Blog Archives

Linear, Quadratic, and Regularized Discriminant Analysis

Linear, Quadratic, and Regularized Discriminant Analysis

Discriminant analysis encompasses methods that can be used for both classification and dimensionality reduction. Linear discriminant analysis (LDA) is particularly popular because it is both a classifier and a dimensionality reduction technique. Quadratic discriminant analysis (QDA) is a variant of LDA that allows for non-linear separation of data. Finally, regularized discriminant analysis (RDA) is a compromise between LDA and...

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An Introduction to Probabilistic Programming with Stan in R

An Introduction to Probabilistic Programming with Stan in R

Probabilistic programming enables us to implement statistical models without having to worry about the technical details. It is particularly useful for Bayesian models that are based on MCMC sampling. In this article, I investigate how Stan can be used through its implementation in R, RStan. This post is largely based on the GitHub documentation of Rstan and its vignette. Introduction...

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Performance Measures for Feature Selection

In a recent post, I have discussed performance measures for model selection. This time, I write about a related topic: performance measures that are suitable for selecting models when performing feature selection. Since feature selection is concerned with reducing the number of dependent variables, suitable performance measures evaluate the trade-off between the number of features, \(p\), and the fit...

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The Case Against Precision as a Model Selection Criterion

The Case Against Precision as a Model Selection Criterion

Recently, I have introduced sensitivity and specificity as performance measures for model selection. Besides these measures, there is also the notion of recall and precision. Precision and recall originate from information retrieval but are also used in machine learning settings. However, the use of precision and recall can be problematic in some situations. In this post, I discuss the...

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Dimensionality Reduction for Visualization and Prediction

Dimensionality Reduction for Visualization and Prediction

Dimensionality reduction has two primary use cases: data exploration and machine learning. It is useful for data exploration because dimensionality reduction to few dimensions (e.g. 2 or 3 dimensions) allows for visualizing the samples. Such a visualization can then be used to obtain insights from the data (e.g. detect clusters and identify outliers). For machine learning, dimensionality reduction is useful because...

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Radar plots

Radar plots

Radar plots visualize several variables using a radial layout. This plot is most suitable for visualizing and comparing the properties associated with individual objects. In the following, we will use a radar plot for comparing the characteristics of whiskeys from different distilleries. A data set on whiskey Some of you may already know that radar plots are well-suited for visualizing whiskey...

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Interpreting Generalized Linear Models

Interpreting Generalized Linear Models

Interpreting generalized linear models (GLM) obtained through glm is similar to interpreting conventional linear models. Here, we will discuss the differences that need to be considered. Basics of GLMs GLMs enable the use of linear models in cases where the response variable has an error distribution that is non-normal. Each distribution is associated with a specific canonical link function. A link...

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Finding a Suitable Linear Model for Ozone Prediction

Finding a Suitable Linear Model for Ozone Prediction

In a previous post, I have introduced the airquality data set in order to demonstrate how linear models are interpreted. In this post, I will start with a basic linear model and, from there, try to find a linear model with a better fit. Data preprocessing Since the airquality data set contains some missing values, we will remove those before we...

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Interpreting Linear Prediction Models

Interpreting Linear Prediction Models

Although linear models are one of the simplest machine learning techniques, they are still a powerful tool for predictions. This is particularly due to the fact that linear models are especially easy to interpret. Here, I discuss the most important aspects when interpreting linear models by example of ordinary least-squares regression using the airquality data set. The airquality data set The...

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Box Plot Alternatives: Beeswarm and Violin Plots

Box Plot Alternatives: Beeswarm and Violin Plots

Box plots are great as they do not only indicate the median value but also show the variation of the measurements in terms of the 1st and 3rd quartiles. There are, however, also plots that provide a bit of additional information. Here, we take a closer look at potential alternatives to the box plot: the beeswarm and the violin...

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