How can we predict future events with uncertainty?
Image: Unknown authorUnknown author, CC BY 4.0, via Wikimedia Commons
How can we predict future events with uncertainty?
Imagine you're planning a picnic and want to know if it will rain tomorrow. You check the weather forecast, but it's not certain.
Think of the weather forecast as a series of clues that get more detailed over time. A stopping time is when you finally get a clear answer about tomorrow's weather.
Example
You check the forecast at 9 AM (F1), 12 PM (F2), and 3 PM (F3). You decide to stop checking when you get a definite answer at 12 PM (F2).
Remember this
A stopping time is when you stop looking for more clues because you've got a definitive answer.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
Likelihood function
Why can't we just guess probabilities correctly all the time?
the optional stopping theorem says about martingales and stopping times
Ever wondered why betting on a roulette wheel doesn't change your odds over time?
log-probabilities are used instead of probabilities: avoids numerical underflow
Why can't we just add up tiny chances over time?
Rényi entropy
How do we measure the unpredictability of an event?
Hidden Markov model
Ever wondered how you can predict outcomes without seeing all the details?
Cross-entropy H(p,q) = -Σ p(x) log q(x) measures how well q approximates p
Ever wondered how well we can guess the outcome of a random event?
Swipe through more Machine Learning concepts
Open Pocket Polymath