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Unbiased regression with costly item labels

Consider a common scenario: you observe how units (users, devices, firms) interact with items (websites, products, apps), and each item has an unknown binary trait (is it harmful? is it premium content?). You want to understand how these traits relate to unit characteristics through regression, but labeling items is expensive.

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

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 to

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