Related papers: A Rotated Hyperbolic Wrapped Normal Distribution f…

In many applications, the curvature of the space supporting the data makes the statistical modelling challenging. In this paper we discuss the construction and use of probability distributions wrapped around manifolds using exponential…

Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean…

In this work, we introduce a novel probabilistic representation of deep learning, which provides an explicit explanation for the Deep Neural Networks (DNNs) in three aspects: (i) neurons define the energy of a Gibbs distribution; (ii) the…

Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…

We propose {\it HumanDiffusion,} a diffusion model trained from humans' perceptual gradients to learn an acceptable range of data for humans (i.e., human-acceptable distribution). Conventional HumanGAN aims to model the human-acceptable…

Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not…

We introduce the Distributed-order fRActional Graph Operating Network (DRAGON), a novel continuous Graph Neural Network (GNN) framework that incorporates distributed-order fractional calculus. Unlike traditional continuous GNNs that utilize…

Learning representations according to the underlying geometry is of vital importance for non-Euclidean data. Studies have revealed that the hyperbolic space can effectively embed hierarchical or tree-like data. In particular, the few past…

Graph Neural Networks (GNNs) are widely used for node classification tasks but often fail to generalize when training and test nodes come from different distributions, limiting their practicality. To overcome this, recent approaches adopt…

In the field of medical images, although various works find Swin Transformer has promising effectiveness on pixelwise dense prediction, whether pre-training these models without using extra dataset can further boost the performance for the…

Recent research in representation learning has shown that hierarchical data lends itself to low-dimensional and highly informative representations in hyperbolic space. However, even if hyperbolic embeddings have gathered attention in image…

Distributionally robust optimization (DRO) is a worst-case framework for stochastic optimization under uncertainty that has drawn fast-growing studies in recent years. When the underlying probability distribution is unknown and observed…

Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…

Node embeddings have become an ubiquitous technique for representing graph data in a low dimensional space. Graph autoencoders, as one of the widely adapted deep models, have been proposed to learn graph embeddings in an unsupervised way by…

We propose an adjusted Wasserstein distributionally robust estimator -- based on a nonlinear transformation of the Wasserstein distributionally robust (WDRO) estimator in statistical learning. The classic WDRO estimator is asymptotically…

Real-world datasets often exhibit imbalanced data distribution, where certain class levels are severely underrepresented. In such cases, traditional pattern classifiers have shown a bias towards the majority class, impeding accurate…

Network representation learning (NRL) technique has been successfully adopted in various data mining and machine learning applications. Random walk based NRL is one popular paradigm, which uses a set of random walks to capture the network…

While all kinds of mixed data -from personal data, over panel and scientific data, to public and commercial data- are collected and stored, building probabilistic graphical models for these hybrid domains becomes more difficult. Users spend…

The performance of deep neural networks typically increases with the number of training images. However, not all images have the same importance towards improved performance and robustness. In fetal brain MRI, abnormalities exacerbate the…