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.
The paper reviews Hankel low-rank methods for time series analysis and forecasting.
Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense but are assumed to have a low-rank structure when matricized appropriately. Such a…
Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal processing and bioinformatics. Recently, much progress has been made in theories, algori…
Unified error analysis for low-rank approximation improves data assimilation performance.
Paper introduces robust methods for consensus ranking in AI systems.
Study shows generative priors improve rank-one matrix recovery with optimal sample complexity.
New algorithms improve RPCA for large matrices with upper rank bounds.
Efficient tensor decomposition for count data models achieves near-optimal multiway analysis.
TripleSurv improves survival analysis by ranking samples with time-adaptive adjustments.
This work analyzes tree-based methods from a ranking perspective, providing insights and new statistics.
We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well as the less-studied max-no…
Semidefinite programs (SDP) are important in learning and combinatorial optimization with numerous applications. In pursuit of low-rank solutions and low complexity algorithms, we consider the Burer--Monteiro factorization approach for solving SDPs. We show that all approximate local optima are global optima for the pe…
Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The low-rank tensors are fed into the alternative direction multiplier method (ADMM) …
Paper analyzes robust matrix completion with efficient nonconvex method and leave-one-out analysis.
In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a rank constraint. We consider a matrix completion problem for Hankel matrices an…
Advances robust principal component analysis with transformed ℓ1 regularization.
Paper proposes a new method to separate low rank and sparse matrices without bias.
Experiment shows author rankings can improve peer review scores.
Paper stabilizes persistent homology rank functions for statistical inference.
SurvCORN predicts survival curves using conditional ordinal ranking networks.
TGCCA analyzes higher-order tensors using orthogonal rank-R CP decomposition.
IRCUR accelerates RPCA by using CUR decomposition for efficient low rank estimation.
Constructs explicit p-harmonic functions on specific Lie groups.
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…
New bound for neural networks with full-rank weights, independent of network width.
The purpose of this study was to build a customer selection model based on 20 dimensions, including customer codes, total contribution, assets, deposit, profit, profit rate, trading volume, trading amount, turnover rate, order amount, withdraw amount, withdraw rate, process fee, process fee submitted, process fee retai…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume that the input partially-observed matrix is low rank. The success of these methods…
GD learns matrix solutions incrementally, revealing insights into generalization.
Novel Fréchet regression method handles errors-in-variables with low-rank covariates.
Exact pairwise ranking is achievable but not possible under noisy comparisons.
ScaledGD improves gradient descent for ill-conditioned low-rank matrix estimation.
Paper simplifies calculating causation probabilities and ranks root causes.
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can stabilize invariants characterizing these objects. We outline how so called contour fun…
Dictionary learning and component analysis models are fundamental for learning compact representations that are relevant to a given task (feature extraction, dimensionality reduction, denoising, etc.). The model complexity is encoded by means of specific structure, such as sparsity, low-rankness, or nonnegativity. Unfo…
We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis and the ordinary least squares, we consider an efficient nuclear norm penalized …
New method tests independence using ROC analysis and bipartite ranking.
We explore the algebraic structure of the solution space of convex optimization problem Constrained Minimum Trace Factor Analysis (CMTFA), when the population covariance matrix has an additional latent graphical constraint, namely, a latent star topology. In particular, we have shown that CMTFA can have either a …
Paper introduces a new histogram estimator for nonparametric density estimation that improves performance.
This paper addresses the problem of rank aggregation, which aims to find a consensus ranking among multiple ranking inputs. Traditional rank aggregation methods are deterministic, and can be categorized into explicit and implicit methods depending on whether rank information is explicitly or implicitly utilized. Surpri…
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, and other data types. This framework encompasses many well known techniques in da…
New algorithm learns low-rank matrices with linear number of samples.
This paper introduces depth functions for ranking data, improving statistical summaries.
Learning-to-rank techniques have proven to be extremely useful for prioritization problems, where we rank items in order of their estimated probabilities, and dedicate our limited resources to the top-ranked items. This work exposes a serious problem with the state of learning-to-rank algorithms, which is that they are…
Optimal rank-adaptive matrix estimation from linear measurements.
We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank SVD for matrices and multi-linear SVD for tensors. Then, building …
We simplify SSL by approximating redundant structural components with low-rank factorization.
Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called robust kernel principal component analysis (RKPCA) to decompose a partially cor…
Develops PRPCA for smooth image recovery combining low-rank and smoothness.