Related papers: Matrix Completion with Quantified Uncertainty thro…

Quantitative studies in many fields involve the analysis of multivariate data of diverse types, including measurements that we may consider binary, ordinal and continuous. One approach to the analysis of such mixed data is to use a copula…

This paper introduces a scalable approach for probabilistic top-k similarity ranking on uncertain vector data. Each uncertain object is represented by a set of vector instances that are assumed to be mutually-exclusive. The objective is to…

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…

We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and…

Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…

This paper provides the best bounds to date on the number of randomly sampled entries required to reconstruct an unknown low rank matrix. These results improve on prior work by Candes and Recht, Candes and Tao, and Keshavan, Montanari, and…

Multiple imputation has become one of the standard methods in drawing inferences in many incomplete data applications. Applications of multiple imputation in relatively more complex settings, such as high-dimensional clustered data, require…

We propose to learn latent graphical models when data have mixed variables and missing values. This model could be used for further data analysis, including regression, classification, ranking etc. It also could be used for imputing missing…

A wide range of systems exhibit high dimensional incomplete data. Accurate estimation of the missing data is often desired, and is crucial for many downstream analyses. Many state-of-the-art recovery methods involve supervised learning…

Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…

Systems subject to uncertain inputs produce uncertain responses. Uncertainty quantification (UQ) deals with the estimation of statistics of the system response, given a computational model of the system and a probabilistic model of its…

Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to…

Low-rank Matrix Completion (LRMC) describes the problem where we wish to recover missing entries of partially observed low-rank matrix. Most existing matrix completion work deals with sampling procedures that are independent of the…

We study the problem of imputing missing values in a dataset, which has important applications in many domains. The key to missing value imputation is to capture the data distribution with incomplete samples and impute the missing values…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…

Missing value imputation is an important practical problem. There is a large body of work on it, but there does not exist any work that formulates the problem in a structured output setting. Also, most applications have constraints on the…

Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large language models by decomposing weight updates into low-rank matrices, significantly reducing storage and computational overhead. While effective, standard LoRA…

Large datasets are often affected by cell-wise outliers in the form of missing or erroneous data. However, discarding any samples containing outliers may result in a dataset that is too small to accurately estimate the covariance matrix.…

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

Environmental, Social, and Governance (ESG) datasets are frequently plagued by significant data gaps, leading to inconsistencies in ESG ratings due to varying imputation methods. This paper explores the application of established machine…