Related papers: Data driven Dirichlet sampling on manifolds
Data-Driven Computational Mechanics is a novel computing paradigm that enables the transition from standard data-starved approaches to modern data-rich approaches. At this early stage of development, one can distinguish two mainstream…
While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying…
The recent success of generative adversarial networks and variational learning suggests training a classifier network may work well in addressing the classical two-sample problem. Network-based tests have the computational advantage that…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior…
Sampling from high-dimensional distributions is a fundamental problem in statistical research and practice. However, great challenges emerge when the target density function is unnormalized and contains isolated modes. We tackle this…
High quality upsampling of sparse 3D point clouds is critically useful for a wide range of geometric operations such as reconstruction, rendering, meshing, and analysis. In this paper, we propose a data-driven algorithm that enables an…
We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…
A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or…
In this paper, we present a new method for few-sample supervised feature selection (FS). Our method first learns the manifold of the feature space of each class using kernels capturing multi-feature associations. Then, based on Riemannian…
Subset sampling (also known as Poisson sampling), where the decision to include any specific element in the sample is made independently of all others, is a fundamental primitive in data analytics, enabling efficient approximation by…
As the popularity of graph data increases, there is a growing need to count the occurrences of subgraph patterns of interest, for a variety of applications. Many graphs are massive in scale and also fully dynamic (with insertions and…
We present a new manifold learning algorithm that takes a set of data points lying on or near a lower dimensional manifold as input, possibly with noise, and outputs a simplicial complex that fits the data and the manifold. We have…
Anomalies are samples that significantly deviate from the rest of the data and their detection plays a major role in building machine learning models that can be reliably used in applications such as data-driven design and novelty…
Flow-based models typically define a latent space with dimensionality identical to the observational space. In many problems, however, the data does not populate the full ambient data space that they natively reside in, rather inhabiting a…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
Despite the popularity of the manifold hypothesis, current manifold-learning methods do not support machine learning directly on the latent $d$-dimensional data manifold, as they primarily aim to perform dimensionality reduction into…
This paper investigates the theoretical properties of Dirichlet kernel density estimators for compositional data supported on simplices, for the first time addressing scenarios involving time-dependent observations characterized by strong…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…
We propose a manifold sampling algorithm for minimizing a nonsmooth composition $f= h\circ F$, where we assume $h$ is nonsmooth and may be inexpensively computed in closed form and $F$ is smooth but its Jacobian may not be available. We…