相关论文: Streaming Heteroscedastic Probabilistic PCA with M…

Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the Streaming Tensor Train Approximation (STTA), a new class of algorithms for approximating a given tensor…

When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…

In this work we introduce a new residual for normal linear models that are suitable for situations in which we are dealing with heteroskedasticity of unknown form, they are referred to by principal component analysis (PCA) residuals. These…

Oja's rule [Oja, Journal of mathematical biology 1982] is a well-known biologically-plausible algorithm using a Hebbian-type synaptic update rule to solve streaming principal component analysis (PCA). Computational neuroscientists have…

Scene rearrangement, like table tidying, is a challenging task in robotic manipulation due to the complexity of predicting diverse object arrangements. Web-scale trained generative models such as Stable Diffusion can aid by generating…

A fundamental algorithm for data analytics at the edge of wireless networks is distributed principal component analysis (DPCA), which finds the most important information embedded in a distributed high-dimensional dataset by distributed…

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…

We consider an online version of the robust Principle Component Analysis (PCA), which arises naturally in time-varying source separations such as video foreground-background separation. This paper proposes a compressive online robust PCA…

We seek a generalization of regression and principle component analysis (PCA) in a metric space where data points are distributions metrized by the Wasserstein metric. We recast these analyses as multimarginal optimal transport problems.…

We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables…

The growing adoption of IoT systems in industries like transportation, banking, healthcare, and smart energy has increased reliance on sensor networks. However, anomalies in sensor readings can undermine system reliability, making real-time…

We study principal component analysis (PCA), where given a dataset in $\mathbb{R}^d$ from a distribution, the task is to find a unit vector $v$ that approximately maximizes the variance of the distribution after being projected along $v$.…

This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are…

We study estimation problems in safety-critical applications with streaming data. Since estimation problems can be posed as optimization problems in the probability space, we devise a stochastic projected Wasserstein gradient flow that…

Sparse pseudo-point approximations for Gaussian process (GP) models provide a suite of methods that support deployment of GPs in the large data regime and enable analytic intractabilities to be sidestepped. However, the field lacks a…

Generalization of time series prediction remains an important open issue in machine learning, wherein earlier methods have either large generalization error or local minima. We develop an analytically solvable, unsupervised learning scheme…

Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…

Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…

Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies…

In this paper, we tackle a significant challenge in PCA: heterogeneity. When data are collected from different sources with heterogeneous trends while still sharing some congruency, it is critical to extract shared knowledge while retaining…