Someone reports: "I trained a logistic-regression classifier directly on the raw spin…
PHYSICS · Multi-part · Fermi University Physics · Computational Physics · Monte Carlo and lattice simulation of physical systems · High-performance and data-driven computational physics
Scientific Computing for Physicists, Ch Learning from physical data: regression, classification and principal components
Problem
Someone reports: "I trained a logistic-regression classifier directly on the raw spin configurations si∈{−1,+1} of a 30×30 two-dimensional Ising lattice to distinguish the ordered phase (T<Tc) from the disordered phase (T>Tc). A single Markov chain was run with a temperature schedule sweeping from low to high T, and 5000 configurations were saved, one every sweep. These 5000 configurations were split 80/20 by an ordinary random shuffle into training and test sets. The classifier reached 99% test accuracy, using only the raw spins as features. I conclude that a plain linear model finds the phases perfectly from raw spins, and that no special feature such as m2 is needed."
((a)) Using the spin-flip symmetry argument, explain why a linear classifier on raw spins should not, in general, be able to separate ordered configurations of both signs of magnetisation from the disordered cloud, and say what this implies about the ordered configurations actually saved from this one chain.
((b)) The signed magnetisation m of this lattice has an integrated autocorrelation time of about τint=200 sweeps. Estimate the effective number of independent configurations among the 5000 saved, and use it to explain why the random 80/20 split inflates the reported accuracy.
((c)) State what test would have to be run instead to obtain an honest accuracy figure for this classifier.