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BSc Thesis
Geometric Determinants of Generator Complexity in Optimal 1-Wasserstein GANs
This thesis re-examines the claim in WGAN theory that generator capacity must scale with the number of samples. I pursued it to cut through contradictory statements and isolate what actually drives complexity. The work was completed at Heidelberg University and generalises recent analyses from Stéphanovitch et al.
Goals
Test whether the alleged n-dependence is inherent or a proof artefact. Do so via constructive solutions in settings with explicit geometry—Bernoulli, univariate and multivariate multinomial, and clustered data. Extract a clear criterion that separates easy from hard regimes based on exploitable geometric structure.
Results
The dependence on n is not fundamental; geometry of the empirical measure is decisive. I prove this using explicit constructions of generator functions that extend prior results while keeping the Lipschitz budget fixed. The takeaway is a shift from counting samples to designing generators that adapt to data geometry, pointing to higher-dimensional cluster theorems and richer latent spaces.
Private Project
Mean-Reversion Pairs Trading Model for Financial Markets
This small private project tested a cointegration pairs strategy based on a mean-reversion approach using daily data on selected crypto and ETF pairs. I executed it independently; methods and sources are documented here.
Goals
Assess whether rolling cointegration delivers risk-adjusted returns after costs and identify which pairs/parameter regimes work. Evaluate Sharpe, drawdown, time-in-market against a 50–50 benchmark, and test whether ADF statistics predict performance.
Results
Fundamentally related ETF pairs (e.g., TLT/IEF, EEM/VWO) achieved around-one Sharpe with manageable drawdowns, while crypto pairs underperformed; the edge persisted after realistic costs. ADF alone wasn’t predictive, pointing to richer screening and higher-frequency testing for future iterations.
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