Accurate segmentation of small lesions in Breast Dynamic Contrast-Enhanced MRI (DCE-MRI) is critical for early cancer detection, especially in high-risk patients. While recent deep learning methods have advanced lesion segmentation, they primarily target large lesions and neglect valuable longitudinal and clinical information routinely used by radiologists. In real-world screening, detecting subtle or emerging lesions requires radiologists to compare across timepoints and consider previous radiology assessments, such as the BI-RADS score. We propose LesiOnTime, a novel 3D segmentation approach that mimics clinical diagnostic workflows by jointly leveraging longitudinal imaging and BI-RADS scores. The key components are: (1) a Temporal Prior Attention (TPA) block that dynamically integrates information from previous and current scans; and (2) a BI-RADS Consistency Regularization (BCR) loss that enforces latent space alignment for scans with similar radiological assessments, thus embedding domain knowledge into the training process. Evaluated on a curated in-house longitudinal dataset of high-risk patients with DCE-MRI, our approach outperforms state-of-the-art single-timepoint and longitudinal baselines by 5% in terms of Dice. Ablation studies demonstrate that both TPA and BCR contribute complementary performance gains.

This chapter explores the essential role of Binding Corporate Rules (BCRs) in managing and facilitating secure health data transfers within corporate groups under the EU General Data Protection Regulation (GDPR). BCRs are tailored to ensure compliance with the GDPR and similar international data protection laws, presenting a flexible mechanism for transferring sensitive health and genomic data. The chapter situates BCRs within the broader spectrum of the GDPR international data transfer mechanisms, addressing the unique challenges posed by the sensitive nature of health data and the increased adoption of AI technologies. The European Data Protection Board (EDPB) Recommendations 1/2022 on BCRs, issued following the Schrems II decision, are critically analyzed, highlighting their stringent requirements and the need for a balanced approach that prioritizes data protection and an AI governance framework. The chapter outlines the BCR approval process, stressing the importance of streamlining this process to encourage broader adoption. It underscores the necessity of a multidisciplinary approach in developing BCRs, incorporating recently adopted international standards and frameworks, which offer valuable guidance for organizations to build trustworthy AI management systems. They guarantee the ethical development, deployment, and operation of AI, which is essential for its successful integration and the broader digital transformation. In conclusion, BCRs are positioned as essential tools for secure health data management, fostering transparency, accountability, and collaboration across international borders. The chapter calls for proactive measures to incentivize BCR adoption, streamline approval processes, and promote more innovative approaches, ensuring BCRs remain a robust mechanism for global data protection and compliance.

In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If such locally adaptive smoothness is not accounted for, one can obtain misleading inferences and predictions, with over-smoothing across erratic time intervals and under-smoothing across times exhibiting slow variation. This can lead to miscalibration of predictive intervals, which can be substantially too narrow or wide depending on the time. We propose a continuous multivariate stochastic process for time series having locally varying smoothness in both the mean and covariance matrix. This process is constructed utilizing latent dictionary functions in time, which are given nested Gaussian process priors and linearly related to the observed data through a sparse mapping. Using a differential equation representation, we bypass usual computational bottlenecks in obtaining MCMC and online algorithms for approximate Bayesian inference. The performance is assessed in simulations and illustrated in a financial application.

Bayesian optimization (BO) is a sample-efficient method and has been widely used for optimizing expensive black-box functions. Recently, there has been a considerable interest in BO literature in optimizing functions that are affected by context variable in the environment, which is uncontrollable by decision makers. In this paper, we focus on the optimization of functions' expectations over continuous context variable, subject to an unknown distribution. To address this problem, we propose two algorithms that employ kernel density estimation to learn the probability density function (PDF) of continuous context variable online. The first algorithm is simpler, which directly optimizes the expectation under the estimated PDF. Considering that the estimated PDF may have high estimation error when the true distribution is complicated, we further propose the second algorithm that optimizes the distributionally robust objective. Theoretical results demonstrate that both algorithms have sub-linear Bayesian cumulative regret on the expectation objective. Furthermore, we conduct numerical experiments to empirically demonstrate the effectiveness of our algorithms.

Among various acquisition functions (AFs) in Bayesian optimization (BO), Gaussian process upper confidence bound (GP-UCB) and Thompson sampling (TS) are well-known options with established theoretical properties regarding Bayesian cumulative regret (BCR). Recently, it has been shown that a randomized variant of GP-UCB achieves a tighter BCR bound compared with GP-UCB, which we call the tighter BCR bound for brevity. Inspired by this study, this paper first shows that TS achieves the tighter BCR bound. On the other hand, GP-UCB and TS often practically suffer from manual hyperparameter tuning and over-exploration issues, respectively. To overcome these difficulties, we propose yet another AF called a probability of improvement from the maximum of a sample path (PIMS). We show that PIMS achieves the tighter BCR bound and avoids the hyperparameter tuning, unlike GP-UCB. Furthermore, we demonstrate a wide range of experiments, focusing on the effectiveness of PIMS that mitigates the practical issues of GP-UCB and TS.

Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter $\beta$ is considerably large in the theorem and chosen heuristically in practice. Then, randomized GP-UCB (RGP-UCB) uses a randomized confidence parameter, which follows the Gamma distribution, to mitigate the impact of manually specifying $\beta$. This study first generalizes the regret analysis of RGP-UCB to a wider class of distributions, including the Gamma distribution. Furthermore, we propose improved RGP-UCB (IRGP-UCB) based on a two-parameter exponential distribution, which achieves tighter Bayesian regret bounds. IRGP-UCB does not require an increase in the confidence parameter in terms of the number of iterations, which avoids over-exploration in the later iterations. Finally, we demonstrate the effectiveness of IRGP-UCB through extensive experiments.

Advances in multiplexed in situ imaging are revealing important insights in spatial biology. However, cell type identification remains a major challenge in imaging analysis, with most existing methods involving substantial manual assessment and subjective decisions for thousands of cells. Researchers developed an unsupervised machine learning algorithm, CELESTA, which identifies the cell type of each cell, individually, using the cell's marker expression profile and, when needed, its spatial information. High-quality visualization of biological networks often requires both manual curation for proper alignment and programming to map external data to the graphical components. Nezzle is a network visualization software written in Python, which provides programmable and interactive interfaces for facilitating both manual and automatic curation of the graphical components of networks to create high-quality figures.

In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If such locally adaptive smoothness is not accounted for, one can obtain misleading inferences and predictions, with over-smoothing across erratic time intervals and under-smoothing across times exhibiting slow variation. This can lead to miscalibration of predictive intervals, which can be substantially too narrow or wide depending on the time. We propose a continuous multivariate stochastic process for time series having locally varying smoothness in both the mean and covariance matrix. This process is constructed utilizing latent dictionary functions in time, which are given nested Gaussian process priors and linearly related to the observed data through a sparse mapping. Using a differential equation representation, we bypass usual computational bottlenecks in obtaining MCMC and online algorithms for approximate Bayesian inference. The performance is assessed in simulations and illustrated in a financial application.

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the predictors can be projected to a low dimensional linear subspace with minimal loss of information about the response. As opposed to existing Bayesian dimensionality reduction approaches, the exact posterior distribution conditional on the compressed data is available analytically, speeding up computation by many orders of magnitude while also bypassing robustness issues due to convergence and mixing problems with MCMC. Model averaging is used to reduce sensitivity to the random projection matrix, while accommodating uncertainty in the subspace dimension. Strong theoretical support is provided for the approach by showing near parametric convergence rates for the predictive density in the large p small n asymptotic paradigm. Practical performance relative to competitors is illustrated in simulations and real data applications.

In this paper we propose a new family of Belief Conditioning Rules (BCRs) for belief revision. These rules are not directly related with the fusion of several sources of evidence but with the revision of a belief assignment available at a given time according to the new truth (i.e. conditioning constraint) one has about the space of solutions of the problem.