With Artificial Intelligence (AI) increasingly permeating various aspects of society, including healthcare, the adoption of the Transformers neural network architecture is rapidly changing many applications. Transformer is a type of deep learning architecture initially developed to solve general-purpose Natural Language Processing (NLP) tasks and has subsequently been adapted in many fields, including healthcare. In this survey paper, we provide an overview of how this architecture has been adopted to analyze various forms of healthcare data, including clinical NLP, medical imaging, structured Electronic Health Records (EHR), social media, bio-physiological signals, biomolecular sequences. Furthermore, which have also include the articles that used the transformer architecture for generating surgical instructions and predicting adverse outcomes after surgeries under the umbrella of critical care. Under diverse settings, these models have been used for clinical diagnosis, report generation, data reconstruction, and drug/protein synthesis. Finally, we also discuss the benefits and limitations of using transformers in healthcare and examine issues such as computational cost, model interpretability, fairness, alignment with human values, ethical implications, and environmental impact.

Consider the sequential optimization of an expensive to evaluate and possibly non-convex objective function $f$ from noisy feedback, that can be considered as a continuum-armed bandit problem. Upper bounds on the regret performance of several learning algorithms (GP-UCB, GP-TS, and their variants) are known under both a Bayesian (when $f$ is a sample from a Gaussian process (GP)) and a frequentist (when $f$ lives in a reproducing kernel Hilbert space) setting. The regret bounds often rely on the maximal information gain $\gamma_T$ between $T$ observations and the underlying GP (surrogate) model. We provide general bounds on $\gamma_T$ based on the decay rate of the eigenvalues of the GP kernel, whose specialisation for commonly used kernels improves the existing bounds on $\gamma_T$, and subsequently the regret bounds relying on $\gamma_T$ under numerous settings. For the Matérn family of kernels, where the lower bounds on $\gamma_T$, and regret under the frequentist setting, are known, our results close a huge polynomial in $T$ gap between the upper and lower bounds (up to logarithmic in $T$ factors).

We introduce the safe linear stochastic bandit framework—a generalization of linear stochastic bandits—where, in each stage, the learner is required to select an arm with an expected reward that is no less than a predetermined (safe) threshold with high probability. We assume that the learner initially has knowledge of an arm that is known to be safe, but not necessarily optimal. Leveraging on this assumption, we introduce a learning algorithm that systematically combines known safe arms with exploratory arms to safely expand the set of safe arms over time, while facilitating safe greedy exploitation in subsequent stages. In addition to ensuring the satisfaction of the safety constraint at every stage of play, the proposed algorithm is shown to exhibit an expected regret that is no more than O(√T log(T)) after T stages of play.

A converse method is developed for the source broadcast problem. Specifically, it is shown that the separation architecture is optimal for a variant of the source broadcast problem, and the associated source-channel separation theorem can be leveraged, via a reduction argument, to establish a necessary condition for the original problem, which unifies several existing results in the literature. Somewhat surprisingly, this method, albeit based on the source-channel separation theorem, can be used to prove the optimality of non-separation-based schemes and determine the performance limits in certain scenarios where the separation architecture is suboptimal.

Two outer bounds on the admissible source region for broadcast channels with correlated sources are presented: the first one is strictly tighter than the existing outer bound by Gohari and Anantharam, while the second one provides a complete characterization of the admissible source region in the case where the two sources are conditionally independent given the common part. These outer bounds are deduced from the general necessary conditions established for the lossy source broadcast problem via suitable comparisons between the virtual broadcast channel (induced by the source and the reconstructions) and the physical broadcast channel.

A general necessary condition is established for the lossy source broadcast problem and is further leveraged to derive an outer bound on the admissible source region for broadcast channels with correlated sources. It is shown that the new outer bound is strictly tighter than the existing one by Gohari and Anantharam.

A source-channel separation theorem is established for a certain joint source-channel problem. It is shown that this separation theorem can be used in conjunction with a simple reduction argument to establish a general converse result for the source broadcast problem. Somewhat surprisingly, this converse result, albeit based on the source-channel separation theorem, can be used to prove the optimality of non-separation based schemes (e.g., hybrid coding schemes) and determine the performance limits in certain scenarios where the separation architecture is suboptimal.