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Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem…
Today, machine learning tools, particularly artificial neural networks, have become crucial for diverse applications. However, current digital computing tools to train and deploy artificial neural networks often struggle with massive data…
Count-sketch is a popular matrix sketching algorithm that can produce a sketch of an input data matrix X in O(nnz(X))time where nnz(X) denotes the number of non-zero entries in X. The sketched matrix will be much smaller than X while…
In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…
The Nystr\"om methods have been popular techniques for scalable kernel based learning. They approximate explicit, low-dimensional feature mappings for kernel functions from the pairwise comparisons with the training data. However, Nystr\"om…
Thanks to their easy implementation via Radial Basis Functions (RBFs), meshfree kernel methods have been proved to be an effective tool for e.g. scattered data interpolation, PDE collocation, classification and regression tasks. Their…
Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…
Point clouds are sets of points in two or three dimensions. Most kernel methods for learning on sets of points have not yet dealt with the specific geometrical invariances and practical constraints associated with point clouds in computer…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…
Kernel methods are an important class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be…
In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem…
Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We…
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,…
This article considers "compressive learning," an approach to large-scale machine learning where datasets are massively compressed before learning (e.g., clustering, classification, or regression) is performed. In particular, a "sketch" is…
Nonlinear component analysis such as kernel Principle Component Analysis (KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in machine learning, statistics and data analysis, but they can not scale up to big datasets.…
Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First,…
The class of graph deletion problems has been extensively studied in theoretical computer science, particularly in the field of parameterized complexity. Recently, a new notion of graph deletion problems was introduced, called deletion to…
Estimating the frequency of items on the high-volume, fast data stream has been extensively studied in many areas, such as database and network measurement. Traditional sketches provide only coarse estimates under strict memory constraints.…
Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties. However, at least in their basic form, they have limited…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…