Understanding the source of the universe’s asymmetry between matter and antimatter is one of the major open questions in particle physics. In this work, the sensitivity of novel machine-learning-based inference techniques to $CP$-odd and $CP$-even $HWW$ anomalous couplings is studied in the $WH\to \ell \nu b\overline{b}$ channel ($\ell =e,\mu$), within the standard model effective field theory framework. Two machine-learning simulation-based inference (SBI) methods are explored: a per-event likelihood-ratio estimator, which directly approximates the ratio of probability densities between competing hypotheses, is benchmarked against a per-event optimal-observable estimator optimized for sensitivity to the parameters of interest. Both approaches are also compared to traditional summary statistics, in this case histograms of kinematic and angular observables, as commonly used in experimental analyses. SBI methods provide tighter constraints than one-dimensional summary statistics, though their performance is comparable to two-dimensional histogram analysis. The optimal-observable approach remains promising for its ability to probe multiple couplings simultaneously. Restricting the analysis to a region of high $S/B$ also enhances sensitivity to $CP$-odd operators while preserving sensitivity to $CP$-even operators, which histogram analyses often lose. Although the likelihood-ratio estimator sometimes struggles with likelihood minima and shapes, optimizations that target its robustness could make it more sensitive than both the optimal-observable estimator and the histogram method. These results underscore the potential of advanced simulation-based inference techniques, encouraging further exploration with LHC Run 3 data to surpass current ATLAS and CMS sensitivities.

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• Effective field theory
• Higgs bosons
• CP violation
• Deep learning
• Particle data analysis