Tag: Statistics

Kernel Density Estimation

Motivation

It is important to have an understanding of some of the more traditional approaches to function estimation and classification before delving into the trendier topics of neural networks and decision trees. Many of these methods build on an understanding of each other and thus to truly be a MACHINE LEARNING MASTER, we’ve got to pay our dues. We will therefore start with the slightly less sexy topic of kernel density estimation.

Let X be a random variable with a continuous distribution function (CDF) F(x) = Pr(X \leq x) and probability density function (PDF)

    \[f(x) = \frac{d}{dx} F(x)\]

Our goal is to estimate f(x) from a random sample \lbrace X_1, …, X_n \rbrace. Estimation of f(x) has a number of applications including construction of the popular Naive Bayes classifier,

    \[ \hat{Pr}(C = c | X = x_0) = \frac{\hat{\pi}_c \hat{f}_{c}(x_0)}{\sum_{k=1}^{C} \hat{\pi}_{k} \hat{f}_{k}(x_0)} \]

Continue reading Kernel Density Estimation

Advent of Code 2017 in R: Day 2

Day 2 of the Advent of Code provides us with a tab delimited input consisting of numbers 2-4 digits long and asks us to calculate its “checksum”. checksum is defined as the sum of the difference between each row’s largest and smallest values. Awesome! This is a problem that is well-suited for base R.

I started by reading the file in using read.delim, specifying header = F in order to ensure that numbers within the first row of the data are not treated as variable names.

When working with short problems like this where I know I won’t be rerunning my code or reloading my data often, I will use file.choose() in my read.whatever functions for speed. file.choose() opens Windows Explorer, allowing you to navigate to your file path.

input <- read.delim(file.choose(), header = F)

# Check the dimensions of input to ensure the data read in correctly.
dim(input)

After checking the dimensions of our input, everything looks good. As suspected, this is a perfect opportunity to use some vectorization via the apply function.

row_diff <- apply(input, 1, function(x) max(x) - min(x))
checksum <- sum(row_diff)
checksum

Et voilà, the answer is 45,972! Continue reading Advent of Code 2017 in R: Day 2