Daniel Emaasit
Data Scientist
Haystax Technology
Download slides & code: bit.ly/intro-pml
ML: A Probabilistic Perspective (1/3)
ML: A Probabilistic Perspective (2/3)
Generative Process
Inference
ML: A Probabilistic Perspective (3/3)
\(p(\mathbf{\theta})\) = prior over the parameters
\(p(\textbf{y} \mid \mathbf{\theta})\) = likelihood given the covariates & parameters
\(p(\textbf{y})\) = data distribution to ensure normalization
\(p(\mathbf{\theta} \mid \textbf{y})\) = posterior over the parameters, given observed data
where:
Algorithmic ML | Probabilistic ML | |
---|---|---|
Examples | K-Means, Random Forest | GMM, Gaussian Process |
Specification | Model + Algorithm combined | Model & Inference separate |
Unknowns | Parameters | Random variables |
Inference | Optimization (MLE) | Bayes (MCMC, VI) |
Regularization | Penalty terms | Priors |
Solution | Best fitting parameter | Full posterior distribution |