CHAPTER 30 / 40
Probability & Linear-Algebra Foundations You Reuse
6 lessons · Explore, experiment and understand.
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- Step 125~15m3D · 11Code · 23★Most cinematic
Expectation, Variance & Covariance Algebra
Six identities — linearity of expectation, Var(aX+b)=a²Var(X), the variance-of-a-sum rule, and the covariance/correlation definitions — do 9…
Open lesson - Step 126~10m1Code · 23
The Central Limit Theorem
Average enough independent things — no matter how weirdly they are individually distributed — and the average is approximately Gaussian. Thi…
Open lesson - Step 127~10m1Code · 23
Concentration Inequalities (Markov, Chebyshev, Hoeffding)
How do you bound the chance an estimate is far from the truth without knowing its full distribution? Markov, Chebyshev, and Hoeffding give y…
Open lesson - Step 128~15m3D · 11Code · 23★Most cinematic
The Curse of Dimensionality
In high dimensions geometry stops being intuitive: volume flees to the corners, all points become nearly equidistant, and nearest-neighbor m…
Open lesson - Step 129~15m2Code · 23
A Field Guide to the Distributions ML Uses
Bernoulli, Binomial, Categorical, Poisson, Exponential, Gaussian, Beta, Gamma, Dirichlet — a compact map of the handful of distributions tha…
Open lesson - Step 130~15m3D · 11Code · 23★Most cinematic
The Four Fundamental Subspaces
Every matrix A carves its two spaces into four orthogonal pieces — column space, row space, null space, and left null space. This one pictur…
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