Related papers: $\alpha$-approximate Reductions: a Novel Source of…
Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynomial-time approximation…
In this paper we propose a new framework for analyzing the performance of preprocessing algorithms. Our framework builds on the notion of kernelization from parameterized complexity. However, as opposed to the original notion of…
An $\alpha$-approximate polynomial Turing kernelization is a polynomial-time algorithm that computes an $(\alpha c)$-approximate solution for a parameterized optimization problem when given access to an oracle that can compute…
We extend the notion of lossy kernelization, introduced by Lokshtanov et al. [STOC 2017], to approximate Turing kernelization. An $\alpha$-approximate Turing kernel for a parameterized optimization problem is a polynomial-time algorithm…
We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…
The approximation ratio has become one of the dominant measures in mechanism design problems. In light of analysis of algorithms, we define the \emph{smoothed approximation ratio} to compare the performance of the optimal mechanism and a…
We investigate how to train kernel approximation methods that generalize well under a memory budget. Building on recent theoretical work, we define a measure of kernel approximation error which we find to be more predictive of the empirical…
Kernelization is a general theoretical framework for preprocessing instances of NP-hard problems into (generally smaller) instances with bounded size, via the repeated application of data reduction rules. For the fundamental Max Cut…
Within the area of applied harmonic analysis, various multiscale systems such as wavelets, ridgelets, curvelets, and shearlets have been introduced and successfully applied. The key property of each of those systems are their (optimal)…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix--the minimum rank of a matrix which is entrywise close to the…
We consider the precedence-constrained scheduling problem to minimize the total weighted completion time. For a single machine several $2$-approximation algorithms are known, which are based on linear programming and network flows. We show…
This paper proposes a novel approach to determining the internal parameters of the hashing-based approximate model counting algorithm $\mathsf{ApproxMC}$. In this problem, the chosen parameter values must ensure that $\mathsf{ApproxMC}$ is…
In this paper, we propose a new class of parameter estimation laws for adaptive systems, called \emph{normalized parameter estimation laws}. A key feature of these estimation laws is that they accelerate the convergence of the system state,…
Recent studies showed that the generalization of neural networks is correlated with the sharpness of the loss landscape, and flat minima suggests a better generalization ability than sharp minima. In this paper, we propose a novel method…
This paper proposes the first-ever algorithmic framework for tuning hyper-parameters of stochastic optimization algorithm based on reinforcement learning. Hyper-parameters impose significant influences on the performance of stochastic…
The Robbins-Monro stochastic approximation algorithm is a foundation of many algorithmic frameworks for reinforcement learning (RL), and often an efficient approach to solving (or approximating the solution to) complex optimal control…
Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…
We provide a computationally efficient black-box reduction from mechanism design to algorithm design in very general settings. Specifically, we give an approximation-preserving reduction from truthfully maximizing \emph{any} objective under…