Paper proposes a new model for noisy tensor completion.
problem Handling noise in tensor completion.
method Tensor ring nuclear norm (TRNN) and least-squares estimator.
result Effective recovery of noisy incomplete tensor data.
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48 results for “noisy entries”
Statistically Optimal and Computationally Efficient Low Rank Tensor Completion from Noisy Entriesstat.ML
New method for estimating low rank tensors from noisy data efficiently.
problem Estimating low rank tensors from noisy entries.
method Polynomial-time computable estimating procedure based on power iteration and spectral initialization.
result Achieves minimax optimal rates of convergence for noisy tensor completion.
Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the `Netflix problem') to structure-from-motion and positioning. We study a low complexity algorithm…
We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless…
Develops methods for statistical inference on matrix linear forms from noisy data.
problem Statistical inference on linear forms of a large matrix from noisy observations.
method Double-sample debiasing and low-rank projection for constructing asymptotically normal estimators.
result Asymptotically normal estimators of linear forms allow for confidence intervals and hypothesis testing.
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…
This paper improves matrix completion by estimating uncertainty and performing inference.
problem Estimating a low-rank matrix with noisy and incomplete data and assessing uncertainty.
method Developed a de-biased estimator procedure to compensate for bias in convex and nonconvex estimators.
result Achieved nearly precise non-asymptotic distributional characterizations for de-biased estimators, enabling valid confidence intervals.
An algorithm finds the maximum entry of a stochastic low-rank matrix from noisy observations.
problem Finding the maximum entry of a stochastic low-rank matrix from sequential observations.
method LowRankElim algorithm, which is a statistical approach to find the maximum entry of a non-negative matrix.
result An upper bound on the regret of $O((K + L) \poly(d) Δ^{-1} \log n)$, where and are the number of rows and columns, is the rank of the matrix, and is the minimum gap.
In the noisy tensor completion problem we observe entries (whose location is chosen uniformly at random) from an unknown tensor . We assume that is entry-wise close to being rank . Our goal is to fill in its missing entries using as few observations as possible. Let $n = \max(n…
New method denoises and fills in missing image data without clean training data.
problem Denoising and inpainting images with noisy, incomplete data.
method Robust Hadamard Autoencoders trained on noisy, incomplete data.
result Autoencoders can perform denoising and inpainting simultaneously.
In this paper, we consider the streaming memory-limited matrix completion problem when the observed entries are noisy versions of a small random fraction of the original entries. We are interested in scenarios where the matrix size is very large so the matrix is very hard to store and manipulate. Here, columns of the o…
New algorithm completes noisy tensors quickly and accurately.
problem Reconstructing low-rank tensors from incomplete and noisy data.
method Two-stage nonconvex gradient descent algorithm.
result Achieves near-optimal statistical guarantees and linear time complexity.
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…
We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for learning the column space of the matrix (tensor) and consequently, our results …
The paper completes matrices from non-uniformly sampled entries, especially when columns are randomly selected and fully observed.
problem Matrix completion from non-uniformly sampled entries, including fully and partially observed columns.
method First, recover the column space from fully observed columns. Then, for each partially observed column, find a vector in the recovered column space with the observed entries. For low-rank matrices, recover them from entries.
result The algorithm can exactly recover a low-rank matrix from merely entries.
New method estimates tensors from noisy data with missing entries.
problem Tensor estimation from noisy observations with missing entries.
method Sign series representation for tensor completion, addressing low- and high-rank signals.
result Excess risk bounds, estimation error rates, and sample complexities established.
The paper improves matrix completion with auxiliary covariates using LS estimation.
problem Matrix completion with noisy data and auxiliary covariates.
method Iterative least squares estimation with statistical properties derived.
result Asymptotic normal distributions of estimators for low-rank matrix and coefficient matrix.
Tensor completion improves EEG-based BCI performance with missing data.
problem Improving classification accuracy in BCI systems with noisy EEG data.
method Tensor decomposition models to infer missing entries in multidimensional EEG datasets.
result Tensor completion algorithms enhance BCI classification accuracy with missing data.
New algorithm recovers high-dimensional linear regression vectors without sparsity assumptions.
problem Efficiently recovering unknown vector β* from noisy linear observations in high dimensions.
method Proposes a polynomial-time algorithm based on LLL lattice basis reduction assuming rational entries with the same denominator.
result Algorithm successfully recovers β* for a large class of distributions and non-zero noise, even with small noise and one observation.
The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal inference studies may require unobserved high-level information which needs to be …
Characterizes uncertainty in low-rank matrix completion with noisy data.
problem Uncertainty quantification in low-rank matrix completion with heterogeneous sub-exponential noise.
method Characterizes the distribution of estimated matrix entries under low-rank estimators with heterogeneous sub-exponential noise.
result Explicit formulas for the distribution of estimated matrix entries under Poisson and Binary noise.
We study contextual linear bandit problems under feature uncertainty, where the features are noisy and have missing entries. To address the challenges posed by this noise, we analyze Bayesian oracles given the observed noisy features. Our Bayesian analysis reveals that the optimal hypothesis can significantly deviate f…
The paper tackles noisy matrix completion by developing new statistics and controlling false discovery rate.
problem Testing multiple linear forms for noisy matrix completion with low-rank structure.
method Introducing new statistics with sharp asymptotics for individual tests, controlling FDR via data splitting and aggregation.
result Valid FDR control can be achieved with guaranteed power under nearly optimal sample size requirements.
This paper improves matrix completion by leveraging element importance and non-uniform sampling.
problem The challenge of completing low-rank matrices from noisy, subsampled measurements.
method Employing leverage scores to characterize element importance and devising a biased sampling procedure.
result Theoretical and empirical evidence shows that a smaller number of entries (about ) can recover a low-rank matrix with noise.
Causal Matrix Completionecon.EM
New method corrects bias in missing data for matrix completion.
problem Missing data bias in matrix completion.
method Causal model and synthetic nearest neighbors (SNN) method.
result Synthetic nearest neighbors (SNN) method provides consistent and normal estimates.
The paper analyzes sparse PCA for incomplete data and proves support recovery conditions.
problem Support recovery in sparse PCA with non-random missing data.
method Semidefinite relaxation of the -regularized PCA problem.
result Support of the sparse leading eigenvector can be recovered with high probability.
We consider the problem of reconstructing a low rank matrix from noisy observations of a subset of its entries. This task has applications in statistical learning, computer vision, and signal processing. In these contexts, "noise" generically refers to any contribution to the data that is not captured by the low-rank m…
Active seriation recovers item order from noisy pairwise similarity measurements.
problem Recovering an unknown item ordering from noisy pairwise similarity measurements.
method Proposes an active seriation algorithm that provably recovers the latent ordering with high probability.
result Establishes optimal performance guarantees for successful recovery under a uniform separation condition.
Improves matrix completion by exploiting biased observation patterns.
problem Matrix completion with biased observation patterns.
method Mask Nearest Neighbor (MNN) algorithm: two-stage process.
result MNN achieves competitive performance with 28x smaller mean squared error.
Paper improves robust spectral clustering for noisy data.
problem Noisy data and heavy-tailed entries hinder traditional clustering methods.
method Robust spectral clustering with rank statistics for latent structure recovery.
result Provable recovery of latent block structure in large data matrices.
Paper improves understanding of noisy matrix completion using convex relaxation and nonconvex optimization.
problem Estimating a low-rank matrix from noisy partial entries.
method Combining convex relaxation and the nonconvex Burer-Monteiro approach.
result Convex relaxation achieves near-optimal estimation errors for noisy matrix completion.
The paper tackles matrix estimation from noisy data, focusing on low-rank matrices.
problem Estimating a low-rank matrix from noisy observations.
method The paper analyzes several estimators, including constrained nuclear-norm minimization, nuclear-norm regularized least squares, and a nonconvex constrained low-rank optimization problem.
result The estimators provide upper error bounds that depend on matrix rank, observed fraction, and matrix sums, and are minimax optimal.
Screening is the problem of finding a superset of the set of non-zero entries in an unknown p-dimensional vector β* given n noisy observations. Naturally, we want this superset to be as small as possible. We propose a novel framework for screening, which we refer to as Multiple Grouping (MuG), that groups variables, pe…
We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is low--rank, and the measurements consist of a subset, either of the exact individ…
Algorithm estimates tensors from sparse observations with robust error bounds.
problem Estimating tensors from sparse noisy observations.
method Similarity-based collaborative filtering algorithm for tensor estimation.
result Achieves sample complexity nearly matching conjectured lower bound.
Study uncovers statistical optimality of nonconvex tensor completion methods.
problem Estimating a low-rank tensor from incomplete and corrupted observations.
method Two-stage estimation algorithm for nonconvex optimization.
result Nonconvex tensor completion achieves optimal accuracy.
New model improves matrix completion under noisy conditions.
problem Noisy matrix completion with structured matrices.
method Introduces permutation-rank model, analyzes SVD algorithm.
result Minimax rates equivalent to low-rank model, consistent estimator.
Nonnegative matrix factorization (NMF) factorizes a non-negative matrix into product of two non-negative matrices, namely a signal matrix and a mixing matrix. NMF suffers from the scale and ordering ambiguities. Often, the source signals can be monotonous in nature. For example, in source separation problem, the source…
Study on tensor signal estimation from incomplete data.
problem Estimating a rank-one tensor signal from noisy, incomplete data.
method Reduction to random matrix model for spectral analysis.
result Loss of performance due to incomplete data.
SDP achieves optimal error in noisy phase synchronization.
problem Phase synchronization with noisy measurements.
method SDP relaxation of Maximum Likelihood Estimation (MLE).
result Achieves error bound of under normalized squared loss, matching minimax lower bound.
Nearly Minimax-Optimal Rates for Noisy Sparse Phase Retrieval via Early-Stopped Mirror Descenteess.SP
Paper studies early-stopped mirror descent for noisy sparse phase retrieval.
problem Recovering a sparse signal from noisy quadratic measurements.
method Early-stopped mirror descent with hyperbolic entropy mirror map.
result Achieves nearly minimax-optimal rate of convergence for -sparse signals.
We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their generative models without prior knowledge of the model statistics and the number of generative models. Two algorithms, both using the -distance between estimated power spectral densities…
New algorithm MR-MISSING learns low-dimensional representations from data with missing entries.
problem Learning low-dimensional representations from data with missing entries.
method Extends matrix completion techniques to handle missing data and non-linear manifold structure.
result Demonstrates effectiveness on synthetic and real data sets, providing theoretical guarantees.
Paper tackles subspace estimation from noisy, partial data matrices.
problem Estimating column space of low-rank matrices from noisy and incomplete data.
method Efficient spectral method on sample Gram matrix with diagonal deletion.
result New statistical guarantees for estimation accuracy.
EKSS uses ensembles of KSS for subspace clustering with theoretical guarantees.
problem Subspace clustering with poor empirical performance and lack of theoretical guarantees.
method EKSS leverages ensembles of KSS via evidence accumulation clustering framework.
result EKSS achieves theoretical recovery guarantees and excellent empirical performance.
New algorithm improves signal reconstruction from noisy measurements with side information.
problem Reconstructing unknown signals from noisy linear measurements with side information.
method Integrates side information into approximate message passing (AMP) and tracks performance using state evolution.
result AMP-SI performance is accurately predicted by state evolution.
Proposes a method for tensor completion with sparse factors and missing data.
problem Recovering nonnegative data from noisy observations with missing values.
method Sparse nonnegative Tucker decomposition with norm for sparsity, maximum likelihood estimation, and error bounds.
result The method outperforms existing tensor-based or matrix-based methods in nonnegative tensor data completion.
This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is on settings where the matrix to be estimated is well-approximated by a product …