In this paper, we first study the fundamental limit of clustering networks when a multi-layer network is present. Under the mixture multi-layer stochastic block model (MMSBM), we show that the minimax optimal network clustering error rate, which takes an exponential form and is characterized by the Renyi divergence between the edge probability distributions of the component networks. We propose a novel two-stage network clustering method including a tensor-based initialization algorithm involving both node and sample splitting and a refinement procedure by likelihood-based Lloyd algorithm. Network clustering must be accompanied by node community detection. Our proposed algorithm achieves the minimax optimal network clustering error rate and allows extreme network sparsity under MMSBM. Numerical simulations and real data experiments both validate that our method outperforms existing methods. Oftentimes, the edges of networks carry count-type weights. We then extend our methodology and analysis framework to study the minimax optimal clustering error rate for mixture of discrete distributions including Binomial, Poisson, and multi-layer Poisson networks. The minimax optimal clustering error rates in these discrete mixtures all take the same exponential form characterized by the Renyi divergences. These optimal clustering error rates in discrete mixtures can also be achieved by our proposed two-stage clustering algorithm.

In the field of equation learning, exhaustively considering all possible equations derived from a basis function dictionary is infeasible. Sparse regression and greedy algorithms have emerged as popular approaches to tackle this challenge. However, the presence of multicollinearity poses difficulties for sparse regression techniques, and greedy steps may inadvertently exclude terms of the true equation, leading to reduced identification accuracy. In this article, we present an approach that strikes a balance between comprehensiveness and efficiency in equation learning. Inspired by stepwise regression, our approach combines the coefficient of determination, $R^2$, and the Bayesian model evidence, $p(\boldsymbol y|\mathcal M)$, in a novel way. Our procedure is characterized by a comprehensive search with just a minor reduction of the model space at each iteration step. With two flavors of our approach and the adoption of $p(\boldsymbol y|\mathcal M)$ for bi-directional stepwise regression, we present a total of three new avenues for equation learning. Through three extensive numerical experiments involving random polynomials and dynamical systems, we compare our approach against four state-of-the-art methods and two standard approaches. The results demonstrate that our comprehensive search approach surpasses all other methods in terms of identification accuracy. In particular, the second flavor of our approach establishes an efficient overfitting penalty solely based on $R^2$, which achieves highest rates of exact equation recovery.

We propose a novel algorithm for data augmentation in nonlinear over-parametrized regression. Our data augmentation algorithm borrows from the literature on causality and extends the recently proposed Anchor regression (AR) method for data augmentation, which is in contrast to the current state-of-the-art domain-agnostic solutions that rely on the Mixup literature. Our Anchor Data Augmentation (ADA) uses several replicas of the modified samples in AR to provide more training examples, leading to more robust regression predictions. We apply ADA to linear and nonlinear regression problems using neural networks. ADA is competitive with state-of-the-art C-Mixup solutions.

Fox News Flash top entertainment and celebrity headlines are here. The classic romantic comedy follows nine love stories, including tales about a woman whose husband is cheating on her, a man who's in love with his best friend's wife, and a little boy trying to profess his love to his crush. In its initial run, the movie made nearly $250 million at the global box office, and has since become a must-watch movie during the holiday season. Here is what the film's cast has been up to since its November 2003 release date. "Love Actually" is celebrating its 20th anniversary.

Geospatial observations combined with computational models have become key to understanding the physical systems of our environment and enable the design of best practices to reduce societal harm. Cloud-based deployments help to scale up these modeling and AI workflows. Yet, for practitioners to make robust conclusions, model tuning and testing is crucial, a resource intensive process which involves the variation of model input variables. We have developed the Variational Exploration Module which facilitates the optimization and validation of modeling workflows deployed in the cloud by orchestrating workflow executions and using Bayesian and machine learning-based methods to analyze model behavior. User configurations allow the combination of diverse sampling strategies in multi-agent environments. The flexibility and robustness of the model-agnostic module is demonstrated using real-world applications.

We present a framework SCStory for online story discovery, that helps people digest rapidly published news article streams in real-time without human annotations. To organize news article streams into stories, existing approaches directly encode the articles and cluster them based on representation similarity. However, these methods yield noisy and inaccurate story discovery results because the generic article embeddings do not effectively reflect the story-indicative semantics in an article and cannot adapt to the rapidly evolving news article streams. SCStory employs self-supervised and continual learning with a novel idea of story-indicative adaptive modeling of news article streams. With a lightweight hierarchical embedding module that first learns sentence representations and then article representations, SCStory identifies story-relevant information of news articles and uses them to discover stories. The embedding module is continuously updated to adapt to evolving news streams with a contrastive learning objective, backed up by two unique techniques, confidence-aware memory replay and prioritized-augmentation, employed for label absence and data scarcity problems. Thorough experiments on real and the latest news data sets demonstrate that SCStory outperforms existing state-of-the-art algorithms for unsupervised online story discovery.

Overparameterized large-scale language models have impressive generalization performance of in-context few-shot learning. However, most language models allocate the same amount of parameters or computation to each token, disregarding the complexity or importance of the input data. We argue that in language model pretraining, a variable amount of computation should be assigned to different tokens, and this can be efficiently achieved via a simple routing mechanism. Different from conventional early stopping techniques where tokens can early exit at only early layers, we propose a more general method that dynamically skips the execution of a layer (or module) for any input token with a binary router. In our extensive evaluation across 24 NLP tasks, we demonstrate that the proposed method can significantly improve the 1-shot performance compared to other competitive baselines only at mild extra cost for inference.

Adversarial attacks meticulously generate minuscule, imperceptible perturbations to images to deceive neural networks. Counteracting these, adversarial purification methods seek to transform adversarial input samples into clean output images to defend against adversarial attacks. Nonetheless, extent generative models fail to effectively eliminate adversarial perturbations, yielding less-than-ideal purification results. We emphasize the potential threat of residual adversarial perturbations to target models, quantitatively establishing a relationship between perturbation scale and attack capability. Notably, the residual perturbations on the purified image primarily stem from the same-position patch and similar patches of the adversarial sample. We propose a novel adversarial purification approach named Information Mask Purification (IMPure), aims to extensively eliminate adversarial perturbations. To obtain an adversarial sample, we first mask part of the patches information, then reconstruct the patches to resist adversarial perturbations from the patches. We reconstruct all patches in parallel to obtain a cohesive image. Then, in order to protect the purified samples against potential similar regional perturbations, we simulate this risk by randomly mixing the purified samples with the input samples before inputting them into the feature extraction network. Finally, we establish a combined constraint of pixel loss and perceptual loss to augment the model's reconstruction adaptability. Extensive experiments on the ImageNet dataset with three classifier models demonstrate that our approach achieves state-of-the-art results against nine adversarial attack methods. Implementation code and pre-trained weights can be accessed at \textcolor{blue}{https://github.com/NoWindButRain/IMPure}.

The wide adoption and usage of generative artificial intelligence (AI) models, particularly ChatGPT, has sparked a surge in research exploring their potential applications in the educational landscape. This survey examines academic literature published between November, 2022, and July, 2023, specifically targeting high-impact research from Scopus-indexed Q1 and Q2 journals. This survey delves into the practical applications and implications of generative AI models across a diverse range of educational contexts. Through a comprehensive and rigorous evaluation of recent academic literature, this survey seeks to illuminate the evolving role of generative AI models, particularly ChatGPT, in education. By shedding light on the potential benefits, challenges, and emerging trends in this dynamic field, the survey endeavors to contribute to the understanding of the nexus between artificial intelligence and education. The findings of this review will empower educators, researchers, and policymakers to make informed decisions about the integration of AI technologies into learning environments.

In March 2020, the World Health Organisation declared COVID-19 a global pandemic as it spread to nearly every country. By mid-2021, India had introduced three vaccines: Covishield, Covaxin, and Sputnik. To ensure successful vaccination in a densely populated country like India, understanding public sentiment was crucial. Social media, particularly Reddit with over 430 million users, played a vital role in disseminating information. This study employs data mining techniques to analyze Reddit data and gauge Indian sentiments towards COVID-19 vaccines. Using Python's Text Blob library, comments are annotated to assess general sentiments. Results show that most Reddit users in India expressed neutrality about vaccination, posing a challenge for the Indian government's efforts to vaccinate a significant portion of the population.