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We study the following problem: Given a variable of interest, we would like to find a best linear predictor for it by choosing a subset of $k$ relevant variables obeying a matroid constraint. This problem is a natural generalization of…

Data Structures and Algorithms · Computer Science 2023-01-19 Theophile Thiery , Justin Ward

Submodular function maximization finds application in a variety of real-world decision-making problems. However, most existing methods, based on greedy maximization, assume it is computationally feasible to evaluate F, the function being…

Artificial Intelligence · Computer Science 2020-08-11 Yash Satsangi , Shimon Whiteson , Frans A. Oliehoek

The batched greedy strategy is an approximation algorithm to maximize a set function subject to a matroid constraint. Starting with the empty set, the batched greedy strategy iteratively adds to the current solution set a batch of elements…

Optimization and Control · Mathematics 2017-10-05 Yajing Liu , Zhenliang Zhang , Edwin K. P. Chong , Ali Pezeshki

This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…

Machine Learning · Statistics 2012-06-08 Ali Jalali , Sujay Sanghavi

Despite the great success of deep learning, recent works show that large deep neural networks are often highly redundant and can be significantly reduced in size. However, the theoretical question of how much we can prune a neural network…

Machine Learning · Computer Science 2020-11-02 Mao Ye , Lemeng Wu , Qiang Liu

To cope with the high level of ambiguity faced in domains such as Computer Vision or Natural Language processing, robust prediction methods often search for a diverse set of high-quality candidate solutions or proposals. In structured…

Machine Learning · Computer Science 2014-11-10 Adarsh Prasad , Stefanie Jegelka , Dhruv Batra

The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…

Machine Learning · Computer Science 2023-01-11 Suraj Srinivas , Kyle Matoba , Himabindu Lakkaraju , Francois Fleuret

Ensembles of independently trained neural networks are a state-of-the-art approach to estimate predictive uncertainty in Deep Learning, and can be interpreted as an approximation of the posterior distribution via a mixture of delta…

Machine Learning · Computer Science 2022-07-11 Aleksei Tiulpin , Matthew B. Blaschko

Submodularity in combinatorial optimization has been a topic of many studies and various algorithmic techniques exploiting submodularity of a studied problem have been proposed. It is therefore natural to ask, in cases where the cost…

Data Structures and Algorithms · Computer Science 2023-05-19 Martin Böhm , Jarosław Byrka , Mateusz Lewandowski , Jan Marcinkowski

The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…

Data Structures and Algorithms · Computer Science 2021-11-16 Jason Altschuler , Aditya Bhaskara , Gang Fu , Vahab Mirrokni , Afshin Rostamizadeh , Morteza Zadimoghaddam

We show that the greedy algorithm for adaptive-submodular cover has approximation ratio at least 1.3*(1+ln Q). Moreover, the instance demonstrating this gap has Q=1. So, it invalidates a prior result in the paper ``Adaptive Submodularity: A…

Data Structures and Algorithms · Computer Science 2024-05-27 Blake Harris , Viswanath Nagarajan

Continuous DR-submodular functions are a class of functions that satisfy the Diminishing Returns (DR) property, which implies that they are concave along non-negative directions. Existing works have studied monotone continuous DR-submodular…

Machine Learning · Computer Science 2022-05-31 Omid Sadeghi , Maryam Fazel

The Column Subset Selection Problem provides a natural framework for unsupervised feature selection. Despite being a hard combinatorial optimization problem, there exist efficient algorithms that provide good approximations. The drawback of…

Machine Learning · Computer Science 2018-04-13 Bruno Ordozgoiti , Alberto Mozo , Jesús García López de Lacalle

We consider parametrized linear-quadratic optimal control problems and provide their online-efficient solutions by combining greedy reduced basis methods and machine learning algorithms. To this end, we first extend the greedy control…

Optimization and Control · Mathematics 2023-07-31 Hendrik Kleikamp , Martin Lazar , Cesare Molinari

We investigate the continuous non-monotone DR-submodular maximization problem subject to a down-closed convex solvable constraint. Our first contribution is to construct an example to demonstrate that (first-order) stationary points can…

Data Structures and Algorithms · Computer Science 2024-03-27 Shengminjie Chen , Donglei Du , Wenguo Yang , Dachuan Xu , Suixiang Gao

The priority model was introduced to capture "greedy-like" algorithms. Motivated by the success of advice complexity in the area of online algorithms, the fixed priority model was extended to include advice, and a reduction-based framework…

Data Structures and Algorithms · Computer Science 2022-01-27 Joan Boyar , Kim S. Larsen , Denis Pankratov

The research problem in this work is the relaxation of maximizing non-negative submodular plus modular with the entire real number domain as its value range over a family of down-closed sets. We seek a feasible point $\mathbf{x}^*$ in the…

Data Structures and Algorithms · Computer Science 2022-04-13 Xin Sun , Chenchen Wu , Dachuan Xu , Yang Zhou

Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic…

Machine Learning · Computer Science 2017-11-07 Mohammad Reza Karimi , Mario Lucic , Hamed Hassani , Andreas Krause

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…

Numerical Analysis · Mathematics 2014-07-02 Nam Nguyen , Deanna Needell , Tina Woolf

We present new tight performance guarantees for the greedy maximization of nondecreasing submodular set functions. Our main result first provides a performance guarantee in terms of the overlap of the optimal and greedy solutions. As a…

Optimization and Control · Mathematics 2015-06-02 Jussi Laitila , Atte Moilanen