statistics Archives - Page 8 of 11

The Gradient Descent Algorithm Explained Clearly: From Intuition to Practice

A blindfolded person on a mountain

Imagine standing on a mountainous terrain, completely blindfolded. Your goal: reach the lowest point in the valley. You can’t see anything, but you can feel the slope of the ground beneath your feet. What do you do? You move in the direction where the ground goes down, one step at a time. If it slopes more steeply to the left, you go left. If it drops more to the right, you go right. With each step, you feel the slope again and redirect yourself.

This strategy, so simple and natural, is exactly what neural networks use to learn. Every time an AI model improves — learning to recognize a face, translate a sentence, or generate text — it does so by descending through a mathematical landscape, one step at a time, following the slope.

It’s called gradient descent, and it’s arguably the most important algorithm in modern machine learning.

Infographic: the blindfolded explorer metaphor for gradient descent, with three steps: Sensor, Action, Cycle

The Hypergeometric Distribution

We have seen that the binomial distribution is based on the hypothesis of an infinite population N, a condition that can be practically realized by sampling from a finite population with replacement.

If this does not occur, meaning if we are sampling from a population without replacement, we must use the hypergeometric distribution. (In reality, if N is large, the hypergeometric probability density function tends towards the binomial).

The hypergeometric distribution is used to calculate the probability of obtaining a certain number of successes in a series of binary trials (yes or no), which are dependent and have a variable probability of success.

The hypergeometric distribution allows us to answer questions like:

If I take a sample of size N, in which M elements meet certain requirements, what is the probability of drawing x elements that meet those requirements?

The Negative Binomial Distribution (or Pascal Distribution)

The negative binomial distribution describes the number of trials needed to achieve a certain number of successes in a series of independent trials. For example, it could be used to calculate the probability of getting three heads when flipping a coin 5 times, assuming the coin is balanced and therefore the probability of getting heads on each flip is 50%.

The negative binomial distribution is useful in many fields, including statistics, economics, biology, and physics. And also in “our” SEO.

First Steps into the World of Probability: Sample Space, Events, Permutations, and Combinations

How likely is it that a page reaches the first results page? Or that an A/B test gives a reliable answer? Questions like these — seemingly very different — share the same root: to answer them we need probability and combinatorics. In this post we lay the foundations, exploring together the basic tools that will accompany us throughout the whole path.

Logistic Regression: Predicting the Outcome of an Event

Logistic regression is a statistical model used to predict the probability of an event based on a set of independent variables. It’s particularly useful when you want to classify an event as belonging or not to a specific category (for example, whether a customer will buy a product or not, or whether a patient will develop a disease or not).

It is a Supervised Machine Learning algorithm that can be used to model the probability of a specific class or event. It is used when the data is linearly separable – that is, if there exists a line or plane that can be used to uniquely separate the data into different classes – and the outcome is binary or dichotomous. This means that logistic regression is typically used for binary classification problems (Yes/No, Correct/Incorrect, True/False, etc.),

In this post, I will demonstrate how to perform binomial logistic regression to create a classification model, in order to predict binary responses on a given set of predictors.