Conformal Prediction for Reliable Hyperparameter Selection in Sparse FIR Filter Design

Sparse finite impulse response (FIR) filters reduce computational cost on resource-constrained devices, but selecting the sparsification threshold $\lambda$ is typically left to grid search or hand tuning. We propose a two-stage method: a 67,331-parameter surrogate network predicts $(A_p,A_s,S)$ (passband ripple in dB, stopband attenuation in dB, sparsity in %) from a filter specification and a candidate $\lambda$, and split conformal prediction (CP) calibrates ± intervals around each prediction. We then select $\lambda$ by minimizing a worst-case penalty computed on the conservative ends of the intervals (the upper bound on $A_p$ and the lower bound on $A_s$). On 10,000 test specifications the method reaches 76.5% specification satisfaction, near-parity with grid search (78.4%) with a 1.9 $\times$ speedup, while point-prediction surrogates reach only 39.4%. On feasible specifications (where any grid $\lambda$ satisfies both constraints), the method reaches 97.6%. Stratified (Mondrian) conformal prediction lifts standard CP coverage from 67%–75% to 95.5%, and adaptive recalibration brings passband coverage to 91.3%. The procedure transfers without modification to iteratively reweighted least squares (IRLS) sparsification (76.6%) and to highpass (79.2%) and bandpass (52.4%) filters. The implementation runs on a central processing unit (CPU) and is suitable for edge deployment; code and data are public.