Related papers: Classification with Low Rank and Missing Data

We introduce the notion of relevant information loss for the purpose of casting the signal enhancement problem in information-theoretic terms. We show that many algorithms from machine learning can be reformulated using relevant information…

Rank and select queries on bitmaps are essential building bricks of many compressed data structures, including text indexes, membership and range supporting spatial data structures, compressed graphs, and more. Theoretically considered yet…

The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

A large amount of research on Convolutional Neural Networks has focused on flat Classification in the multi-class domain. In the real world, many problems are naturally expressed as problems of hierarchical classification, in which the…

Complex systems are high-dimensional nonlinear dynamical systems with intricate interactions among their constituents. To make interpretable predictions about their large-scale behavior, it is typically assumed, without a clear statement,…

The goal of classification with rejection is to avoid risky misclassification in error-critical applications such as medical diagnosis and product inspection. In this paper, based on the relationship between classification with rejection…

Learning with high-resource data has demonstrated substantial success in artificial intelligence (AI); however, the costs associated with data annotation and model training remain significant. A fundamental objective of AI research is to…

Why are classifiers in high dimension vulnerable to "adversarial" perturbations? We show that it is likely not due to information theoretic limitations, but rather it could be due to computational constraints. First we prove that, for a…

The vast majority of real world classification problems are imbalanced, meaning there are far fewer data from the class of interest (the positive class) than from other classes. We propose two machine learning algorithms to handle highly…

Ranking is a key aspect of many applications, such as information retrieval, question answering, ad placement and recommender systems. Learning to rank has the goal of estimating a ranking model automatically from training data. In…

A binary classifier capable of abstaining from making a label prediction has two goals in tension: minimizing errors, and avoiding abstaining unnecessarily often. In this work, we exactly characterize the best achievable tradeoff between…

For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…

Motivated by multi-task and meta-learning approaches, we consider the problem of learning structure shared by tasks or users, such as shared low-rank representations or clustered structures. While all previous works focus on well-specified…

Data values in a dataset can be missing or anomalous due to mishandling or human error. Analysing data with missing values can create bias and affect the inferences. Several analysis methods, such as principle components analysis or…

In today's data driven world, storing, processing, and gleaning insights from large-scale data are major challenges. Data compression is often required in order to store large amounts of high-dimensional data, and thus, efficient inference…

Machine learning and statistics typically focus on building models that capture the vast majority of the data, possibly ignoring a small subset of data as "noise" or "outliers." By contrast, here we consider the problem of jointly…

This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with…

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…

Multi-label Classification (MLC) assigns an instance to one or more non-exclusive classes. A challenge arises when the dataset contains a large proportion of instances with no assigned class, referred to as negative data, which can…