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Most state-of-the-art graph kernels only take local graph properties into account, i.e., the kernel is computed with regard to properties of the neighborhood of vertices or other small substructures. On the other hand, kernels that do take…

Kernel methods provide a flexible and theoretically grounded approach to nonlinear and nonparametric learning. While memory and run-time requirements hinder their applicability to large datasets, many low-rank kernel approximations, such as…

Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted…

In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…

Graph kernels are usually defined in terms of simpler kernels over local substructures of the original graphs. Different kernels consider different types of substructures. However, in some cases they have similar predictive performances,…

Kernel Ridge Regression (KRR) is a simple yet powerful technique for non-parametric regression whose computation amounts to solving a linear system. This system is usually dense and highly ill-conditioned. In addition, the dimensions of the…

Generalization beyond a training dataset is a main goal of machine learning, but theoretical understanding of generalization remains an open problem for many models. The need for a new theory is exacerbated by recent observations in deep…

Representation learning is an important step in the machine learning pipeline. Given the current biological sequencing data volume, learning an explicit representation is prohibitive due to the dimensionality of the resulting feature…

Kernel ridge regression, KRR, is a generalization of linear ridge regression that is non-linear in the data, but linear in the model parameters. Here, we introduce an equivalent formulation of the objective function of KRR, which opens up…

Understanding the structural and functional characteristics of proteins are crucial for developing preventative and curative strategies that impact fields from drug discovery to policy development. An important and popular technique for…

Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…

We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…

We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…

Time series data analytics has been a problem of substantial interests for decades, and Dynamic Time Warping (DTW) has been the most widely adopted technique to measure dissimilarity between time series. A number of global-alignment kernels…

The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their…

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…

Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on…

The compositionality and sparsity of high-throughput sequencing data poses a challenge for regression and classification. However, in microbiome research in particular, conditional modeling is an essential tool to investigate relationships…

Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or…

We describe and analyze a simple random feature scheme (RFS) from prescribed compositional kernels. The compositional kernels we use are inspired by the structure of convolutional neural networks and kernels. The resulting scheme yields…