This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two essentially separate communities, and this makes it difficult to seamlessly transfer results between them. Our aim is to overcome this potential difficulty. To this end, we review several old and new results and concepts from either side, and juxtapose algorithmic quantities from each framework to highlight close similarities. We also provide discussions on subtle philosophical and theoretical differences between the two approaches. Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences

Trace Lasso-L1 Graph Cut (TL-L1GC) This work proposes an adaptive trace lasso regularized L1-norm based graph cut method for dimensionality reduction of Hyperspectral images, called as `Trace Lasso-L1 Graph Cut’ (TL-L1GC). The underlying idea of this method is to generate the optimal projection matrix by considering both the sparsity as well as the correlation of the data samples. The conventional L2-norm used in the objective function is sensitive to noise and outliers. Therefore, in this work L1-norm is utilized as a robust alternative to L2-norm. Besides, for further improvement of the results, we use a penalty function of trace lasso with the L1GC method. It adaptively balances the L2-norm and L1-norm simultaneously by considering the data correlation along with the sparsity. We obtain the optimal projection matrix by maximizing the ratio of between-class dispersion to within-class dispersion using L1-norm with trace lasso as the penalty. Furthermore, an iterative procedure for this TL-L1GC method is proposed to solve the optimization function. The effectiveness of this proposed method is evaluated on two benchmark HSI datasets. …

In our last note we used wrapr::qe() to help quote expressions. In this note we will discuss quoting and code-capturing interfaces (interfaces that capture user source code) a bit more.

Do you subscribe to the Data is Plural newsletter from Jeremy Singer-Vine? You probably should, because it is a treasure trove of interesting datasets arriving in your email inbox. In the November 28 edition, Jeremy linked to the Small World of Words project, and I was entranced. I love stuff like that, all about words and how people think of them. I have been mulling around a blog post ever since, and today I finally have my post done, so let’s see what’s up!

Teppo Felin sends along this article with Mia Felin, Joachim Krueger, and Jan Koenderink on “surprise-hacking,” and writes:

In a new paper in Monthly Weather Review, minimum CRPS and maximum likelihood estimation are compared for fitting heteroscedastic (or nonhomogenous) regression models under different response distributions. Minimum CRPS is more robust to distributional misspecification while maximum likelihood is slightly more efficient under correct specification. An R implementation is available in the crch package.

In our last note we used wrapr::qe() to help quote expressions. In this note we will discuss quoting and code-capturing interfaces (interfaces that capture user source code) a bit more.

Our linl package for writing LaTeX letter with (R)markdown had a fairly minor release today, following up on the previous release well over a year ago. This version just contains one change which Mark van der Loo provided a few months ago with a clean PR. As another user was just bitten the same issue when using an included letterhead – which was fixed but unreleased – we decided it was time for a release. So there it is.

The knitr and rmarkdown packages are used in conjunction with pandoc to convert R code and figures to a variety of formats including PDF, and word. Here, I’m exploring how to convert HTML back to markdown format. This post came about when I was searching how to convert XML to markdown, which I still haven’t found an easy way to do. Pandoc is not the only way to convert HTML to markdown (see turndown, html2text)

The ancient philosopher Confucius has been credited with saying “study your past to know your future.” This wisdom applies not only to life but to machine learning also. Specifically, the availability and application of labeled data (things past) for the labeling of previously unseen data (things future) is fundamental to supervised machine learning.