Probability for Machine Learning
Use random variables, conditional probability and distributions the way ML models do
A taste of a lesson
A density value of 2.5 came out of my Gaussian. How can a probability be bigger than 1?
It is not a probability, it is a density. For continuous variables, the probability of any exact value is zero; probabilities come from the area under the density curve over an interval. A narrow Gaussian, say with standard deviation 0.1, must be tall to have total area 1, so its peak is about 4. Your 2.5 means values near that point are relatively likely. Check: if the density is roughly 2.5 across an interval of width 0.02, what is the approximate probability of landing in it?
Written by the teacher as an example. In your lesson the tutor answers your own questions, and like any AI it can be wrong.
What you will be able to do
- Work with joint, marginal and conditional distributions using the sum and product rules
- Apply Bayes rule and conditional independence in model contexts
- Compute expectations, variances and covariances and use linearity
- Describe Bernoulli, categorical and Gaussian distributions including the multivariate case
- Distinguish generative and discriminative models probabilistically
Lesson plan
- 1 Random variables Define discrete and continuous random variables correctly. Start
- 2 Joint, marginal, conditional Move between joint, marginal and conditional distributions. Start
- 3 Bayes and conditional independence Apply Bayes rule and recognise conditional independence. Start
- 4 Expectation and variance Compute and manipulate expectations, variances and covariances. Start
- 5 Core distributions Use Bernoulli, categorical and Gaussian distributions. Start
- 6 Probability inside models Read models as probabilistic statements. Start
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About this tutor
An intermediate tutor for learners with basic probability intuition who want the formal tools machine learning relies on. You will work with random variables, joint, marginal and conditional distributions, the sum and product rules, Bayes rule and conditional independence. Lessons cover expectation, variance and covariance, the Bernoulli, categorical and Gaussian distributions including the multivariate Gaussian, and how classifiers output conditional probabilities. You finish able to read probabilistic descriptions of models and to tell generative from discriminative approaches.
Reviews
4.3
3 ratingsSample
- Riya P.Sample
Solid and precise. Quick simulations to check answers were a nice habit to pick up.
- Zofia M.Sample
The density versus probability explanation cleared up a confusion I had carried since university.
- Emmanuel K.Sample
Good bridge from intuition to notation. The generative versus discriminative lesson was very clear.
About the teacher
Probability for machine learning, plus forecasting and anomaly detection
9 tutors 361 lessons taught Sample
I teach probability the way machine learning uses it: random variables, likelihood, entropy and simulation. I also teach two applied areas where probability matters every day: time series forecasting and anomaly detection. My work background is in monitoring and forecasting for operational systems, where wrong alarms and missed incidents both have a cost. I teach through small simulations, coin and...
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