Related papers: Efficient Convex Algorithms for Universal Kernel L…
In this paper we consider a general problem set-up for a wide class of convex and robust distributed optimization problems in peer-to-peer networks. In this set-up convex constraint sets are distributed to the network processors who have to…
A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any…
The canonical duality theory has provided with a unified analytic solution to a range of discrete and continuous problems in global optimization, which can transform a nonconvex primal problem to a concave maximization dual problem over a…
In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise…
The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…
Quantum machine learning is considered one of the current research fields with immense potential. In recent years, Havl\'i\v{c}ek et al. [Nature 567, 209-212 (2019)] have proposed a quantum machine learning algorithm with quantum-enhanced…
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
Deep Convolutional Neural Networks (CNNs) are widely employed in modern computer vision algorithms, where the input image is convolved iteratively by many kernels to extract the knowledge behind it. However, with the depth of convolutional…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
Non-linear, especially convex, objective functions have been extensively studied in recent years in which approaches relies crucially on the convexity property of cost functions. In this paper, we present primal-dual approaches based on…
The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…
The ability to express a learning task in terms of a primal and a dual optimization problem lies at the core of a plethora of machine learning methods. For example, Support Vector Machine (SVM), Least-Squares Support Vector Machine…
Binary Classification plays an important role in machine learning. For linear classification, SVM is the optimal binary classification method. For nonlinear classification, the SVM algorithm needs to complete the classification task by…
Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…
We propose a novel methodology for solving a two-stage adjustable robust convex optimisation problem with a general (proximable) convex objective function and constraints defined by sum-of-squares (SOS) convex polynomials. These problems…
Multiple Kernel Learning, or MKL, extends (kernelized) SVM by attempting to learn not only a classifier/regressor but also the best kernel for the training task, usually from a combination of existing kernel functions. Most MKL methods seek…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…