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A Program of Experiments With Risk, Context, and Organizational Constraints

An experimentation program is a portfolio problem: at each time $t$, given what we currently know and today's constraints (backlog, traffic budget, test and implementation costs), we must choose a slate of ideas to test, decide how much traffic to allocate, and determine which experiments to continue, stop,

The Elephant in the Sampling Frame: Lessons from Basu's Parable

In Basu's circus story (PDF), the owner wants to estimate the weight of fifty elephants and suggests weighing Sambo, who looked “average” three years ago, and reporting $50y$. A statistician counters with a contrived sampling plan: choose Sambo with probability $99/100$ and pick any of the other

How to Make Things Slower So They Go Faster

In a service with capacity $\mu$ requests per second and background load $\lambda_0$, the usable headroom is $H = \mu - \lambda_0 > 0$. When $M$ clients align, e.g., after a cache expiry, at a cron boundary, or as a service returns from an outage, the bucketed arrival rate

Bandwidth Selection Without Grid Search

Bandwidth selection is often framed as "scan a grid and pick the CV minimum." For common univariate problems, you can do better. The leave‑one‑out (LOO) cross‑validation objectives admit closed‑form derivatives in the bandwidth $h$. With analytic gradients (and Hessians when useful), a one‑dimensional

Rank‑Preserving Calibration for Multiclass Probabilities

We often need to adjust a fitted $E[Y|X]$ so that the aggregate $E[Y]$ (or class totals) matches known targets (see here). In binary classification, a single logit shift (or a global temperature) is a monotone transform of the model scores, so if person A had a higher

Generalization Gap in Over‑Parameterized Models

Textbook bias–variance intuition implies that worst‑case test error should eventually rise as model capacity overtakes the sample size because the variance term in the bound grows while the bias term has already bottomed out (see Vapnik and Chervonenkis, 1971; Bartlett and Mendelson, 2002). Those worst‑case guarantees shrink

Burning ₹168 to Earn ₹100

Tamil Nadu’s civil service hopefuls give up nearly 1.68 times as much in lost earnings (and coaching fees) as the state will ever pay in salary (see Table 2.5 in Mangal, 2023 (PDF); see MR as well). At first pass, this looks like over-dissipation: candidates appear

A Lightweight ALS Solver for Iterative GLS

When generalized least squares spans hundreds of equations, the error covariance becomes the problem. Every loop that updates $\beta$ drags along a $K \times K$ inverse; storing it costs about $O(K^2)$ memory and inverting it costs about $O(K^3)$ time. Even when we model the covariance statistically

One Record, Many Assertions

Agent evaluations tend to acquire a new expectation type for every capability: messages, tool calls, state changes, delegations, UI actions, memory, artifacts, audit logs. The result is usually a fragmented test system in which closely related requirements are represented and evaluated differently. A cleaner design separates three artifacts: trial record