相关论文: Efficient L1-Norm Principal-Component Analysis via…
Recently, Musco and Woodruff (FOCS, 2017) showed that given an $n \times n$ positive semidefinite (PSD) matrix $A$, it is possible to compute a $(1+\epsilon)$-approximate relative-error low-rank approximation to $A$ by querying…
We present an $O(1)$-round fully-scalable deterministic massively parallel algorithm for computing the min-plus matrix multiplication of unit-Monge matrices. We use this to derive a $O(\log n)$-round fully-scalable massively parallel…
The brain may adopt the strategy of lateral predictive coding (LPC) to construct optimal internal representations for salient features in input sensory signals, reducing the energetic cost of information transmission. Here we first consider…
We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…
Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…
We describe a new algorithm and R package for peak detection in genomic data sets using constrained changepoint algorithms. These detect changes from background to peak regions by imposing the constraint that the mean should alternately…
Learning augmented is a machine learning concept built to improve the performance of a method or model, such as enhancing its ability to predict and generalize data or features, or testing the reliability of the method by introducing noise…
We give a stochastic optimization algorithm that solves a dense $n\times n$ real-valued linear system $Ax=b$, returning $\tilde x$ such that $\|A\tilde x-b\|\leq \epsilon\|b\|$ in time: $$\tilde O((n^2+nk^{\omega-1})\log1/\epsilon),$$ where…
Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…
Fast computation of a matrix product $W^\top X$ is a workhorse of modern LLMs. To make their deployment more efficient, a popular approach is that of using a low-precision approximation $\widehat W$ in place of true $W$ ("weight-only…
Post-selection strategies that discard low-confidence computational results can significantly improve the effective fidelity of quantum error correction at the cost of reduced acceptance rates, which can be particularly useful for offline…
Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis (PCA) and the calculation of truncated singular value decompositions (SVD). The present…
Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…
We propose an iterative algorithm that computes the maximum-likelihood estimate in quantum state tomography. The optimization error of the algorithm converges to zero at an $O ( ( 1 / k ) \log D )$ rate, where $k$ denotes the number of…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
In this paper, elliptic optimal control problems involving the $L^1$-control cost ($L^1$-EOCP) is considered. To numerically discretize $L^1$-EOCP, the standard piecewise linear finite element is employed. However, different from the finite…
We show that any randomized first-order algorithm which minimizes a $d$-dimensional, $1$-Lipschitz convex function over the unit ball must either use $\Omega(d^{2-\delta})$ bits of memory or make $\Omega(d^{1+\delta/6-o(1)})$ queries, for…
This paper establishes the strict optimality in precision for frequency and distribution estimation under local differential privacy (LDP). We prove that a linear estimator with a symmetric and extremal configuration, and a constant support…
Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art…
This work develops a sparse and outlier-insensitive method to fit a one-dimensional subspace that can be used as a replacement for eigenvector methods such as principal component analysis (PCA). The method is insensitive to outlier…