Algorithm 1 Approximate Attribution Enhancement (AAE)

Require:  Original feature set $\mathcal{X}={\left\{x_k\right\}}_{k=1}^n$, target size $N_{\mathrm{aug}}$, membership threshold a, seed s Ensure:  Membership-weighted augmented set W   1:Estimate per-dimension variances and form the diagonal training-fold covariance matrix D   ▹ Equation (9)   2:Compute the central sample ${\lambda }_{cen}$ and partition counts $N_F$, $N_C$   3:Initialise $W\leftarrow {\left\{({\lambda }_k,1)\right\}}_{k=1}^n$   4:Initialise the pseudorandom generator with seed s   5:while $\left|W\right|<n+N_{\mathrm{aug}}$ do   6:      Draw a reference ${\lambda }_k$ and sample a target membership ${\mu }_W\ge a$   7:      Solve for the candidate ${\lambda }_k^{\prime }$ by attribution inversion                   ▹ Equation (12)   8:      Apply biased far/near acceptance with coefficients $\alpha ,\beta$                 ▹ Equation (13)   9:      if ${\mu }_W\left({\lambda }_k^{\prime }\right)\ge a$ then 10:           Assign a soft label by membership-weighted averaging over neighbours 11:           $W\leftarrow W\cup \left\{({\lambda }_k^{\prime },{\mu }_W\left({\lambda }_k^{\prime }\right))\right\}$ 12:      end if 13:end while 14:return W                                       ▹ Equation (14)