A key problem in the application of Archimedean Copulas istheselection oftheparametric formofϕaswellasthelimitations onthe expressiveness of commonly used copula.

A central problem in machine learning and statistics is to model joint densities of random variables from data. Copulas are joint cumulative distribution functions with uniform marginal distributions and are used to capture interdependencies in isolation from marginals. Copulas are widely used within statistics, but have not gained traction in the context of modern deep learning. In this paper, we introduce ACNet, a novel differentiable neural network architecture that enforces structural properties and enables one to learn an important class of copulas--Archimedean Copulas. Unlike Generative Adversarial Networks, Variational Autoencoders, or Normalizing Flow methods, which learn either densities or the generative process directly, ACNet learns a generator of the copula, which implicitly defines the cumulative distribution function of a joint distribution. We give a probabilistic interpretation of the network parameters of ACNet and use this to derive a simple but efficient sampling algorithm for the learned copula. Our experiments show that ACNet is able to both approximate common Archimedean Copulas and generate new copulas which may provide better fits to data.

This is the most common metric in the machine learning community.

A central problem in machine learning and statistics is to model joint densities of random variables from data. Copulas are joint cumulative distribution functions with uniform marginal distributions and are used to capture interdependencies in isolation from marginals. Copulas are widely used within statistics, but have not gained traction in the context of modern deep learning. In this paper, we introduce ACNet, a novel differentiable neural network architecture that enforces structural properties and enables one to learn an important class of copulas--Archimedean Copulas. Unlike Generative Adversarial Networks, Variational Autoencoders, or Normalizing Flow methods, which learn either densities or the generative process directly, ACNet learns a generator of the copula, which implicitly defines the cumulative distribution function of a joint distribution.

Time series data in real-world scenarios contain a substantial amount of nonlinear information, which significantly interferes with the training process of models, leading to decreased prediction performance. Therefore, during the time series forecasting process, extracting the local and global time series patterns and understanding the potential nonlinear features among different time observations are highly significant. To address this challenge, we introduce multi-resolution convolution and deformable convolution operations. By enlarging the receptive field using convolution kernels with different dilation factors to capture temporal correlation information at different resolutions, and adaptively adjusting the sampling positions through additional offset vectors, we enhance the network's ability to capture potential nonlinear features among time observations. Building upon this, we propose ACNet, an adaptive convolutional network designed to effectively model the local and global temporal dependencies and the nonlinear features between observations in multivariate time series. Specifically, by extracting and fusing time series features at different resolutions, we capture both local contextual information and global patterns in the time series. The designed nonlinear feature adaptive extraction module captures the nonlinear features among different time observations in the time series. We evaluated the performance of ACNet across twelve real-world datasets. The results indicate that ACNet consistently achieves state-of-the-art performance in both short-term and long-term forecasting tasks with favorable runtime efficiency.

Anime4KCPP provides an optimized bloc97's Anime4K algorithm version 0.9, and it also provides its own CNN algorithm ACNet, it provides a variety of way to use, including preprocessing and real-time playback, it aims to be a high performance tools to process both image and video. This project is for learning and the exploration task of algorithm course in SWJTU. Anime4K is a simple high-quality anime upscale algorithm. The version 0.9 does not use any machine learning approaches, and can be very fast in real-time processing or pretreatment. ACNet is a CNN based anime upscale algorithm. It aims to provide both high-quality and high-performance.

A central problem in machine learning and statistics is to model joint densities of random variables from data. Copulas are joint cumulative distribution functions with uniform marginal distributions and are used to capture interdependencies in isolation from marginals. Copulas are widely used within statistics, but have not gained traction in the context of modern deep learning. In this paper, we introduce ACNet, a novel differentiable neural network architecture that enforces structural properties and enables one to learn an important class of copulas--Archimedean Copulas. Unlike Generative Adversarial Networks, Variational Autoencoders, or Normalizing Flow methods, which learn either densities or the generative process directly, ACNet learns a generator of the copula, which implicitly defines the cumulative distribution function of a joint distribution. We give a probabilistic interpretation of the network parameters of ACNet and use this to derive a simple but efficient sampling algorithm for the learned copula. Our experiments show that ACNet is able to both approximate common Archimedean Copulas and generate new copulas which may provide better fits to data.

This paper presents a novel adaptively connected neural network (ACNet) to improve the traditional convolutional neural networks (CNNs) {in} two aspects. First, ACNet employs a flexible way to switch global and local inference in processing the internal feature representations by adaptively determining the connection status among the feature nodes (e.g., pixels of the feature maps) \footnote{In a computer vision domain, a node refers to a pixel of a feature map{, while} in {the} graph domain, a node denotes a graph node.}. We can show that existing CNNs, the classical multilayer perceptron (MLP), and the recently proposed non-local network (NLN) \cite{nonlocalnn17} are all special cases of ACNet. Second, ACNet is also capable of handling non-Euclidean data. Extensive experimental analyses on {a variety of benchmarks (i.e.,} ImageNet-1k classification, COCO 2017 detection and segmentation, CUHK03 person re-identification, CIFAR analysis, and Cora document categorization) demonstrate that {ACNet} cannot only achieve state-of-the-art performance but also overcome the limitation of the conventional MLP and CNN \footnote{Corresponding author: Liang Lin (linliang@ieee.org)}. The code is available at \url{https://github.com/wanggrun/Adaptively-Connected-Neural-Networks}.