The Book

Inspired by Paul Erdős’ description of beautiful proofs, this website highlights deep and elegant insights that, in my humble opinion, deserve their own pages in The Book. I planned, AI drafted, and I edited: the decide-execute-deliver sandwich.

A two-dimensional map of the public pages, with numbered points and a title key. The complete linked listing is below.

MPNet embeddings + MDS

Aliasing on Purpose

Shapley Values

Estimation

An experiment can estimate an average without measuring every effect separately.

Iterative Hessian Mixing

Differential Privacy

Linear Algebra

Estimation

A Gaussian sketch hides a person when their row accounts for little of its covariance. Added noise can create that condition.

Shrinking Toward Zero

Estimation

Probability

The James–Stein estimator lowers total mean squared error by shrinking several Gaussian measurements together.

Shapley Values at Legendre Nodes

Shapley Values

Probability

Turning an exponential sum over coalitions into an exact polynomial integral.

Neyman Allocation

Estimation

Sampling

Optimization

Dividing a sample budget between groups by equalizing the benefit of another observation.

Three Noises for the Argmax

Sampling

Differential Privacy

One conditioning calculation explains how different noises change who wins.

Prune and Clone

Sampling

Estimation

Language Models

Reusing promising attempts while preserving the original probability of success.

A PSA on Shapley Values

Shapley Values

Estimation

Choose the game, fit a surrogate, and extract its Shapley values.

The Even–Odd Decomposition

Shapley Values

Estimation

Pairing groups of players offers a way to estimate individual contributions more accurately.

Exponential Minimum Sampling

Sampling

Language Models

Shared randomness lets a provider recognize generated text without changing its sampling distribution.

Tilting at Rare Events

Sampling

Estimation

Language Models

When a thousand tries give no successes, change where you sample without changing the probability you want to measure.

The Infinite Gaussian Vector

Estimation

Probability

A prediction between measurements should come with some idea of how uncertain it is.

Why Sums Become Gaussian

Probability

Adding independent Gaussian noise gives more Gaussian noise. A rotation explains why.

Hutch++ and the Split Spectrum

Linear Algebra

Estimation

Estimating a matrix’s diagonal sum using only a few matrix-vector products.

Implicit Control Variate

Sampling

Estimation

Fixing the number of samples removes the same variance as a constant adjustment tuned to the unknown population average.

Three Faces of Leverage Scores

Linear Algebra

Sampling

Why an observation’s influence on a fitted model also tells us which graph edges to keep.

A Determinant Counts Spanning Trees

Linear Algebra

A graph can have too many spanning trees to list, yet one determinant counts them all.

One Data Shapley Vector Is Not Enough

Shapley Values

Optimization

Choosing the most useful training points individually can give us a poor training set.

Piecewise-Constant Shapley Values

Shapley Values

Assigning credit to individuals can be cheaper when many groups produce the same value.

Rotate, Round, and Debias

Linear Algebra

Estimation

Compressing embeddings to preserve the scores used for ranking their matches.

Speculative Decoding via Maximal Coupling

Language Models

Sampling

A small model can help a large model write faster without changing the distribution of its text.

The Greedy \(1-1/e\) Guarantee

Optimization

Why choosing whatever helps most right now guarantees at least 63% of the best possible coverage.

The Tournament Is a Distribution Update

Language Models

Sampling

A tournament helps mark generated text, but we can compute its outcome without playing the matches.

Volume Sampling Improves Leverage Sampling

Linear Algebra

Sampling

Two important rows can carry the same information. Volume sampling chooses them as part of a set.