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Uncertainty quantification is crucial for the deployment of image restoration models in safety-critical domains, like autonomous driving and biological imaging. To date, methods for uncertainty visualization have mainly focused on per-pixel…
We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eigenvectors as a step function applied to the spectrum of the…
An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal…
This paper presents a novel algorithm for uncertainty quantification of water distribution system measurement data including nodal demands/consumptions as well as real pressure and flow measurements. This procedure, referred to as…
We present a high-dimensional analysis of three popular algorithms, namely, Oja's method, GROUSE and PETRELS, for subspace estimation from streaming and highly incomplete observations. We show that, with proper time scaling, the…
We study semiparametric factor models in high-dimensional panels where the factor loadings consist of a nonparametric component explained by observed covariates and an idiosyncratic component capturing unobserved heterogeneity. A key…
When confronted with massive data streams, summarizing data with dimension reduction methods such as PCA raises theoretical and algorithmic pitfalls. Principal curves act as a nonlinear generalization of PCA and the present paper proposes a…
We formalize sequential decision-making with information acquisition as the probing-augmented user-centric selection (PUCS) framework, where a learner first probes a subset of arms to obtain side information on resources and rewards, and…
This paper addresses the challenge of efficient principal component analysis (PCA) in high-dimensional spaces by analyzing a compressively sampled variant of Oja's algorithm with adaptive sensing. Traditional PCA methods incur substantial…
Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…
Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and…
Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…
We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors…
Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…
We study the problem of recovering the subspace spanned by the first $k$ principal components of $d$-dimensional data under the streaming setting, with a memory bound of $O(kd)$. Two families of algorithms are known for this problem. The…
In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the…
In this paper, we propose to estimate the invariant subspace across heterogeneous multiple networks using a novel bias-corrected joint spectral embedding algorithm. The proposed algorithm recursively calibrates the diagonal bias of the sum…
Despite recent progress in video generation, inference speed remains a major bottleneck. A common acceleration strategy involves reusing model outputs via caching mechanisms at fixed intervals. However, we find that such fixed-frequency…
Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…
We investigate the computational issues related to the memory size in the estimation of quadratic covariation, taking into account the specifics of financial ultra-high-frequency data. In multivariate price processes, we consider both…