Here you can find the several functions for creating probability density functions, cumulative distributions functions, calculating the percentiles, as well as p - probability that we get some results under assumption that hypothesis (usually called zero hypothesis) is true. Here you can see the very good examples for understanding basic statistical concepts.
Here you can find the different plots of different distribution types. We plot first Uniform distribution, then Normal and Gamma distribution. For Normal and Gamma distribution we variate the key parameters (mean and standard deviation for normal, alpha and beta for Gamma) in order to get more familiar with distribution characheristics.
Here you can find the basic explanation of the conditional probability and Bayes theorem with simulated example of one contraintuitive example (this is why Bayes is so hard for me). Then we develop one example of Bayes network modelled by pomegranate package. I succeded to get intuitions through this example which I made up. You could ask some questions and then the Network could give you the most probable answers based on chain conditional probability.
Here you can find simple step by step explanation of the Beta distribution and get intuition when you can use it. We start from Binomal distribution and its modeling of a lot of Bernuli events, then we illustrate the Law of Large numbers, which should help in understanding the purpose and usefullnes of the large samples in contrast to the small ones, then we illustrate the central limit theorem on the example of the many Binomial distribution answers, and at the end we illustrate the Beta distribution, which is the most abstract, becease it simulates probability function on probabilities. This blog helped me a lot in understanding Beta distibution (https://towardsdatascience.com/beta-distribution-intuition-examples-and-derivation-cf00f4db57af) but I did a lot of changes and some more common sense explanation for better intuition.
Here we make the illustration how we can use the Box-Cox transformation to transform some data distribution to normal, by searcing and finding the adequate parameter lambda.
A Box Cox transformation is a transformation of non-normal dependent variables into a normal shape. Box and Cox proposed a parametric power transformation technique defined by a single parameter λ, aimed at reducing anomalies in the data and ensuring that the usual assumptions for a linear model hold. This transformation results from modifying the family of power transformations defined by Tukey to account for the discontinuity at λ = 0.
Explanation of gradient and programming of gradient descent from the scratch and plotting for several epochs
This code is essence of machine learning. Understending how gradient descent works is the most fundamental thing. It is easier to understand it how it works on linear regression, and then it will be no pain to understand how it works in Deep Learning, Reinforcment learing function approximation and how more advanced optimisers works (e.g. famous Adam).
Receiver Operating Characteristics (ROC) curve gives us the estimation for model performance based on comparing true positive and false positive rate for various tresholds of our binary target variable.
Good excersice for understanding the sensitivity, recall and f1 as harmonic mean of the first to metrics. According to problem, carefull selection of adequate metric can be a crucial thing.
This is simple method for checking multicolinearity in predictors. All predictors are interchangebly taken as a predictor, while looped predictor is a target, then we take metrics where
is coefficient of determination.
Plotting different types of distributions and examples of distributions in relation to Tukey's lambda
The Tukey Lambda PPCC plot, with shape parameter λ, is particularly useful for symmetric distributions. It indicates whether a distribution is short or long tailed and it can further indicate several common distributions. Specifically,
: distribution is approximately Cauchy
: distribution is exactly logistic
: distribution is approximately normal
: distribution is U-shaped
: distribution is exactly uniform
Here we use the simplest example of Monte Carlo simulation in the task when we want to know the most probable sum of rolling 12 six sided dices.
We use Gibbs sampling when we are unable to sample directly from multivariate distribution consisted of two or more univariate distributions, but we can do sampling from various (in this case two) conditional distributions. The point of Gibbs sampling is that given a multivariate distribution it is simpler to sample from a conditional distribution than to marginalize by integrating over a joint distribution. Code is from blog: https://towardsdatascience.com/gibbs-sampling-8e4844560ae5 but with some additions and clarifications.