Related papers: Distributional Reduction: Unifying Dimensionality …
Modern high-dimensional methods often adopt the "bet on sparsity" principle, while in supervised multivariate learning statisticians may face "dense" problems with a large number of nonzero coefficients. This paper proposes a novel…
The goal of unsupervised representation learning is to extract a new representation of data, such that solving many different tasks becomes easier. Existing methods typically focus on vectorized data and offer little support for relational…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data…
A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…
Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…
Dimensionality reduction (DR) is a popular method for preparing and analyzing high-dimensional data. Reduced data representations are less computationally intensive and easier to manage and visualize, while retaining a significant…
Dimension reduction (DR) aims to learn low-dimensional representations of high-dimensional data with the preservation of essential information. In the context of manifold learning, we define that the representation after…
Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…
Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein…
We reformulate unsupervised dimension reduction problem (UDR) in the language of tempered distributions, i.e. as a problem of approximating an empirical probability density function by another tempered distribution, supported in a…
Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…
Learning low-dimensional representations from multi-view relational data is challenging when underlying geometries differ across views. We propose Bary-GWMDS, a Gromov-Wasserstein-based method that operates directly on distance matrices to…
We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…
This paper proposes an unsupervised method for learning a unified representation that serves both discriminative and generative purposes. While most existing unsupervised learning approaches focus on a representation for only one of these…
Unsupervised feature selection is an important method to reduce dimensions of high dimensional data without labels, which is benefit to avoid ``curse of dimensionality'' and improve the performance of subsequent machine learning tasks, like…
We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are…
In large-scale distributed scenarios, increasingly complex tasks demand more intelligent collaboration across networks, requiring the joint extraction of structural representations from data samples. However, conventional task-specific…
Recent empirical studies have demonstrated that diffusion models can effectively learn the image distribution and generate new samples. Remarkably, these models can achieve this even with a small number of training samples despite a large…
Unsupervised learning of feature representations is a challenging yet important problem for analyzing a large collection of multimedia data that do not have semantic labels. Recently proposed neural network-based unsupervised learning…