The DO Loop

Rick WicklinJune 1, 2020 0

The Kullback–Leibler divergence between continuous probability distributions

In a previous article, I discussed the definition of the Kullback-Leibler (K-L) divergence between two discrete probability distributions. For completeness, this article shows how to compute the Kullback-Leibler divergence between two continuous distributions. When f and g are discrete distributions, the K-L divergence is the sum of f(x)*log(f(x)/g(x)) over all

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Advanced Analytics | Machine Learning

Rick WicklinMay 28, 2020 1

Minimizing the Kullback–Leibler divergence

The Kullback–Leibler divergence is a measure of dissimilarity between two probability distributions. An application in machine learning is to measure how distributions in a parametric family differ from a data distribution. This article shows that if you minimize the Kullback–Leibler divergence over a set of parameters, you can find a

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Advanced Analytics | Machine Learning

Rick WicklinMay 26, 2020 0

The Kullback–Leibler divergence between discrete probability distributions

If you have been learning about machine learning or mathematical statistics, you might have heard about the Kullback–Leibler divergence. The Kullback–Leibler divergence is a measure of dissimilarity between two probability distributions. It measures how much one distribution differs from a reference distribution. This article explains the Kullback–Leibler divergence and shows

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Programming Tips

Rick WicklinMay 20, 2020 4

Bilinear interpolation in SAS

This article shows how to perform two-dimensional bilinear interpolation in SAS by using a SAS/IML function. It is assumed that you have observed the values of a response variable on a regular grid of locations. A previous article showed how to interpolate inside one rectangular cell. When you have a

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Programming Tips

Rick WicklinMay 18, 2020 0

What is bilinear interpolation?

I've previously written about linear interpolation in one dimension. Bilinear interpolation is a method for two-dimensional interpolation on a rectangle. If the value of a function is known at the four corners of a rectangle, an interpolation scheme gives you a way to estimate the function at any point in

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Analytics | Data Visualization

Rick WicklinMay 13, 2020 2

Find points where a regression curve has zero slope

This article shows how to find local maxima and maxima on a regression curve, which means finding points where the slope of the curve is zero. An example appears at the right, which shows locations where the loess smoother in a scatter plot has local minima and maxima. Except for

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Analytics | Programming Tips

Rick WicklinMay 11, 2020 0

Cubic spline interpolation in SAS

I recently showed how to use linear interpolation in SAS. Linear interpolation is a common way to interpolate between a set of planar points, but the interpolating function (the interpolant) is not smooth. If you want a smoother interpolant, you can use cubic spline interpolation. This article describes how to

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Analytics | Data Visualization

Rick WicklinMay 6, 2020 3

What does 'flatten the curve' mean? To which curve does it apply?

During this coronavirus pandemic, there are many COVID-related graphs and curves in the news and on social media. The public, politicians, and pundits scrutinize each day's graphs to determine which communities are winning the fight against coronavirus. Interspersed among these many graphs is the oft-repeated mantra, "Flatten the curve!" As

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Analytics | Programming Tips

Rick WicklinMay 4, 2020 0

Linear interpolation in SAS

SAS programmers sometimes ask about ways to perform one-dimensional linear interpolation in SAS. This article shows three ways to perform linear interpolation in SAS: PROC IML (in SAS/IML software), PROC EXPAND (in SAS/ETS software), and PROC TRANSREG (in SAS/STAT software). Of these, PROC IML Is the simplest to use and

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Analytics

Rick WicklinApril 29, 2020 1

How many imputations are enough?

Recently I read an excellent blog post by Paul von Hippel entitled "How many imputations do you need?". It is based on a paper (von Hippel, 2018), which provides more details. Suppose you are faced with data that has many missing values. One way to address the missing values is

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