Related papers: Generative Locally Linear Embedding
In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates…
Embedding is a useful technique to project a high-dimensional feature into a low-dimensional space, and it has many successful applications including link prediction, node classification and natural language processing. Current approaches…
We propose a visualization technique that utilizes neural network embeddings and a generative network to reconstruct original data. This method allows for independent manipulation of individual image embeddings through its non-parametric…
Graph embedding provides an efficient solution for graph analysis by converting the graph into a low-dimensional space which preserves the structure information. In contrast to the graph structure data, the i.i.d. node embedding can be…
Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…
Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect of uncertainty quantification. Despite their flexibility and efficiency, classical surrogate models…
Graph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semi-structured data as graphs where nodes correspond to primitives (parts, interest points, segments, etc.)…
We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…
Neural samplers such as variational autoencoders (VAEs) or generative adversarial networks (GANs) approximate distributions by transforming samples from a simple random source---the latent space---to samples from a more complex distribution…
Variational Autoencoder (VAE)-based generative models offer flexible representation learning by incorporating meta-priors, general premises considered beneficial for downstream tasks. However, the incorporated meta-priors often involve…
We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…
Manifold learning techniques play a pivotal role in machine learning by revealing lower-dimensional embeddings within high-dimensional data, thus enhancing both the efficiency and interpretability of data analysis by transforming the data…
Inverse lithography (ILT) is critical for modern semiconductor manufacturing but suffers from highly non-convex objectives that often trap optimization in poor local minima. Generative AI has been explored to warm-start ILT, yet most…
Most existing word embedding methods can be categorized into Neural Embedding Models and Matrix Factorization (MF)-based methods. However some models are opaque to probabilistic interpretation, and MF-based methods, typically solved using…
Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this paper, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data…
Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…
Nonlinear dimensional reduction with the manifold assumption, often called manifold learning, has proven its usefulness in a wide range of high-dimensional data analysis. The significant impact of t-SNE and UMAP has catalyzed intense…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network…
In this paper we propose a new sampling-free approach to solve Bayesian model inversion problems that is an extension of the previously proposed spectral likelihood expansions (SLE) method. Our approach, called stochastic spectral…