A discrete example
Suppose P(A) = 0.2, P(B) = 0.3 and P(C) = 0.5. The cumulative boundaries are 0.2, 0.5 and 1.0. For a uniform draw u in [0, 1), map u < 0.2 to A, 0.2 ≤ u < 0.5 to B, and the rest to C.
One outcome versus a frequency
Move the draw across the colored intervals. A occupies 20% of the line, B occupies 30%, and C occupies 50%. The line shows how a uniform number maps to one outcome. The slider chooses a number directly; it does not generate randomness. Slide the draw across 0.2 and 0.5. The selected outcome changes at the interval boundaries, whose widths correspond to the specified probabilities.
INTERACTIVE EXPLORATION
Map a draw to an outcome
Move a uniform draw u through [0, 1). The fixed probabilities are P(A) = 0.2, P(B) = 0.3 and P(C) = 0.5.
Sampling in models
Generative models use sampling in different ways, such as drawing a token from a predicted distribution or drawing a latent variable. A deterministic argmax choice is different from sampling.
Check your understanding
Which outcome corresponds to u = 0.35 in the example?
B: 0.2 ≤ 0.35 < 0.5.