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The field of kernelization studies polynomial-time preprocessing routines for hard problems in the framework of parameterized complexity. Although a framework for proving kernelization lower bounds has been discovered in 2008 and…

Kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same…

In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…

Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time…

Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…

We introduce algorithms that use predictions from machine learning applied to the input to circumvent worst-case analysis. We aim for algorithms that have near optimal performance when these predictions are good, but recover the…

Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the…

We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…

Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…

Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like…

Low-bit width neural networks have been extensively explored for deployment on edge devices to reduce computational resources. Existing approaches have focused on gradient-based optimization in a two-stage train-and-compress setting or as a…

Small cell enchantment is emerging as the key technique for wireless network evolution. One challenging problem for small cell enhancement is how to achieve high data rate with as-low-as-possible control and computation overheads. As a…

We develop algorithms with low regret for learning episodic Markov decision processes based on kernel approximation techniques. The algorithms are based on both the Upper Confidence Bound (UCB) as well as Posterior or Thompson Sampling…

Submodular maximization is one of the central topics in combinatorial optimization. It has found numerous applications in the real world. In the past decades, a series of algorithms have been proposed for this problem. However, most of the…

In this work, we broadly connect kernel-based filtering (e.g. approaches such as the bilateral filters and nonlocal means, but also many more) with general variational formulations of Bayesian regularized least squares, and the related…

We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…

Combinatorial optimization problems arise in a wide range of applications from diverse domains. Many of these problems are NP-hard and designing efficient heuristics for them requires considerable time and experimentation. On the other…

In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…

Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…