A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Efficiently reduces rank of non-negative matrices with quadratic time complexity.
PSMM method optimizes matrix sufficient dimension reduction.
New method solves matrix completion problems to certifiable optimality.
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation matrix completion in various fields such as the financial market and the low-ra…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor selection and rank reduction are the most popular strategies for obtaining lower-d…
New method finds efficient low-rank neural networks during training.
New algorithms estimate matrix leverage scores using rank revealing and randomization.
We present Matrix Krasulina, an algorithm for online k-PCA, by generalizing the classic Krasulina's method (Krasulina, 1969) from vector to matrix case. We show, both theoretically and empirically, that the algorithm naturally adapts to data low-rankness and converges exponentially fast to the ground-truth principal su…
Paper develops a new weighted low-rank matrix approximation technique.
Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest eigenvalue of the sample covariance matrix over a sliding window to detect the change. T…
Novel method for efficient low-rank matrix estimation and bandit algorithms.
New methods recover best rank-r approximations from few entries.
This paper sets fundamental limits for rank-one matrix estimation with varying noise levels.
New method compresses neural networks up to 14x with minimal performance loss.
The study proposes a method for risk reduction without relying on risk measurement.
We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs projected gradient descent based on a novel semi-stochastic gradient specifically desi…
The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the objective is to find a low-rank approximation that meets rank and convex constraints, w…
Paper improves robust spectral clustering for noisy data.
Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern high-dimensional data and interactions thereof can be modeled as lying approximat…
Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood (ML) principle, which seeks to maximize the likelihood under the assumption that t…
RFM reduces feature space for linear models, improving sparse recovery.
Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to detect the existence of a low-dimensional manifold of a given dimension that lies …
IRCUR accelerates RPCA by using CUR decomposition for efficient low rank estimation.
Study on tensor signal estimation from incomplete data.
Low-rank approximations of data matrices are an important dimensionality reduction tool in machine learning and regression analysis. We consider the case of categorical variables, where it can be formulated as the problem of finding low-rank approximations to Boolean matrices. In this paper we give what is to the best …
Deep MF extracts hierarchical features from large data sets.
Proposes a new method for multivariate functional regression.
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 establish its rate of convergence and show how it relates to the number of nodes emp…
Method reduces categorical data to lower dimensions using density matrices.
Paper relaxes factor analysis for noisy data, improving robustness.
The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the most important factors in predicting outcomes. However, the economic importance of …
Partial convexification improves tractability of low-rank spectral optimization problems.
Develops a new nonparametric trace regression model for high-dimensional data.
Principal Components Analysis (PCA) is one of the most widely used dimension reduction techniques. Robust PCA (RPCA) refers to the problem of PCA when the data may be corrupted by outliers. Recent work by Cand{è}s, Wright, Li, and Ma defined RPCA as a problem of decomposing a given data matrix into the sum of a low-ran…
New method models matrix time series using tensor CP-decomposition.
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 this paper we develop an approach for dimension reduction that exploits the assumpt…
New algorithms accelerate solving nonlinear matrix decomposition with ReLU.
Nonnegative matrix factorization (NMF), a dimensionality reduction and factor analysis method, is a special case in which factor matrices have low-rank nonnegative constraints. Considering the stochastic learning in NMF, we specifically address the multiplicative update (MU) rule, which is the most popular, but which h…
Discovering the underlying low dimensional structure of high dimensional data has attracted a significant amount of researches recently and has shown to have a wide range of applications. As an effective dimension reduction tool, singular value decomposition is often used to analyze high dimensional matrices, which are…
Randomized SVD shows phase transitions in noisy data.
A new method for distributed PCA using matrix β-mean.
Develops precise expressions for random projections for better machine learning tasks.
The paper analyzes how good initial guesses affect the amount of data needed for low-rank matrix recovery.
Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions. The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR). The key challenges of averaging, adding, and subtracting multipl…
We prove, using the subspace embedding guarantee in a black box way, that one can achieve the spectral norm guarantee for approximate matrix multiplication with a dimensionality-reducing map having rows. Here is the maximum stable rank, i.e. squared ratio of Frobenius and op…
NMF and PCC linked, improving data denoising and feature stability.
SVD training reduces DNN rank and computation load without SVD per step.
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification. Previous theoretical results on randomized reduction methods hinge on strong assumptio…