专家（MOE）模型的混合物是对数据中的异质性建模的流行框架，由于其灵活性以及可用的统计估计和模型选择工具的丰富性，用于统计和机器学习中的回归和分类问题。这种灵活性来自于允许MOE模型中的混合物重量（或门控函数）与专家（或组件密度）一起取决于解释变量。与经典的有限混合物和回归模型的有限混合物相比，这允许由更复杂的数据生成过程产生的数据建模，该过程的混合参数与协变量无关。从计算的角度来看，当解释变量的数量可能大于样本量时，MOE模型在高维度中的使用是挑战的，尤其是从理论的角度来看，文献是对于统计估计和特征选择问题，仍缺乏处理维度诅咒的结果。我们考虑具有软马克斯门控函数和高斯专家的有限MOE模型，用于在异质数据上进行高维回归，并通过Lasso进行$ L_1 $调查的估计。我们专注于拉索估计属性，而不是其特征选择属性。我们在LASSO函数的正规化参数上提供了一个下限，该参数确保了根据Kullback-Leibler损失，Lasso估算器满足了$ L_1 $ -ORACLE不平等。

Modern deep neural networks have achieved superhuman performance in tasks from image classification to game play. Surprisingly, these various complex systems with massive amounts of parameters exhibit the same remarkable structural properties in their last-layer features and classifiers across canonical datasets. This phenomenon is known as "Neural Collapse," and it was discovered empirically by Papyan et al. \cite{Papyan20}. Recent papers have theoretically shown the global solutions to the training network problem under a simplified "unconstrained feature model" exhibiting this phenomenon. We take a step further and prove the Neural Collapse occurrence for deep linear network for the popular mean squared error (MSE) and cross entropy (CE) loss. Furthermore, we extend our research to imbalanced data for MSE loss and present the first geometric analysis for Neural Collapse under this setting.

Air pollution is an emerging problem that needs to be solved especially in developed and developing countries. In Vietnam, air pollution is also a concerning issue in big cities such as Hanoi and Ho Chi Minh cities where air pollution comes mostly from vehicles such as cars and motorbikes. In order to tackle the problem, the paper focuses on developing a solution that can estimate the emitted PM2.5 pollutants by counting the number of vehicles in the traffic. We first investigated among the recent object detection models and developed our own traffic surveillance system. The observed traffic density showed a similar trend to the measured PM2.5 with a certain lagging in time, suggesting a relation between traffic density and PM2.5. We further express this relationship with a mathematical model which can estimate the PM2.5 value based on the observed traffic density. The estimated result showed a great correlation with the measured PM2.5 plots in the urban area context.

Test log-likelihood is commonly used to compare different models of the same data and different approximate inference algorithms for fitting the same probabilistic model. We present simple examples demonstrating how comparisons based on test log-likelihood can contradict comparisons according to other objectives. Specifically, our examples show that (i) conclusions about forecast accuracy based on test log-likelihood comparisons may not agree with conclusions based on other distributional quantities like means; and (ii) that approximate Bayesian inference algorithms that attain higher test log-likelihoods need not also yield more accurate posterior approximations.

Fake videos represent an important misinformation threat. While existing forensic networks have demonstrated strong performance on image forgeries, recent results reported on the Adobe VideoSham dataset show that these networks fail to identify fake content in videos. In this paper, we propose a new network that is able to detect and localize a wide variety of video forgeries and manipulations. To overcome challenges that existing networks face when analyzing videos, our network utilizes both forensic embeddings to capture traces left by manipulation, context embeddings to exploit forensic traces' conditional dependencies upon local scene content, and spatial attention provided by a deep, transformer-based attention mechanism. We create several new video forgery datasets and use these, along with publicly available data, to experimentally evaluate our network's performance. These results show that our proposed network is able to identify a diverse set of video forgeries, including those not encountered during training. Furthermore, our results reinforce recent findings that image forensic networks largely fail to identify fake content in videos.

Artificial intelligence methods including deep neural networks (DNN) can provide rapid molecular classification of tumors from routine histology with accuracy that matches or exceeds human pathologists. Discerning how neural networks make their predictions remains a significant challenge, but explainability tools help provide insights into what models have learned when corresponding histologic features are poorly defined. Here, we present a method for improving explainability of DNN models using synthetic histology generated by a conditional generative adversarial network (cGAN). We show that cGANs generate high-quality synthetic histology images that can be leveraged for explaining DNN models trained to classify molecularly-subtyped tumors, exposing histologic features associated with molecular state. Fine-tuning synthetic histology through class and layer blending illustrates nuanced morphologic differences between tumor subtypes. Finally, we demonstrate the use of synthetic histology for augmenting pathologist-in-training education, showing that these intuitive visualizations can reinforce and improve understanding of histologic manifestations of tumor biology.

Recognizing handwriting images is challenging due to the vast variation in writing style across many people and distinct linguistic aspects of writing languages. In Vietnamese, besides the modern Latin characters, there are accent and letter marks together with characters that draw confusion to state-of-the-art handwriting recognition methods. Moreover, as a low-resource language, there are not many datasets for researching handwriting recognition in Vietnamese, which makes handwriting recognition in this language have a barrier for researchers to approach. Recent works evaluated offline handwriting recognition methods in Vietnamese using images from an online handwriting dataset constructed by connecting pen stroke coordinates without further processing. This approach obviously can not measure the ability of recognition methods effectively, as it is trivial and may be lack of features that are essential in offline handwriting images. Therefore, in this paper, we propose the Transferring method to construct a handwriting image dataset that associates crucial natural attributes required for offline handwriting images. Using our method, we provide a first high-quality synthetic dataset which is complex and natural for efficiently evaluating handwriting recognition methods. In addition, we conduct experiments with various state-of-the-art methods to figure out the challenge to reach the solution for handwriting recognition in Vietnamese.

Image captioning is currently a challenging task that requires the ability to both understand visual information and use human language to describe this visual information in the image. In this paper, we propose an efficient way to improve the image understanding ability of transformer-based method by extending Object Relation Transformer architecture with Attention on Attention mechanism. Experiments on the VieCap4H dataset show that our proposed method significantly outperforms its original structure on both the public test and private test of the Image Captioning shared task held by VLSP.

成功的人工智能系统通常需要大量标记的数据来从文档图像中提取信息。在本文中，我们研究了改善人工智能系统在理解文档图像中的性能的问题，尤其是在培训数据受到限制的情况下。我们通过使用加强学习提出一种新颖的填充方法来解决问题。我们的方法将信息提取模型视为策略网络，并使用策略梯度培训来更新模型，以最大程度地提高补充传统跨凝结损失的综合奖励功能。我们使用标签和专家反馈在四个数据集上进行的实验表明，我们的填充机制始终提高最先进的信息提取器的性能，尤其是在小型培训数据制度中。

预测基金绩效对投资者和基金经理都是有益的，但这是一项艰巨的任务。在本文中，我们测试了深度学习模型是否比传统统计技术更准确地预测基金绩效。基金绩效通常通过Sharpe比率进行评估，该比例代表了风险调整的绩效，以确保基金之间有意义的可比性。我们根据每月收益率数据序列数据计算了年度夏普比率，该数据的时间序列数据为600多个投资于美国上市大型股票的开放式共同基金投资。我们发现，经过现代贝叶斯优化训练的长期短期记忆（LSTM）和封闭式复发单元（GRUS）深度学习方法比传统统计量相比，预测基金的Sharpe比率更高。结合了LSTM和GRU的预测的合奏方法，可以实现所有模型的最佳性能。有证据表明，深度学习和结合能提供有希望的解决方案，以应对基金绩效预测的挑战。