Related papers: Classification with Low Rank and Missing Data

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

Ranking is at the core of Information Retrieval. Classic ranking optimization studies often treat ranking as a sorting problem with the assumption that the best performance of ranking would be achieved if we rank items according to their…

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

We propose a new model for supervised learning to rank. In our model, the relevance labels are assumed to follow a categorical distribution whose probabilities are constructed based on a scoring function. We optimize the training objective…

We develop an approach to subspace system identification using multiple data records and present a simple rank-based test for the adequacy of these data for fitting the unique linear, noise-free, dynamic model of prescribed state-vector,…

In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations,…

We establish minimax convergence rates for classification of functional data and for nonparametric regression with functional design variables. The optimal rates are of logarithmic type under smoothness constraints on the functional density…

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…

Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…

We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows…

Algorithmic decision systems are increasingly used in areas such as hiring, school admission, or loan approval. Typically, these systems rely on labeled data for training a classification model. However, in many scenarios, ground-truth…

Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…

We introduce a new nonparametric framework for classification problems in the presence of missing data. The key aspect of our framework is that the regression function decomposes into an anova-type sum of orthogonal functions, of which some…

The data processing inequality is an information-theoretic principle stating that the information content of a signal cannot be increased by processing the observations. In particular, it suggests that there is no benefit in enhancing the…

Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…

Response selection plays a vital role in building retrieval-based conversation systems. Despite that response selection is naturally a learning-to-rank problem, most prior works take a point-wise view and train binary classifiers for this…

A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…

Subspace inference for neural networks assumes that a subspace of their parameter space suffices to produce a reliable uncertainty quantification. In this work, we underpin the validity of this assumption by using low rank techniques. We…

Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how…

Classification of high-dimensional low sample size (HDLSS) data poses a challenge in a variety of real-world situations, such as gene expression studies, cancer research, and medical imaging. This article presents the development and…