Related papers: Estimating Dataset Dimension via Singular Metrics …

Existing manifold learning methods are not appropriate for image retrieval task, because most of them are unable to process query image and they have much additional computational cost especially for large scale database. Therefore, we…

We propose a variational autoencoder (VAE)-based model for building forward and inverse structure-property linkages, a problem of paramount importance in computational materials science. Our model systematically combines VAE with…

In this paper, we propose a new method to perform data augmentation in a reliable way in the High Dimensional Low Sample Size (HDLSS) setting using a geometry-based variational autoencoder. Our approach combines a proper latent space…

Layout design with complex constraints is a challenging problem to solve due to the non-uniqueness of the solution and the difficulties in incorporating the constraints into the conventional optimization-based methods. In this paper, we…

Learning from an imbalanced distribution presents a major challenge in predictive modeling, as it generally leads to a reduction in the performance of standard algorithms. Various approaches exist to address this issue, but many of them…

Building fair deep neural networks (DNNs) is a crucial step towards achieving trustworthy artificial intelligence. Delving into deeper factors that affect the fairness of DNNs is paramount and serves as the foundation for mitigating model…

Measuring the similarity between data points often requires domain knowledge, which can in parts be compensated by relying on unsupervised methods such as latent-variable models, where similarity/distance is estimated in a more compact…

The existing approaches to intrinsic dimension estimation usually are not reliable when the data are nonlinearly embedded in the high dimensional space. In this work, we show that the explicit accounting to geometric properties of unknown…

Autoencoders have emerged as powerful models for visualization and dimensionality reduction based on the fundamental assumption that high-dimensional data is generated from a low-dimensional manifold. A critical challenge in autoencoder…

Current deep learning-based manifold learning algorithms such as the variational autoencoder (VAE) require fully sampled data to learn the probability density of real-world datasets. Once learned, the density can be used for a variety of…

In this paper, we target the problem of sufficient dimension reduction with symmetric positive definite matrices valued responses. We propose the intrinsic minimum average variance estimation method and the intrinsic outer product gradient…

The analysis of neural representation has become an integral part of research aiming to better understand the inner workings of neural networks. While there are many different approaches to investigate neural representations, an important…

Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables and these models use a nonlinear function (generator) to map latent samples into the data space.…

A fundamental task in data exploration is to extract simplified low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches to this task…

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…

In the field of machine learning, it is still a critical issue to identify and supervise the learned representation without manually intervening or intuition assistance to extract useful knowledge or serve for the downstream tasks. In this…

It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…

Active area of research in AI is the theory of manifold learning and finding lower-dimensional manifold representation on how we can learn geometry from data for providing better quality curated datasets. There are however various issues…

Quantification of the number of variables needed to locally explain complex data is often the first step to better understanding it. Existing techniques from intrinsic dimension estimation leverage statistical models to glean this…

The variational autoencoder (VAE) is a popular, deep, latent-variable model (DLVM) due to its simple yet effective formulation for modeling the data distribution. Moreover, optimizing the VAE objective function is more manageable than other…