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Most modern commodity imaging systems we use directly for photography—or indirectly rely on for downstream applications—employ optical systems of multiple lenses that must balance deviations from perfect optics, manufacturing constraints, tolerances, cost, and footprint. Although optical designs often have complex interactions with downstream image processing or analysis tasks, today’s compound optics are designed in isolation from these interactions. Existing optical design tools aim to minimize optical aberrations, such as deviations from Gauss’ linear model of optics, instead of application-specific losses, precluding joint optimization with hardware image signal processing (ISP) and highly parameterized neural network processing. In this article, we propose an optimization method for compound optics that lifts these limitations. We optimize entire lens systems jointly with hardware and software image processing pipelines, downstream neural network processing, and application-specific end-to-end losses. To this end, we propose a learned, differentiable forward model for compound optics and an alternating proximal optimization method that handles function compositions with highly varying parameter dimensions for optics, hardware ISP, and neural nets. Our method integrates seamlessly atop existing optical design tools, such as Zemax . We can thus assess our method across many camera system designs and end-to-end applications. We validate our approach in an automotive camera optics setting—together with hardware ISP post processing and detection—outperforming classical optics designs for automotive object detection and traffic light state detection. For human viewing tasks, we optimize optics and processing pipelines for dynamic outdoor scenarios and dynamic low-light imaging. We outperform existing compartmentalized design or fine-tuning methods qualitatively and quantitatively, across all domain-specific applications tested. 

Risk prediction models are crucial for assessing the pretest probability of cancer and are applied to stratify patient management strategies. These models are frequently based on multivariate regression analysis, requiring that all risk factors be specified, and do not convey the confidence in their predictions. We present a framework for uncertainty analysis that accounts for variability in input values. Uncertain or missing values are replaced with a range of plausible values. These ranges are used to compute individualized risk confidence intervals. We demonstrate our approach using the Gail model to evaluate the impact of uncertainty on management decisions. Up to 13% of cases (uncertain) had a risk interval that falls within the decision threshold (e.g., 1.67% 5-year absolute risk). A small number of cases changed from low- to high-risk when missing values were present. Our analysis underscores the need for better communication of input assumptions that influence the resulting predictions.