The Importance of Probability in Data Science
kdnuggets.com
kdnuggets.com
That said, this article is weird ("theoretical probability" vs. "experimental probability"... huh?) and is not exactly something I would want to share around. It almost seems like the author wrote it for their own benefit, after themselves recently realizing that probability is important and useful/essential in data science, and wanting to share what they learned. I'm not sure it's worth anyone's time to read it.
That raised my eyebrows as well. It looks like it's a Thing They Teach In Schools These Days: https://www.statisticshowto.com/theoretical-probability/
My guess is they're trying to get kids to think about inductive Vs deductive reasoning. And it may set a foundation for understanding the difference between a posterior and a priori distributions. But it comes across as if they're a different type of object, which feels a little off.
I flip a coin twice. It lands heads-up both times. Then the experimental probability of this coin landing heads-up is 1.
You give me a coin which you guarantee has a 50/50 chance of landing heads-up. The theoretical probability of it landing heads-up twice is 1/4.
Either type of probability can be used in statistics.
Statistics (the old school kind) is just about computing summary metrics for large amounts of data.
Probability is about deriving properties of a sample from the population, based on population parameters.
Statistical inference (what is usually meant by "statistics" these days) is about figuring out what sort of population parameters could have produced the sample at hand -- i.e. probability but backwards.
For instance I was expecting a few case studies where a blind application of sklearn defaults led to issues fixed with proper probabilistic thinking.
I remain unconvinced about the importance of probabilities for data science, even more so when I doubt 1% of practicing data scientists could explain what a measure is.
Yes, it's very weird. I can't tell if the author can't express themselves well enough in English, doesn't understand the topic, or something else happened (editorialization, SEO garbage...)
> Likelihood is applied when you want to increase the chances of a specific event or outcome occurring.
???
> if 12 cars go down a particular road at 11 am every day, we can use Poisson distribution to figure out how many cars go down that road at 11 am in a month.
???
> if we’re looking at how many chocolate bars were sold in a day, we would use the normal distribution. However, if we want to look into how many were sold in a specific hour, we will use t-distribution
???
GPTZero thinks it's written by a human, for what its worth... i guess the author is a bit confused or unable to clearly articulate ideas.
I'm not saying that this is a "problem" in the sense that one should discard probability and statistics - but rather that in order to truly know what's going on, you need to actually study the topics. Deeper than surface-level knowledge. It's not something you can learn over the course of a tutorial or two.
If a statistican from the 50s walked into a modern start up office, they'd laugh at the lack of validation and testing and not be at all shocked when none of the predictions worked
Nooooo. I want to report this article to the fake news / harmful speech authorities. Never a better case has been made against free speech and pro censorship.
We are all drilled to some extend to accept probability theory, but there are some truly mind bending exercises in interpreting probability.
How do you define probability for a event that can only happen once, e.g. what is the probability of our cosmic microwave background pattern ?
How do you define conditional probability when conditioning on the assumption that an impossible event has occurred, e.g. what is the probability of the Color of my wall changing assuming Garfield the cartoon cat would enter the room?
I mean mathematically you cannot apply a measure to something outside the space the measure has been defined on (the probability space is defined as the powerset of the set of possible values), so at least from a theory standpoint this question isn't that deep.
Its a bit like asking if the set of all sets that do not contain themselves is contained in itself. The question makes no sense in set theory, but it leads to important extensions.
Edit: Have a look at the Borel–Kolmogorov paradox, and approaches to consolidate it https://link.springer.com/article/10.1007/s11229-016-1070-8
Tangential, but related. For the Deep learning folks I recommend having a look at tensorflow probability or some pytorch analogue. For instance, following [1] you see that bolting the capability to model at least aleatoric uncertainty is super simple.
The benefits are enormous. In fact, apart from technical aspects that such an approach can unlock (eg if the output is favorable but the uncertainty is too high still don't act on the predictions because the cost of a acting on a false positive is >> than non acting on a false negative) I found that being able to output the model uncertainty goes a long way in convincing non technical stakeholders about trusting predictions.
[1] https://blog.tensorflow.org/2019/03/regression-with-probabil...
Edit: wow, I don't think I've seen "support vector machine" mentioned even once anywhere in the last 2 years. Times have changed! I wonder how this toolbox has been updated in the age of deep learning and probabilistic programming.
The importance of control structures in imperative programming.
> Conditional probability is the possibility of an event/outcome occurring based on an existing event/outcome.
From https://www.investopedia.com/terms/c/conditional_probability...
> Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome.
"Sure you can copy my homework, just change it a bit".
And "bare" probability can be seen as conditioned on the outcome space, P(A) = P(A|Omega)
Something like a visual explanation showing how a conditional distribution is like a single row or column from a 2D table would be so much easier for people to understand.
The bayesian interpretation, which is easily the most general, is happy to take the arguments of the probability function inscrutably as bare propositions.
I agree that conditional probability is best demonstrated graphically. The sample space is a big rectangle, and events are represented as polygons or other closed shapes, with area proportional to their probability. Conditional probability elegantly falls out of this representation by treating one of these event-shapes as a new "sub sample space" and computing fractions of areas.
So this area model at once creates a lot of confusion elsewhere.
Then you can blow your students' minds with the possibility that the "rectangle" is actually the unknowably massive timeline of the entire universe, from the Big Bang until its heat death, and all of our models and reasoning are conditional on some subset of that gigantic world-rectangle. In my opinion, the power of this philosophical leap is lost without the basic geometric intuition.
Think about it like PCA. Do you lose some information? Yes. But you can do a lot with only the first few principle components (i.e. basic concepts).
Things like events, sets, measures, etc add important details like why you have to divide the selected row / column by its sum to get a true conditional distribution; how many dimensions the array should have; constraints, properties, and relationships of subarrays, etc. But that all becomes a lot easier to understand once you have the basic intuition. And once you get good enough you can start to let go of the grounding in arrays and ground in other concepts and then think about it more abstractly.