Related papers: Submodularity in Action: From Machine Learning to …
A key problem in emerging complex cyber-physical networks is the design of information and control topologies, including sensor and actuator selection and communication network design. These problems can be posed as combinatorial set…
In this work, we study the problem of privately maximizing a submodular function in the streaming setting. Extensive work has been done on privately maximizing submodular functions in the general case when the function depends upon the…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…
Several studies point out different causes of performance degradation in supervised machine learning. Problems such as class imbalance, overlapping, small-disjuncts, noisy labels, and sparseness limit accuracy in classification algorithms.…
Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (1) not naturally amenable to gradient-based optimization, and (2) incompatible…
Submodular optimization is a fundamental problem with many applications in machine learning, often involving decision-making over datasets with sensitive attributes such as gender or age. In such settings, it is often desirable to produce a…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances…
In this paper, we showcase the interplay between discrete and continuous optimization in network-structured settings. We propose the first fully decentralized optimization method for a wide class of non-convex objective functions that…
Emerging applications of control, estimation, and machine learning, ranging from target tracking to decentralized model fitting, pose resource constraints that limit which of the available sensors, actuators, or data can be simultaneously…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Submodularity is an important concept in combinatorial optimization, and it is often regarded as a discrete analog of convexity. It is a fundamental fact that the set of minimizers of any submodular function forms a distributive lattice.…
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…
Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem…
Set function optimization is essential in AI and machine learning. We focus on a subadditive set function that generalizes submodularity, and examine the subadditivity of non-submodular functions. We also deal with a minimax subadditive…
In this paper we study the adaptivity of submodular maximization. Adaptivity quantifies the number of sequential rounds that an algorithm makes when function evaluations can be executed in parallel. Adaptivity is a fundamental concept that…
The sheer scale of modern datasets has resulted in a dire need for summarization techniques that identify representative elements in a dataset. Fortunately, the vast majority of data summarization tasks satisfy an intuitive diminishing…