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Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the…
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…
This article studies sufficient conditions on families of approximating kernels which provide $N$--term approximation errors from an associated nonlinear approximation space which match the best known orders of $N$--term wavelet expansion.…
In this work we consider the problem of learning a positive semidefinite kernel matrix from relative comparisons of the form: "object A is more similar to object B than it is to C", where comparisons are given by humans. Existing solutions…
Similarity learning has received a large amount of interest and is an important tool for many scientific and industrial applications. In this framework, we wish to infer the distance (similarity) between points with respect to an arbitrary…
Spurious correlations threaten the validity of statistical classifiers. While model accuracy may appear high when the test data is from the same distribution as the training data, it can quickly degrade when the test distribution changes.…
This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…
The analysis of human microbiome data is often based on dimension-reduced graphical displays and clustering derived from vectors of microbial abundances in each sample. Common to these ordination methods is the use of biologically motivated…
The state-of-the-art CNN models give good performance on sentence classification tasks. The purpose of this work is to empirically study desirable properties such as semantic coherence, attention mechanism and reusability of CNNs in these…
Data mining research into time series classification (TSC) has focussed on alternative distance measures for nearest neighbour classifiers. It is standard practice to use 1-NN with Euclidean or dynamic time warping (DTW) distance as a straw…
We derive simple closed-form estimates for the test risk and other generalization metrics of kernel ridge regression (KRR). Relative to prior work, our derivations are greatly simplified and our final expressions are more readily…
Many deep neural networks are built by using stacked convolutional layers of fixed and single size (often 3$\times$3) kernels. This paper describes a method for training the size of convolutional kernels to provide varying size kernels in a…
The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of optimization problems, new Karhunen-Lo\`eve transforms, and…
Evaluating graphs learned by causal discovery algorithms is difficult: The number of edges that differ between two graphs does not reflect how the graphs differ with respect to the identifying formulas they suggest for causal effects. We…
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…
In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques,…
I argue that regularizing terms in standard regression methods not only help against overfitting finite data, but sometimes also yield better causal models in the infinite sample regime. I first consider a multi-dimensional variable…
Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms…
We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student…
This paper introduces kdiff, a novel kernel-based measure for estimating distances between instances of time series, random fields and other forms of structured data. This measure is based on the idea of matching distributions that only…