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 algorithms estimate matrix norms without matrix multiplication.
Paper analyzes singular subspace estimation in noisy matrix models.
New proof shows norms can't explain deep learning's implicit regularization.
The paper provides guarantees for an alternating minimization algorithm in dictionary learning.
Study shows minimizing the norm of the ERM solution stabilizes kernel ridge-less regression.
Unified analysis of MPLE for Ising models with bounded operator norm or infinity norm.
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A distribution-free analysis shows that by observing just a single linear measure…
We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the ca…
We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the target matrix by the scaled Lasso and then adjusts the matrix estimator to be symmet…
Paper introduces a new approach for matrix completion with improved convergence guarantees.
We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix . Instead of observing a subset of the noisy continuous-valued entries of a matrix , we observe a subset of noisy 1-bit (or binary) measurements generated according to a probabilistic model. W…
Paper proposes an efficient algorithm for clustering with sparse feature selection.
We introduce a new family of matrix norms, the "local max" norms, generalizing existing methods such as the max norm, the trace norm (nuclear norm), and the weighted or smoothed weighted trace norms, which have been extensively used in the literature as regularizers for matrix reconstruction problems. We show that this…
Paper addresses LSTM stability for thermal systems using infinity-norm.
Paper refines null space conditions for nuclear norm minimization in low-rank matrix recovery.
Study on products of large random matrices and neural network gradients stability.
Recently, matrix norm has been widely applied to many areas such as computer vision, pattern recognition, biological study and etc. As an extension of vector norm, the mixed matrix norm is often used to find jointly sparse solutions. Moreover, an efficient iterative algorithm has been designed…
New method estimates neuronal connectivity from partially observed data.
The paper defines curvature at infinity for flat manifolds.
New nonconvex regularizers improve low-rank matrix recovery efficiency and accuracy.
The -support norm is a regularizer which has been successfully applied to sparse vector prediction problems. We show that it belongs to a general class of norms which can be formulated as a parameterized infimum over quadratics. We further extend the -support norm to matrices, and we observe that it is a special …
Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a range of applications and the standard trace-norm relaxation can behave very poorly …
Paper finds a fast method for a matrix norm proximal operator.
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…
The Schatten quasi-norm can be used to bridge the gap between the nuclear norm and rank function, and is the tighter approximation to matrix rank. However, most existing Schatten quasi-norm minimization (SQNM) algorithms, as well as for nuclear norm minimization, are too slow or even impractical for large-scale problem…
The paper tackles matrix estimation from noisy data, focusing on low-rank matrices.
The paper analyzes error bounds and KL properties for noisy matrix recovery problems.
Paper tackles low-rank matrix recovery with column -norm regularization.
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery using a random subset of entries observed with additive noise under general non-unif…
SpINNEr uses matrix regression to analyze brain connectivity, improving accuracy over other methods.
Recently theoretical guarantees have been obtained for matrix completion in the non-uniform sampling regime. In particular, if the sampling distribution aligns with the underlying matrix's leverage scores, then with high probability nuclear norm minimization will exactly recover the low rank matrix. In this article, we…
Study shows how networks converge to minimum norm solutions with regularization.
Exact risk and learning rate curves derived for adaptive SGD on high-dimensional problems.
New method for factor analysis using nuclear and norms.
Estimates parameters of a rectified Gaussian distribution using ReLU networks.
We show that for a complete Ricci shrinker there exists a sequence of points tending to infinity whose norms of the Ricci tensor grow at most linearly.
Social trust prediction addresses the significant problem of exploring interactions among users in social networks. Naturally, this problem can be formulated in the matrix completion framework, with each entry indicating the trustness or distrustness. However, there are two challenges for the social trust problem: 1) t…
Selective sampling improves matrix completion with known structure.
Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being non-convex and discont…
The study computes Bergman kernels and point process asymptotics on Kähler manifolds.
The spectral -support norm enjoys good estimation properties in low rank matrix learning problems, empirically outperforming the trace norm. Its unit ball is the convex hull of rank matrices with unit Frobenius norm. In this paper we generalize the norm to the spectral -support norm, whose additional para…
New nonconvex regularizer speeds up low-rank matrix completion.
Paper proposes DP-Thresholding for estimating sparse high-dimensional covariance matrices with differential privacy.
Paper solves TRPCA problem for tensor data with new tensor nuclear norm.
Noise Collector detects sparse signals from noisy data efficiently.
Efficient algorithms for low-rank bandits using subspace recovery.
Numerous applications in data mining and machine learning require recovering a matrix of minimal rank. Robust principal component analysis (RPCA) is a general framework for handling this kind of problems. Nuclear norm based convex surrogate of the rank function in RPCA is widely investigated. Under certain assumptions,…
We propose a set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the overlapped trace norm and the latent norms with the matrix trace norm, and then, w…