Probabilistic Machine Learning
Move beyond single-number guesses by modeling uncertainty directly. Learn to output full predictive distributions, separate data noise from model ignorance, and infer hidden structures.
Like Duolingo, but for Probabilistic Machine Learning. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
A short one: 11 levels across 2 sections, about 22 minutes end to end, roughly 4 days at five minutes a day. It moves through Predicting with Calibrated Uncertainty and Latent Structure and Inference Decisions. It assumes you already know the basics.
Free forever · No credit card · iPhone & Android
Key ideas in Probabilistic Machine Learning
- Point predictions correspond to only predicting the distribution's mean.
- The model must output both mean and standard deviation parameters.
- Variance outputs require constraints like softplus to guarantee positivity.
- Mean squared error implicitly assumes a constant fixed variance for all errors.
- Negative log-likelihood scales loss by inverse predicted variance.
- Confident mispredictions cause log-likelihood loss to spike dramatically.
- Heteroscedastic models adapt their uncertainty estimate to each specific input.
- Homoscedastic models enforce a single shared global noise assumption.
- Aleatoric uncertainty represents irreducible real-world observation noise.
- A calibrated 90% interval contains true observations exactly 90% of the time.
- Intervals containing fewer actual targets than expected reveal overconfidence.
- Intervals containing more actual targets than nominal indicate underconfidence.
- Aleatoric uncertainty is inherent measurement noise that additional training points cannot eliminate
- Epistemic uncertainty stems from model ignorance in regions sparse in training data
- Collecting more labeled samples shrinks epistemic uncertainty but leaves aleatoric noise unchanged
- Standard backprop settles on a single point estimate for each weight matrix
You've tried the other tabs
Thirty open tabs. Four facts you actually kept.
You watched. You nodded. By Sunday it was gone.
One answer, then back to scrolling.
Eight weeks. You meant to finish. You didn't.
Tomo gives Probabilistic Machine Learning the Duolingo treatment: levels, streaks, and quick quizzes that test what you just learned. That game loop is what the tabs above never had, so it's the one you actually finish.
Here's what playing it feels like
A real question from this course. Take your best guess.
When a regular neural network outputs just one single number, what part of the whole prediction bell is it giving you?
Get it right to open this lesson and 10 more in the app.
Where Probabilistic Machine Learning takes you
- 1
Predicting with Calibrated Uncertainty
- Predicting distributions instead of single numbers
- Separating data noise from model ignorance
- 2
Latent Structure and Inference Decisions
- Uncovering hidden causes with latent variables
- Navigating the tradeoffs of approximate inference
2 sections · 4 units · 11 levels. Built to play, not to enroll.
Tomo is in ChatGPT
Tomo is also a ChatGPT plugin: the same playable courses, built and played inside your chat.
Add Tomo to ChatGPT- What to ask
- “Make me a Tomo course on black holes.” “Turn this chat into a Tomo course.”
- What you get
- Quick questions with instant feedback, hearts and stars, ready to play in about a minute.
- Where it goes
- No sign-up to start. Connect your Tomo account and your streak carries on in the app.
You pick the voice
Probabilistic Machine Learning is taught in the Explain Like I'm 5 style: no big words. promise.. Want a different feel? In the app you can spin up the same topic in any of Tomo's teaching styles. Same facts, totally different vibe.
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Start Probabilistic Machine Learning today.
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