Related papers: Adaptive Multinomial Matrix Completion
The inductive matrix completion (IMC) problem is to recover a low rank matrix from few observed entries while incorporating prior knowledge about its row and column subspaces. In this work, we make three contributions to the IMC problem:…
This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse…
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are…
Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…
We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on $n$ independent samples from them. Curiously, we show that estimating the IPM itself between…
Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of…
The learning of the deep networks largely relies on the data with human-annotated labels. In some label insufficient situations, the performance degrades on the decision boundary with high data density. A common solution is to directly…
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…
Medical imaging classifiers can achieve high predictive accuracy, but quantifying their uncertainty remains an unresolved challenge, which prevents their deployment in medical clinics. We present an algorithm that can modify any classifier…
This paper studies inference in linear models with a high-dimensional parameter matrix that can be well-approximated by a ``spiked low-rank matrix.'' A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero…
The task of predicting missing entries of a matrix, from a subset of known entries, is known as \textit{matrix completion}. In today's data-driven world, data completion is essential whether it is the main goal or a pre-processing step.…
The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the…
We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Motivated by the problem of tuning hyperparameters in machine learning, we present a new approach for gradually and adaptively optimizing an unknown function using estimated gradients. We validate the empirical performance of the proposed…
We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…