Related papers: Fast Search Method for Large Polarization Kernels
The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventional kernel-based interpolation techniques. The multi-scale…
Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…
In recent years there has been much interest in the Monte Carlo tree search algorithm, a new, adaptive, randomized optimization algorithm. In fields as diverse as Artificial Intelligence, Operations Research, and High Energy Physics,…
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…
This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods. Given a training set consisting of pairs of noisy PDE solutions and source/boundary terms on a mesh, kernel…
Polar codes have attracted a lot of attention during past few years and have been adopted as a coding scheme for 5G standard. Successive-cancellation list (SCL) decoder provides high level error-correction performance for polar codes, but…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
Neural kernels have drastically increased performance on diverse and nonstandard data modalities but require significantly more compute, which previously limited their application to smaller datasets. In this work, we address this by…
Quantum reading provides a general framework where to formulate the statistical discrimination of quantum channels. Several paths have been taken for such a problem. However, there is much to be done in the avenue of optimizing channel…
We apply the discrepancy method and a chaining approach to give improved bounds on the coreset complexity of a wide class of kernel functions. Our results give randomized polynomial time algorithms to produce coresets of size…
This paper focuses on the frozen set design for precoded polar codes decoded by the successive cancellation list (SCL) algorithm. We propose a novel frozen set design method, whose computational complexity is low due to the use of…
The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…
Polar coding is a recently proposed coding technique that can provably achieve the channel capacity. The polar code structure, which is based on the original 2x2 generator matrix, polarises the channels, i.e., a portion of the channel…
Kernel-based statistical methods are efficient, but their performance depends heavily on the selection of kernel parameters. In literature, the optimization studies on kernel-based chemometric methods is limited and often reduced to grid…
Consider the problem of constructing a polar code of block length $N$ for the transmission over a given channel $W$. Typically this requires to compute the reliability of all the $N$ synthetic channels and then to include those that are…
Modern program runtime is dominated by segments of repeating code called kernels. Kernels are accelerated by increasing memory locality, increasing data-parallelism, and exploiting producer-consumer parallelism among kernels - which…
Most blind deconvolution methods usually pre-define a large kernel size to guarantee the support domain. Blur kernel estimation error is likely to be introduced, yielding severe artifacts in deblurring results. In this paper, we first…
Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…
Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the…
In this paper, a genetic algorithm, one of the evolutionary algorithms optimization methods, is used for the first time for the problem of finding extremal binary self-dual codes. We present a comparison of the computational times between a…