Simulating prospective magnetic resonance imaging (MRI) scans from a given individual brain image is challenging, as it requires accounting for canonical changes in aging and/or disease progression while also considering the individual brain's current status and unique characteristics. While current deep generative models can produce high-resolution anatomically accurate templates for population-wide studies, their ability to predict future aging trajectories for individuals remains limited, particularly in capturing subject-specific neuroanatomical variations over time. In this study, we introduce Individualized Brain Synthesis (InBrainSyn), a framework for synthesizing high-resolution subject-specific longitudinal MRI scans that simulate neurodegeneration in both Alzheimer's disease (AD) and normal aging. InBrainSyn uses a parallel transport algorithm to adapt the population-level aging trajectories learned by a generative deep template network, enabling individualized aging synthesis. As InBrainSyn uses diffeomorphic transformations to simulate aging, the synthesized images are topologically consistent with the original anatomy by design. We evaluated InBrainSyn both quantitatively and qualitatively on AD and healthy control cohorts from the Open Access Series of Imaging Studies - version 3 dataset. Experimentally, InBrainSyn can also model neuroanatomical transitions between normal aging and AD. An evaluation of an external set supports its generalizability. Overall, with only a single baseline scan, InBrainSyn synthesizes realistic 3D spatiotemporal T1w MRI scans, producing personalized longitudinal aging trajectories. The code for InBrainSyn is available at: https://github.com/Fjr9516/InBrainSyn.

We study the design and analysis of switchback experiments conducted on a single aggregate unit. The design problem is to partition the continuous time space into intervals and switch treatments between intervals, in order to minimize the estimation error of the treatment effect. We show that the estimation error depends on four factors: carryover effects, periodicity, serially correlated outcomes, and impacts from simultaneous experiments. We derive a rigorous bias-variance decomposition and show the tradeoffs of the estimation error from these factors. The decomposition provides three new insights in choosing a design: First, balancing the periodicity between treated and control intervals reduces the variance; second, switching less frequently reduces the bias from carryover effects while increasing the variance from correlated outcomes, and vice versa; third, randomizing interval start and end points reduces both bias and variance from simultaneous experiments. Combining these insights, we propose a new empirical Bayes design approach. This approach uses prior data and experiments for designing future experiments. We illustrate this approach using real data from a ride-sharing platform, yielding a design that reduces MSE by 33% compared to the status quo design used on the platform.

Supervised, semi-supervised, and unsupervised learning estimate a function given input/output samples. Generalization of the learned function to unseen data can be improved by incorporating side information into learning. Side information are data that are neither from the input space nor from the output space of the function, but include useful information for learning it. In this paper we show that learning with side information subsumes a variety of related approaches, e.g. multi-task learning, multi-view learning and learning using privileged information. Our main contributions are (i) a new perspective that connects these previously isolated approaches, (ii) insights about how these methods incorporate different types of prior knowledge, and hence implement different patterns, (iii) facilitating the application of these methods in novel tasks, as well as (iv) a systematic experimental evaluation of these patterns in two supervised learning tasks.