Causality Archives

Occam’s Razor: A Probabilistic View

Posted on March 13, 2018 Written by The Cthaeh 7 Comments

“Simple explanations are better than complex explanations.” — have you heard this statement before? It’s the most simplified version of the principle called Occam’s razor. More specifically, the principle says:

A simple theory is always preferable to a complex theory, if the complex theory doesn’t offer a better explanation.

Does it make sense? If it’s not immediately convincing, that’s okay. There have been debates around Occam’s razor’s validity and applicability for a very long time.

In this post, I’m going to give an intuitive introduction to the principle and its justification. I’m going to show that, despite historical debates, there is a sense in which Occam’s razor is always valid. In fact, I’m going to try to convince you this principle is so true that it doesn’t even need to be stated on its own.

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When Dependence Between Events Is Conditional

Posted on November 26, 2016 Written by The Cthaeh 9 Comments

In this post, I want to talk about conditional dependence and independence between events. This is an important concept in probability theory and a central concept for graphical models.

In my two-part post on Bayesian belief networks, I introduced an important type of graphical models. You can read Part 1 and Part 2 by following these links.

This is actually an informal continuation of the two Bayesian networks posts. Even though I initially wanted to include it at the end of Part 2, I decided it’s an important enough topic that deserves its own space.

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What Are Bayesian Belief Networks? (Part 2)

Posted on November 20, 2016 Written by The Cthaeh 11 Comments

In the first part of this post, I gave the basic intuition behind Bayesian belief networks (or just Bayesian networks) — what they are, what they’re used for, and how information is exchanged between their nodes.

In this post, I’m going to show the math underlying everything I talked about in the previous one. It’s going to be a bit more technical, but I’m going to try to give the intuition behind the relevant equations.

If you stick to the end, I promise you’ll get a much deeper understanding of Bayesian networks. To the point of actually being able to use them for real-world calculations.

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What Are Bayesian Belief Networks? (Part 1)

Posted on November 3, 2016 Written by The Cthaeh 22 Comments

In my introductory Bayes’ theorem post, I used a “rainy day” example to show how information about one event can change the probability of another. In particular, how seeing rainy weather patterns (like dark clouds) increases the probability that it will rain later the same day.

Bayesian belief networks, or just Bayesian networks, are a natural generalization of these kinds of inferences to multiple events or random processes that depend on each other.

This is going to be the first of 2 posts specifically dedicated to this topic. Here I’m going to give the general intuition for what Bayesian networks are and how they are used as causal models of the real world. I’m also going to give the general intuition of how information propagates within a Bayesian network.

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The Inverse Problem and Bayes’ Theorem

Posted on March 6, 2016 Written by The Cthaeh 7 Comments

The inverse problem is fundamentally related to the subject of causality. Think about a scenario…

What will happen if you grab a solid rock and throw it at your neighbor’s window? The most common result is that the window will break. If your neighbor later asks if you know anything about the incident, you can confidently inform him that his window was broken because you threw a rock at it earlier. Cause and effect — sounds pretty straightforward.

But what if it wasn’t you who broke the window and, in fact, you have no idea what broke it? Did someone else throw a rock at it? Was there a large temperature difference between the center and the periphery of the glass which caused a spontaneous breakage? Or was it a spontaneous breakage caused by a fabric defect?

You see, unlike the previous question, this one is actually not straightforward to answer. It involves solving the sо-called inverse problem: inferring the causes of a particular effect.

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