Md. Asif Uddin

    Chapter 4 VIII.4

    Experimental Design

    An experiment is designed to make one comparison, and seed variance decides whether that comparison is visible at all.

    An experiment is designed to make one comparison.

    How this chapter is built

    M2Substantive

    The derivations are the chapter. A reader who skips the algebra has not learned it.

    basics2/9what the words mean
    concept2/2what to picture
    theory0/2why it works, and when it does not
    mathematics0/9derive it, then compute it
    practice0/6build it, break it, read the papers

    Five strands, not one. Mathematics is the spine; the other four are the body. A chapter cannot pay its way out of teaching with problems, nor out of problems with teaching.

    Before you start

    The problem

    Two numbers differ. Whether that difference is a result depends on run-to-run variation that a single run cannot show, and on an ablation design that can attribute it.

    The batch gradient as an estimateTwo panels, each showing the true gradient direction as a solid arrow and several batch estimates around it. With a small batch the estimates scatter widely; with a large batch they cluster near the true direction.batch of 8noisy direction, many cheap stepsbatch of 512clean direction, few costly stepsNoise in the estimate is not purely a defect: it is also what lets a small batch escape a shallowbasin that a large one would settle into.
    Fig. 4 — The batch gradient as an estimate of the true one. A small batch scatters widely and steps often; a large batch points true and steps rarely.

    What this chapter covers

    • Baseline
    • Ablation
    • Controls
    • Hyperparameters
    • Reproducibility
    • Random seeds
    • Experiment tracking

    Apparatus

    The mathematics this chapter leans on, held in Book 0 so it can be assumed here without being taught here. Not a gate — follow a link when a step stops making sense.

    Estimators, bias and variance 0.ST.01 · Hypothesis tests 0.ST.03 · Variance and covariance 0.PR.03

    Notation

    • VarVariance
    • θ̂An estimate, as against the quantity it estimates
    • 𝔼Expectation

    Propositions

    Not yet written. The topics above are the plan for this chapter; each will become a proposition with its own figure.

    Worked problems

    0/3 problems0/3 variants0/6 exercisesowes 9 more

    Not yet written. At M2 this chapter owes 3 worked problems across 3 distinct variants, and 6 exercises, every one with a published solution. The build enforces that from the day the chapter is marked published.