Related papers: Fair Column Subset Selection
This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…
Subset selection for matrices is the task of extracting a column sub-matrix from a given matrix $B\in\mathbb{R}^{n\times m}$ with $m>n$ such that the pseudoinverse of the sampled matrix has as small Frobenius or spectral norm as possible.…
We explain theoretically a curious empirical phenomenon: "Approximating a matrix by deterministically selecting a subset of its columns with the corresponding largest leverage scores results in a good low-rank matrix surrogate". To obtain…
Selecting a subset of the $k$ "best" items from a dataset of $n$ items, based on a scoring function, is a key task in decision-making. Given the rise of automated decision-making software, it is important that the outcome of this process,…
A CUR approximation of a matrix $A$ is a particular type of low-rank approximation $A \approx C U R$, where $C$ and $R$ consist of columns and rows of $A$, respectively. One way to obtain such an approximation is to apply column subset…
The problem of extracting a well conditioned submatrix from any rectangular matrix (with normalized columns) has been studied for some time in functional and harmonic analysis; see…
Subset selection for the rank $k$ approximation of an $n\times d$ matrix $A$ offers improvements in the interpretability of matrices, as well as a variety of computational savings. This problem is well-understood when the error measure is…
Fair top-$k$ selection, which ensures appropriate proportional representation of members from minority or historically disadvantaged groups among the top-$k$ selected candidates, has drawn significant attention. We study the problem of…
We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nystr\"om approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
Decision trees are highly interpretable models for solving classification problems in machine learning (ML). The standard ML algorithms for training decision trees are fast but generate suboptimal trees in terms of accuracy. Other discrete…
Submodular maximization subject to matroid constraints is a central problem with many applications in machine learning. As algorithms are increasingly used in decision-making over datapoints with sensitive attributes such as gender or race,…
Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An…
The American winner-take-all congressional district system empowers politicians to engineer electoral outcomes by manipulating district boundaries. Existing computational solutions mostly focus on drawing unbiased maps by ignoring political…
In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…
Leverage score sampling provides an appealing way to perform approximate computations for large matrices. Indeed, it allows to derive faithful approximations with a complexity adapted to the problem at hand. Yet, performing leverage scores…
This paper studies the estimation of ranked-list discrete choice models with single and multiple purchases. In this setting, each consumer type is characterized by a ranking over a subset of products and a desired number of purchases, and…
The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces. It has recently attracted much interest, as it has several…
As machine learning has become more prevalent, researchers have begun to recognize the necessity of ensuring machine learning systems are fair. Recently, there has been an interest in defining a notion of fairness that mitigates…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…