Thesis walkthrough

From distorted measurements to ordinal unfolding

01 / an inverse problem

Measurements are never quite the truth

Any real detector distorts what it measures: limited resolution, acceptance, and noise turn a true distribution into a measured one. Recovering the former is a deconvolution problem.

02 / classification in disguise

DSEA+ reframes deconvolution as classification

Rather than invert an often unstable matrix directly, DSEA+ iterates: train a classifier, estimate the spectrum from its confidences, reweight the training data, and repeat until convergence.

03 / a gap in the assumptions

Any classifier will do — almost

DSEA+ accepts probabilistic classifiers, but its target bins are ordered. Unlike unrelated color categories, bin 5 is closer to bin 6 than to bin 9 — a distance that common softmax classifiers do not encode.

04 / ordinal regression for neural nets

CORN: rank instead of raw category

CORN casts ordinal classification as chained binary questions: does an event exceed rank k? Its probabilities are linked so predictions remain rank-consistent by construction.

05 / making the two compatible

Adapting CORN to fit DSEA+

CORN natively returns one predicted rank per event. DSEA+ needs complete per-class confidence distributions and weighted training samples, so both extensions bridge the methods.

06 / does it help?

Testing the combination

Bayesian hyperparameter search, cross-validation, and bootstrapped uncertainties test whether respecting ordinality improves the unfolded result over a non-ordinal baseline.

Inverse problem

Recover distributions, not individual events

The central task is to infer an underlying spectrum from detector-distorted observations while managing limited data and numerical instability.

Method

Iterative, classifier-based unfolding

DSEA+ turns deconvolution into a data-reweighting loop driven by calibrated class-confidence estimates.

Ordinal learning

Use the structure of ordered targets

CORN encodes rank order directly, providing a principled alternative to treating every target bin as unrelated.

The end

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