How do we predict the likelihood of various outcomes in uncertain situations?
Image: Ole Hedeager, CC BY-SA 4.0, via Wikimedia Commons
How do we predict the likelihood of various outcomes in uncertain situations?
Imagine you're a chef trying to predict how popular different dishes will be at your restaurant.
Think of the Dirichlet distribution as a recipe that helps you mix your predictions for each dish's popularity, considering how much you know about them so far.
Example
If you've tried 3 dishes and know 2 are popular, the Dirichlet distribution helps you predict the third dish's popularity by considering the popularity of the first two.
Remember this
The Dirichlet distribution helps you blend your predictions for different outcomes based on past experiences, ensuring a balanced and informed forecast.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
Markov chain Monte Carlo
MCMC samples from complex posterior distributions
Entropy H = -Σ p(x) log₂ p(x) measures average surprise in bits
How do we measure uncertainty in everyday decisions?
Metropolis–Hastings algorithm
Metropolis-Hastings algorithm samples from difficult distributions
Bayesian inference
Ever wondered how doctors update diagnoses as new symptoms arise?
log-probabilities are used instead of probabilities: avoids numerical underflow
Why can't we just add up tiny chances over time?
cross-entropy equals negative log-likelihood for classification
Why does knowing the wrong probability help us measure information loss?
Swipe through 100 ML concepts daily
Open Pocket Polymath