One arrow, three lengths: 5 Euclidean, 7 Manhattan, 4 max norm. They are one formula with a dial p, and the unit ball morphs from a diamond at p equals 1, to a circle at 2, to a square at infinity.
Full video: https://t.co/sZX2YhWHUd
K-means slices two crescents in half because it only ever makes round blobs around a center. DBSCAN counts neighbors inside a radius, floods along the dense regions, and leaves stranded points labeled as noise.
Full video: https://t.co/chqdBuUcLc
The Beta distribution is a distribution over a probability. Alpha tracks wins, beta tracks losses, the mean sits at alpha over alpha plus beta, and their sum acts like how much evidence you have seen.
Full video: https://t.co/niPlP2HmB5
UMAP asks one question in 784 dimensions: who are my nearest neighbors. That gives a graph. Throw the coordinates away, scatter the points on a plane, treat each edge as a spring, and let it relax.
Full video: https://t.co/ODby9Hbpdq
When two features are nearly identical, X transpose X goes nearly singular and the coefficients blow up. Ridge adds lambda times the identity before inverting, which is a small ridge along the diagonal, and the inverse stays calm.
Full video: https://t.co/nKkhhYD4oC
Lasso zeroes coefficients because the L1 penalty is the negative log of a Laplace prior, and that prior has a razor sharp peak at zero. Ridge uses a Gaussian, which is round, so it never quite gets there.
Full video: https://t.co/95LsUO9iVJ
A 2D Gaussian is not four numbers, it is a shape. The diagonal entries stretch the iso-density ellipse along each axis, the off-diagonal entry tilts it, and the sign picks the direction.
Full video: https://t.co/DpyxPgnJo0
Draw a circle for H(X) and one for H(Y). The overlap is I(X;Y), the crescents are the conditional entropies, and the whole shape gives you I(X;Y) = H(X) + H(Y) - H(X,Y).
Full video: https://t.co/vb6MI7Olh5
A histogram's shape depends on where you draw the bins. KDE drops a kernel on each point and sums them, so the bandwidth replaces the bin width and the bins go away entirely.
Full video: https://t.co/LbhHsstfRh
Fisher scores every projection direction as between-class separation over within-class variance. Maximize it and the answer is S_W inverse times the difference of the class means.
Full video: https://t.co/ITF8b6fnAE
A Q-Q plot pairs the quantiles of two distributions at each probability. Identical distributions land on the y equals x diagonal, and every deviation has its own shape.
Full video: https://t.co/4tgVP3ghPg
AdaBoost reweights the points it got wrong each round, so the next stump is forced onto them. The final answer is a weighted vote where confident stumps shout and weak ones whisper.
Full video: https://t.co/VSMqCLteLX
Learnt Covariance & Correlation today โ
Covariance tells you the direction, Correlation tells you both direction AND strength. Small difference, big impact on how you read data ๐
@datamlistic explains it really well ๐
https://t.co/gHi687p89m
#Statistics#DataScience#Python
You cannot push a gradient through a sampling step. Rewrite z as mu plus sigma times epsilon and the randomness moves into epsilon, leaving mu and sigma learnable.
Full video: https://t.co/urFzwCJC12
Normalization squashes to zero and one using min and max, so one outlier collapses your whole cluster into a stripe. Standardization uses mean and standard deviation and barely moves.
Full video: https://t.co/vtIpLzcPNJ
The bootstrap gets you a confidence interval with no normal assumption: resample your data with replacement hundreds of times, take the middle 95 percent of the means.
Full video: https://t.co/E1XCEOsIRa
A token's key and value never change once computed, so cache them, throw away the queries, and attention goes from O(N squared) recompute to O(N) append-and-reuse. The KV cache is just memoization.
Full video: https://t.co/2bIcUSRpsE
Spectral clustering isn't a new algorithm. It's k-means run on the smallest eigenvectors of the graph Laplacian, where two rings k-means couldn't split fall apart cleanly.
Full video: https://t.co/VcoBk5u5pJ
Maximizing the ELBO fits the data and tightens the approximate posterior in a single move. One bound, two problems.
Full video: https://t.co/6ElT5lhj9U