scholarly journals Estimation of copulas via Maximum Mean Discrepancy

Author(s):  
Pierre Alquier ◽  
Badr-Eddine Chérief-Abdellatif ◽  
Alexis Derumigny ◽  
Jean-David Fermanian
Author(s):  
Jieyang Peng ◽  
Andreas Kimmig ◽  
Zhibin Niu ◽  
Jiahai Wang ◽  
Xiufeng Liu ◽  
...  

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 142
Author(s):  
Jiancheng Sun

The analysis of chaotic time series is usually a challenging task due to its complexity. In this communication, a method of complex network construction is proposed for univariate chaotic time series, which provides a novel way to analyze time series. In the process of complex network construction, how to measure the similarity between the time series is a key problem to be solved. Due to the complexity of chaotic systems, the common metrics is hard to measure the similarity. Consequently, the proposed method first transforms univariate time series into high-dimensional phase space to increase its information, then uses Gaussian mixture model (GMM) to represent time series, and finally introduces maximum mean discrepancy (MMD) to measure the similarity between GMMs. The Lorenz system is used to validate the correctness and effectiveness of the proposed method for measuring the similarity.


2020 ◽  
Vol 34 (07) ◽  
pp. 11848-11855 ◽  
Author(s):  
Badri Patro ◽  
Anupriy ◽  
Vinay Namboodiri

In this paper, we aim to obtain improved attention for a visual question answering (VQA) task. It is challenging to provide supervision for attention. An observation we make is that visual explanations as obtained through class activation mappings (specifically Grad-CAM) that are meant to explain the performance of various networks could form a means of supervision. However, as the distributions of attention maps and that of Grad-CAMs differ, it would not be suitable to directly use these as a form of supervision. Rather, we propose the use of a discriminator that aims to distinguish samples of visual explanation and attention maps. The use of adversarial training of the attention regions as a two-player game between attention and explanation serves to bring the distributions of attention maps and visual explanations closer. Significantly, we observe that providing such a means of supervision also results in attention maps that are more closely related to human attention resulting in a substantial improvement over baseline stacked attention network (SAN) models. It also results in a good improvement in rank correlation metric on the VQA task. This method can also be combined with recent MCB based methods and results in consistent improvement. We also provide comparisons with other means for learning distributions such as based on Correlation Alignment (Coral), Maximum Mean Discrepancy (MMD) and Mean Square Error (MSE) losses and observe that the adversarial loss outperforms the other forms of learning the attention maps. Visualization of the results also confirms our hypothesis that attention maps improve using this form of supervision.


Author(s):  
D. F. Luna-Naranjo ◽  
J. V. Hurtado-Rincon ◽  
D. Cárdenas-Peña ◽  
V. H. Castro ◽  
H. F. Torres ◽  
...  

2019 ◽  
Vol 12 (S8) ◽  
Author(s):  
Zhixun Zhao ◽  
Hui Peng ◽  
Xiaocai Zhang ◽  
Yi Zheng ◽  
Fang Chen ◽  
...  

Abstract Background The early diagnosis of lung cancer has been a critical problem in clinical practice for a long time and identifying differentially expressed gene as disease marker is a promising solution. However, the most existing gene differential expression analysis (DEA) methods have two main drawbacks: First, these methods are based on fixed statistical hypotheses and not always effective; Second, these methods can not identify a certain expression level boundary when there is no obvious expression level gap between control and experiment groups. Methods This paper proposed a novel approach to identify marker genes and gene expression level boundary for lung cancer. By calculating a kernel maximum mean discrepancy, our method can evaluate the expression differences between normal, normal adjacent to tumor (NAT) and tumor samples. For the potential marker genes, the expression level boundaries among different groups are defined with the information entropy method. Results Compared with two conventional methods t-test and fold change, the top average ranked genes selected by our method can achieve better performance under all metrics in the 10-fold cross-validation. Then GO and KEGG enrichment analysis are conducted to explore the biological function of the top 100 ranked genes. At last, we choose the top 10 average ranked genes as lung cancer markers and their expression boundaries are calculated and reported. Conclusion The proposed approach is effective to identify gene markers for lung cancer diagnosis. It is not only more accurate than conventional DEA methods but also provides a reliable method to identify the gene expression level boundaries.


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