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Given an ideal triangulation of a connected 3-manifold with non-empty boundary consisting of a disjoint union of tori, a point of the deformation variety is an assignment of complex numbers to the dihedral angles of the tetrahedra subject…
The multiresolution Gaussian process (GP) has gained increasing attention as a viable approach towards improving the quality of approximations in GPs that scale well to large-scale data. Most of the current constructions assume full…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…
We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or equi-generic…
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high…
Deep learning has been widely applied to 3D medical image segmentation tasks. However, due to the diversity of imaging modalities, the high-dimensional nature of the data, and the heterogeneity of anatomical structures, achieving both…
The joint problem of reconstruction / feature extraction is a challenging task in image processing. It consists in performing, in a joint manner, the restoration of an image and the extraction of its features. In this work, we firstly…
The vast applications of deep generative models are anchored in three core capabilities -- generating new instances, reconstructing inputs, and learning compact representations -- across various data types, such as discrete text/protein…
Learning 3D human pose prior is essential to human-centered AI. Here, we present GFPose, a versatile framework to model plausible 3D human poses for various applications. At the core of GFPose is a time-dependent score network, which…
Transfer learning is fundamental for addressing problems in settings with little training data. While several transfer learning approaches have been proposed in 3D, unfortunately, these solutions typically operate on an entire 3D object or…
Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…
Functional Principal Component Analysis (FPCA) has become a widely-used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or in…
3D human pose estimation has wide applications in fields such as intelligent surveillance, motion capture, and virtual reality. However, in real-world scenarios, issues such as occlusion, noise interference, and missing viewpoints can…
For a long time, the point cloud completion task has been regarded as a pure generation task. After obtaining the global shape code through the encoder, a complete point cloud is generated using the shape priorly learnt by the networks.…
Graph Transformers (GTs) have recently achieved significant success in the graph domain by effectively capturing both long-range dependencies and graph inductive biases. However, these methods face two primary challenges: (1) multi-view…
We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue…
Today's typical application of geometric morphometrics to a quantitative comparison of organismal anatomies begins by standardizing samples of homologously labelled point configurations for location, orientation, and scale, and then renders…
Graph convolutional networks (GCNs) have achieved great success in dealing with data of non-Euclidean structures. Their success directly attributes to fitting graph structures effectively to data such as in social media and knowledge…
Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the…