Enhanced Data-Driven Product Development via Gradient Based Optimization and Conformalized Monte Carlo Dropout Uncertainty Estimation

TL;DR

This work addresses efficient design optimization under multiple correlated properties by learning a differentiable surrogate $\hat{f}$ with a multi-output neural network and searching the input space via Projected Gradient Descent to maximize performance while respecting feasible ranges: $x^* = \arg\max_x \hat{f}(x)$ subject to $x \in \mathcal{H}$. It advances uncertainty quantification by introducing ConfMC, which combines Monte Carlo Dropout with Nested Conformal Prediction to yield adaptive, finite-sample coverage guarantees without retraining when adjusting coverage levels, constructing intervals based on quantiles $[Q(\hat{t}/2), Q(1-\hat{t}/2)]$ to achieve $P(Y \in C(X_{\text{new}})) \ge 1-\alpha$. The methodology supports multi-target optimization with a joint objective and feature-wise gradient masking, enabling selective feature updates within user-defined bounds. Empirical validation across five real-world datasets shows ConfMC achieves target coverage with adaptive interval widths and avoids retraining, while demonstrating practical industrial deployment that improves design iterations and engineer trust. The work thus offers a scalable, uncertainty-aware framework for data-driven product design with actionable, model-agnostic uncertainty estimates in real-world settings.

Abstract

Data-Driven Product Development (DDPD) leverages data to learn the relationship between product design specifications and resulting properties. To discover improved designs, we train a neural network on past experiments and apply Projected Gradient Descent to identify optimal input features that maximize performance. Since many products require simultaneous optimization of multiple correlated properties, our framework employs joint neural networks to capture interdependencies among targets. Furthermore, we integrate uncertainty estimation via \emph{Conformalised Monte Carlo Dropout} (ConfMC), a novel method combining Nested Conformal Prediction with Monte Carlo dropout to provide model-agnostic, finite-sample coverage guarantees under data exchangeability. Extensive experiments on five real-world datasets show that our method matches state-of-the-art performance while offering adaptive, non-uniform prediction intervals and eliminating the need for retraining when adjusting coverage levels.

Figures (2)

• Figure 1: Empirical $Y$-conditional coverage. MC prediction intervals severely undercover, standard CP produces constant-width PIs, while CQR and Conf-MC generate adaptive, variable-width intervals.
• Figure 2: Web interface implementing the proposed method with user-selected coverage and error tolerance. Blue dots: tested products; green dot: search start; red dot: search end; red rectangle: prediction intervals at the chosen error rate.