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.
Paper explores robustness of CCS model for matrix completion.
Unified approach for robust low rank matrix estimation with adversaries.
New robust loss functions improve matrix completion accuracy.
New method solves robust matrix completion using nonlinear equations.
Paper analyzes robust matrix completion with efficient nonconvex method and leave-one-out analysis.
New method improves robust low-rank matrix completion for computer vision.
New method for robust matrix completion with mixed data types.
In this paper, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by usin…
Due to the insufficient measurements in the distribution system state estimation (DSSE), full observability and redundant measurements are difficult to achieve without using the pseudo measurements. The matrix completion state estimation (MCSE) combines the matrix completion and power system model to estimate voltage b…
Paper tackles robust matrix completion with heavy-tailed noise.
Transfer knowledge from multiple sources to improve matrix completion.
In this paper we develop a new framework that captures the common landscape underlying the common non-convex low-rank matrix problems including matrix sensing, matrix completion and robust PCA. In particular, we show for all above problems (including asymmetric cases): 1) all local minima are also globally optimal; 2) …
Novel LRMC tackles missing data and outliers in large-scale low-rank data recovery.
A new method for robust matrix completion overcomes limitations of existing approaches.
This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return arbitrarily poor results, if even a single column is corrupted. One direct appl…
UPCA solves data matrix completion with permuted columns.
Recent SVD-free matrix factorization formulations have enabled rank minimization for systems with millions of rows and columns, paving the way for matrix completion in extremely large-scale applications, such as seismic data interpolation. In this paper, we consider matrix completion formulations designed to hit a targ…
This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but little was known for non-convex problems. We propose a novel analytical framework an…
We solve robust regression and matrix completion problems with sparse and low-rank models.
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…
Unified Python package N benchmarks NN-based matrix completion methods.
New estimator for causal effects in large datasets.
Subspace recovery from corrupted and missing data is crucial for various applications in signal processing and information theory. To complete missing values and detect column corruptions, existing robust Matrix Completion (MC) methods mostly concentrate on recovering a low-rank matrix from few corrupted coefficients w…
Efficiently completes low-rank matrices with nearly linear time complexity.
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank approximations, similar algorithms appears recently in the literature under different name…
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…
This paper improves sample efficiency in noisy inductive matrix completion with side-information.
We study the problem of subspace tracking in the presence of missing data (ST-miss). In recent work, we studied a related problem called robust ST. In this work, we show that a simple modification of our robust ST solution also provably solves ST-miss and robust ST-miss. To our knowledge, our result is the first `compl…
Paper proposes iLPA for solving DC composite optimization problems, with applications to matrix completion with outliers.
This paper considers the problem of matrix completion when the observed entries are noisy and contain outliers. It begins with introducing a new optimization criterion for which the recovered matrix is defined as its solution. This criterion uses the celebrated Huber function from the robust statistics literature to do…
Method completes mixed matrix from complex surveys with heterogeneous missingness.
We introduce RSE to measure robustness in estimation problems.
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 …
Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and partially observed signals respectively. We combine the distance preserving measur…
Flat minima lead to better generalization in low-rank matrix recovery models.
Framework for robust matrix estimation with side information.
New guarantees for recovering matrices as low-rank plus sparse from fewer measurements.
The paper studies the problem of recovering a spectrally sparse object from a small number of time domain samples. Specifically, the object of interest with ambient dimension is assumed to be a mixture of complex multi-dimensional sinusoids, while the underlying frequencies can assume any value in the unit disk…
We investigate task clustering for deep-learning based multi-task and few-shot learning in a many-task setting. We propose a new method to measure task similarities with cross-task transfer performance matrix for the deep learning scenario. Although this matrix provides us critical information regarding similarity betw…
Paper tackles robust Euclidean distance estimation with sparse outliers.
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the low-rank and the structural constraints onto separate factors. We formulate the optim…
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation guarantees. Each iteration of the algorithm involves (approximately) finding the left an…
Singular Value Decomposition (and Principal Component Analysis) is one of the most widely used techniques for dimensionality reduction: successful and efficiently computable, it is nevertheless plagued by a well-known, well-documented sensitivity to outliers. Recent work has considered the setting where each point has …
New method improves reliability of recommender systems in face of fake accounts and manipulation.
This paper presents GRASTA (Grassmannian Robust Adaptive Subspace Tracking Algorithm), an efficient and robust online algorithm for tracking subspaces from highly incomplete information. The algorithm uses a robust -norm cost function in order to estimate and track non-stationary subspaces when the streaming data …
Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have applications in a variety of numerical problems including system identification, latent var…
Unified framework for nonconvex matrix completion with linearly parameterized factors.
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…