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Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
This paper proposes a greedy heuristic named as Big step greedy heuristic and investigates the application of Big step greedy heuristic for maximum k-coverage problem. Greedy algorithms construct the solution in multiple steps, the…
Randomized greedy algorithms form one of the simplest yet most effective approaches for computing approximate matchings in graphs. In this paper, we focus on the class of vertex-iterative (VI) randomized greedy matching algorithms, which…
Planning problems where effects of actions are non-deterministic can be modeled as Markov decision processes. Planning problems are usually goal-directed. This paper proposes several techniques for exploiting the goal-directedness to…
A class of fast greedy block Kaczmarz methods combined with general greedy strategy and average technique are proposed for solving large consistent linear systems. Theoretical analysis of the convergence of the proposed method is given in…
Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this…
The problem of selecting a small-size representative summary of a large dataset is a cornerstone of machine learning, optimization and data science. Motivated by applications to recommendation systems and other scenarios with query-limited…
Fingerprint-based indoor localization methods are promising due to the high availability of deployed access points and compatibility with commercial-off-the-shelf user devices. However, to train regression models for localization, an…
Determinantal point processes (DPPs) have garnered attention as an elegant probabilistic model of set diversity. They are useful for a number of subset selection tasks, including product recommendation. DPPs are parametrized by a positive…
Submodular functions are a broad class of set functions, which naturally arise in diverse areas. Many algorithms have been suggested for the maximization of these functions. Unfortunately, once the function deviates from submodularity, the…
Recently, greedy algorithm has received much attention as a cost-effective means to reconstruct the sparse signals from compressed measurements. Much of previous work has focused on the investigation of a single candidate to identify the…
In some practical learning tasks, such as traffic video analysis, the number of available training samples is restricted by different factors, such as limited communication bandwidth and computation power. Determinantal Point Process (DPP)…
Subset selection is a popular topic in recent years and a number of subset selection methods have been proposed. Among those methods, hypervolume subset selection is widely used. Greedy hypervolume subset selection algorithms can achieve…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
Determinantal point processes (DPPs) are a useful probabilistic model for selecting a small diverse subset out of a large collection of items, with applications in summarization, stochastic optimization, active learning and more. Given a…
Gradient-based learning imposes (deep) neural networks to be differentiable at all steps. This includes model-based architectures constructed by unrolling iterations of an iterative algorithm onto layers of a neural network, known as…
Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient…
The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Clustering problems such as $k$-means and $k$-median are staples of unsupervised learning, and many algorithmic techniques have been developed to tackle their numerous aspects. In this paper, we focus on the class of greedy approximation…