Related papers: Distributional Principal Autoencoders

Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by…

Generative modeling aims to generate new data samples that resemble a given dataset, with diffusion models recently becoming the most popular generative model. One of the main challenges of diffusion models is solving the problem in the…

We construct a new kind of encoder, leveraging the expressive power of diffusion models. In a traditional variational autoencoder, the encoder and decoder jointly negotiate a latent representation of the input. This is made possible by the…

The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…

Distributions are fundamental statistical elements that play essential theoretical and practical roles. The article discusses experiences of training neural networks to classify univariate empirical distributions and to represent them on…

Our goal is to predict future video frames given a sequence of input frames. Despite large amounts of video data, this remains a challenging task because of the high-dimensionality of video frames. We address this challenge by proposing the…

This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and…

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…

In data-driven drug discovery, designing molecular descriptors is a very important task. Deep generative models such as variational autoencoders (VAEs) offer a potential solution by designing descriptors as probabilistic latent vectors…

Diffusion probabilistic models (DPMs) have shown remarkable results on various image synthesis tasks such as text-to-image generation and image inpainting. However, compared to other generative methods like VAEs and GANs, DPMs lack a…

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…

There has been a growing interest in statistical inference from data satisfying the so-called manifold hypothesis, assuming data points in the high-dimensional ambient space to lie in close vicinity of a submanifold of much lower dimension.…

The autoencoder is an unsupervised learning paradigm that aims to create a compact latent representation of data by minimizing the reconstruction loss. However, it tends to overlook the fact that most data (images) are embedded in a…

Conformal Autoencoders are a neural network architecture that imposes orthogonality conditions between the gradients of latent variables to obtain disentangled representations of data. In this work we show that orthogonality relations…

Data-driven flow-field reconstruction typically relies on autoencoder architectures that compress high-dimensional states into low-dimensional latent representations. However, classical approaches such as variational autoencoders (VAEs)…

In this paper, we show that the performance of a learnt generative model is closely related to the model's ability to accurately represent the inferred \textbf{latent data distribution}, i.e. its topology and structural properties. We…

Autoencoders have achieved great success in various computer vision applications. The autoencoder learns appropriate low dimensional image representations through the self-supervised paradigm, i.e., reconstruction. Existing studies mainly…

Denoising diffusion models produce high-fidelity image samples by capturing the image distribution in a progressive manner while initializing with a simple distribution and compounding the distribution complexity. Although these models have…

The Principal Component Analysis (PCA) is a data dimensionality reduction technique well-suited for processing data from sensor networks. It can be applied to tasks like compression, event detection, and event recognition. This technique is…