance measures are the main tools to analyze the black-box mechanism of random forests. Although the Mean Decrease Accuracy (MDA) is widely accepted as the most efficient variable importance measure for random forests, little is known about its theoretical properties. In fact, the exact MDA definition varies across the main random forest software. In this article, our objective is to rigorously analyze the behavior of the main MDA implementations. Consequently, we mathematically formalize the various implemented MDA algorithms, and then establish their limits when the sample size increases. In particular, we break down these limits in three components: the first two are related to Sobol indices, which are well-defined measures of a variable contribution to the output variance, widely used in the sensitivity analysis field, as opposed to the third term, whose value increases with dependence within input variables. Thus, we theoretically demonstrate that the MDA does not target the right quantity when inputs are dependent, a fact that has already been noticed experimentally. To address this issue, we define a new importance measure for random forests, the Sobol-MDA, which fixes the flaws of the original MDA. We prove the consistency of the Sobol-MDA and show its good empirical performance through experiments on both simulated and real data. An open source implementation in R and C++ is available online.

First-order stochastic optimization methods are currently the most widely used class of methods for training deep neural networks. However, the choice of the optimizer has become an ad-hoc rule that can significantly affect the performance. For instance, SGD with momentum (SGD+M) is typically used in computer vision (CV) and Adam is used for training transformer models for Natural Language Processing (NLP). Using the wrong method can lead to significant performance degradation. Inspired by the dual averaging algorithm, we propose Modernized Dual Averaging (MDA), an optimizer that is able to perform as well as SGD+M in CV and as Adam in NLP. Our method is not adaptive and is significantly simpler than Adam. We show that MDA induces a decaying uncentered $L_2$-regularization compared to vanilla SGD+M and hypothesize that this may explain why it works on NLP problems where SGD+M fails.