Related papers: Latent Space Non-Linear Statistics

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…

The manifold hypothesis states that many kinds of high-dimensional data are concentrated near a low-dimensional manifold. If the topology of this data manifold is non-trivial, a continuous encoder network cannot embed it in a one-to-one…

Learning useful representations is a key ingredient to the success of modern machine learning. Currently, representation learning mostly relies on embedding data into Euclidean space. However, recent work has shown that data in some domains…

Latent space models have been widely adopted in modeling network data. Developing statistical inference for estimated model parameters enables quantifying associated uncertainty and is pivotal for downstream tasks. Despite recent progress…

Manifold learning is a fundamental task at the core of data analysis and visualisation. It aims to capture the simple underlying structure of complex high-dimensional data by preserving pairwise dissimilarities in low-dimensional…

Graph Neural Networks leverage the connectivity structure of graphs as an inductive bias. Latent graph inference focuses on learning an adequate graph structure to diffuse information on and improve the downstream performance of the model.…

Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…

Generative adversarial networks (GANs) have proven to be surprisingly efficient for image editing by inverting and manipulating the latent code corresponding to a natural image. This property emerges from the disentangled nature of the…

Although Deep Learning (DL) has achieved success in complex Artificial Intelligence (AI) tasks, it suffers from various notorious problems (e.g., feature redundancy, and vanishing or exploding gradients), since updating parameters in…

It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…

Riemannian geometry provides us with powerful tools to explore the latent space of generative models while preserving the underlying structure of the data. The latent space can be equipped it with a Riemannian metric, pulled back from the…

We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on…

What is the shortest path between two data points lying in a high-dimensional space? While the answer is trivial in Euclidean geometry, it becomes significantly more complex when the data lies on a curved manifold -- requiring a Riemannian…

The ability to accurately model random fields plays a critical role in science and engineering for problems involving uncertain, spatially-varying quantities such as heterogeneous material properties and turbulent flows. Deep generative…

Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…

The advent of generative adversarial networks (GAN) has enabled new capabilities in synthesis, interpolation, and data augmentation heretofore considered very challenging. However, one of the common assumptions in most GAN architectures is…

Generative models rely on the key idea that data can be represented in terms of latent variables which are uncorrelated by definition. Lack of correlation is important because it suggests that the latent space manifold is simpler to…

Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…

Circular and non-flat data distributions are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A principled approach to accounting for the…

As machine learning systems get widely adopted for high-stake decisions, quantifying uncertainty over predictions becomes crucial. While modern neural networks are making remarkable gains in terms of predictive accuracy, characterizing…