Related papers: Low-Precision Streaming PCA
This work studies the problem of sequentially recovering a sparse vector $x_t$ and a vector from a low-dimensional subspace $l_t$ from knowledge of their sum $m_t = x_t + l_t$. If the primary goal is to recover the low-dimensional subspace…
We introduce primed-PCA (pPCA), a two-step algorithm for speeding up the approximation of principal components. This algorithm first runs any approximate-PCA method to get an initial estimate of the principal components (priming), and then…
Post-training quantization (PTQ) is essential for deploying large diffusion transformers on resource-constrained hardware, but aggressive 4-bit quantization significantly degrades generative performance. Low-rank approximation methods have…
Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general,…
When applying principal component analysis (PCA) for dimension reduction, the most varying projections are usually used in order to retain most of the information. For the purpose of anomaly and change detection, however, the least varying…
Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…
Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…
In many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. Latent variable analyses are increasingly employed to systematise these inferences, and Principal…
Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large…
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 this paper, we study the problem of sparse Principal Component Analysis (PCA) in the high-dimensional setting with missing observations. Our goal is to estimate the first principal component when we only have access to partial…
The $k$-principal component analysis ($k$-PCA) problem is a fundamental algorithmic primitive that is widely-used in data analysis and dimensionality reduction applications. In statistical settings, the goal of $k$-PCA is to identify a top…
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…
Principal component analysis (PCA) can be significantly limited when there is too few examples of the target data of interest. We propose a transfer learning approach to PCA (TL-PCA) where knowledge from a related source task is used in…
Principal component analysis (PCA) is a powerful data reductionmethod for Structural Health Monitoring. However, its computa-tional cost and data memory footprint pose a significant challengewhen PCA has to run on limited capability…
We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA),…
Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…
Kernel Principal Component Analysis (KPCA) is a popular dimensionality reduction technique with a wide range of applications. However, it suffers from the problem of poor scalability. Various approximation methods have been proposed in the…
We develop and analyze algorithms for instrumental variable regression by viewing the problem as a conditional stochastic optimization problem. In the context of least-squares instrumental variable regression, our algorithms neither require…
We initiate a broad study of classical problems in the streaming model with insertions and deletions in the setting where we allow the approximation factor $\alpha$ to be much larger than $1$. Such algorithms can use significantly less…