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.
New method for hyperparameter tuning in sparse matrix factorization.
Paper develops a decoder for sparse codes without encoder matrix, achieving optimal recovery.
Ranky solves SVD for large sparse matrices in distributed systems.
New matrix reveals cluster info in sparse directed graphs.
Unified spectral clustering for sparse networks with heterogeneous degrees.
We study a data model in which the data matrix D can be expressed as D = L + S + C, where L is a low rank matrix, S an element-wise sparse matrix and C a matrix whose non-zero columns are outlying data points. To date, robust PCA algorithms have solely considered models with either S or C, but not both. As such, existi…
Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with tra…
New GPU kernels boost deep learning speed and memory efficiency.
This paper develops a new class of nonconvex regularizers for low-rank matrix recovery. Many regularizers are motivated as convex relaxations of the matrix rank function. Our new factor group-sparse regularizers are motivated as a relaxation of the number of nonzero columns in a factorization of the matrix. These nonco…
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where finding a factorization corresponds to finding edges in different layers and valu…
Robust method learns nonlinear structures robustly to noise.
Study confirms sparse coding in whole brain using MRI data.
SKI accelerates GP inference with sparse grids to handle higher dimensions.
Paper proposes a new method to separate low rank and sparse matrices without bias.
Paper introduces a novel matrix-wise sparse MNNLS formulation and algorithm.
New method discovers causal relationships in sparse linear data.
The paper improves Bayesian precision matrix estimation for high-dimensional sparse data.
New method infers graph from dependent matrix data.
New method improves robust low-rank matrix completion for computer vision.
A new NMF variant tackles underdetermined problems with sparse and separable assumptions.
In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming a low-rank structure for the matrix, one natural solution would be to first app…
We develop a method to factorize symmetric sparse Boolean matrices efficiently.
Bayesian model infers factor dimensionality and sparse loading matrix adaptively.
The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem -hard. In this work, we prove that, if the matrix is positive semidefinite and its …
The paper tackles sparse graph learning under Laplacian-related constraints, improving upon existing methods.
New method tackles high-dimensional SBL without covariance matrices.
We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of the elliptical data. To cope with heavy-tailed elliptical distributions, a mult…
We propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models. It uses a sparse precision GP formulation and sparse matrix routines to speed up the computations. Due to the state-space formulation used in the algorithm, the time complexity of the basic SpInGP is linear, and becaus…
Study on signal recovery from low-rank matrix with sparse noise.
Proposes a new method for selecting regularization parameters in sparse precision matrix estimation.
Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection methods. In sparse linear models, LASSO is well-known in extracting the desired …
New guarantees for recovering matrices as low-rank plus sparse from fewer measurements.
A new R package for high-dimensional regression and precision matrix estimation.
Algorithms for Gaussian process, marginal likelihood methods or restricted maximum likelihood methods often require derivatives of log determinant terms. These log determinants are usually parametric with variance parameters of the underlying statistical models. This paper demonstrates that, when the underlying matrix …
We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the modified ADMM method has an optimal convergence rate of , w…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set, adapting it to specific data. V…
New method decomposes corrupted data matrices into sparse and low-rank components.
We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the original data matrix, then one can recover a near optimal solution to the optimiza…
S-VNNs improve VNNs by sparsifying covariance matrices.
We find a closed-form determinant for a specific sparse covariance matrix model.
We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness conditions. Based on projected gradient descent and the double thresholding operator, …
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the resid…
NoTMF forecasts sparse urban road movement speeds with nonstationary temporal matrix factorization.
We consider the problem of matrix completion with side information (\textit{inductive matrix completion}). In real-world applications many side-channel features are typically non-informative making feature selection an important part of the problem. We incorporate feature selection into inductive matrix completion by p…
Dantzig Selector (DS) is widely used in compressed sensing and sparse learning for feature selection and sparse signal recovery. Since the DS formulation is essentially a linear programming optimization, many existing linear programming solvers can be simply applied for scaling up. The DS formulation can be explained a…
A new method for sparse PCA using orthogonal rotations and soft-thresholding.
In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is robust to the noise. We formulate efficient block coordinate descent algorithm and …
Inductive Matrix Completion (IMC) is an important class of matrix completion problems that allows direct inclusion of available features to enhance estimation capabilities. These models have found applications in personalized recommendation systems, multilabel learning, dictionary learning, etc. This paper examines a g…