Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. On a 20% test split of the UCI digits, 360 images, logistic regression, an RBF SVM and 3-NN score 0.967, 0.986 and 0.986, and one test set’s 95% binomial interval is about +-0....
Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Two character transformers, identical in architecture, parameters, seed, steps, schedule and training problems. The one manipulated variable is the order of the lines in the training file. Packed in generation order, every reversed sum lands directly beneath the forward form of the same sum - 5,076 of 5,076, which is all of them - and ‘reverse the line above’ answers the question with no arithmetic....
Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Split conformal at alpha = 0.1 on 24,576 held-out predictions split in half delivers 0.8961 coverage against a finite-sample guarantee of 0.9001, and over 200 calibration splits a mean of 0.8999. Exactly what was promised....
Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Give every cohort the same completed fertility and let each one postpone by d years relative to the last. The period TFR is then exactly Q/(1+d), the period mean age of childbearing rises at d/(1+d) rather than at d, and dividing the first by one minus the second returns Q to five decimal places — the Bongaarts-Feeney adjustment, which on this schedule is an identity rather than a correction....
Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. The residual is the check everybody runs after a solve, and it is the one check that cannot detect the most common way a solve goes wrong. The condition number can: it converts the precision of the inputs into an error bar on the output, before any statistics are involved....
Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. On 2,000 simulated least-squares datasets of 100 rows, where the exact test error of each fitted model is known, the correlation between the 10-fold CV estimate and that error is -0.01. The CV estimates spread 2....
Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. A model calibrated by construction - labels drawn from its own probabilities - scores an ECE of 0.085 on 200 predictions, 0.035 on 1,000 and 0.008 on 20,000 at 15 bins, and the fitted slope against bins/n is 0....
Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Give every worker a universal raise of g and hire entrants below the median. The median slides m/2 ranks, order statistics near the median are spaced 1/(n f(M)) apart, so the median falls once the entry share passes 2 g M f(M) - which for a lognormal is 0....
Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Forming X’X squares the condition number, so the formula everybody learns spends twice the digits of the two factorisations nobody is taught. Underneath, least squares is a right angle — the fit is the foot of a perpendicular onto the column space — and reading it that way explains why QR needs no inversion at all, and why the one check that defines a least-squares solution is blind to a normal-equations fit that is wrong by 321 percent....
Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Fit a step on all the rows, then cross-validate, and compare with the same step fitted inside the folds. Standardising leaks +0.05 points on the breast cancer data and mean imputation -0....