Skin carcinoma is the most prevalent form of cancer globally, accounting for over $8 billion in annual healthcare expenditures. Early diagnosis, accurate and timely treatment are critical to improving patient survival rates. In clinical settings, physicians document patient visits using detailed SOAP (Subjective, Objective, Assessment, and Plan) notes. However, manually generating these notes is labor-intensive and contributes to clinician burnout. In this work, we propose skin-SOAP, a weakly supervised multimodal framework to generate clinically structured SOAP notes from limited inputs, including lesion images and sparse clinical text. Our approach reduces reliance on manual annotations, enabling scalable, clinically grounded documentation while alleviating clinician burden and reducing the need for large annotated data. Our method achieves performance comparable to GPT-4o, Claude, and DeepSeek Janus Pro across key clinical relevance metrics. To evaluate this clinical relevance, we introduce two novel metrics MedConceptEval and Clinical Coherence Score (CCS) which assess semantic alignment with expert medical concepts and input features, respectively.

For assessing various performance indicators of companies, the focus is shifting from strictly financial (quantitative) publicly disclosed information to qualitative (textual) information. This textual data can provide valuable weak signals, for example through stylistic features, which can complement the quantitative data on financial performance or on Environmental, Social and Governance (ESG) criteria. In this work, we use various multi-task learning methods for financial text classification with the focus on financial sentiment, objectivity, forward-looking sentence prediction and ESG-content detection. We propose different methods to combine the information extracted from training jointly on different tasks; our best-performing method highlights the positive effect of explicitly adding auxiliary task predictions as features for the final target task during the multi-task training. Next, we use these classifiers to extract textual features from annual reports of FTSE350 companies and investigate the link between ESG quantitative scores and these features.

Bayesian optimization offers a sample-efficient framework for navigating the exploration-exploitation trade-off in the vast design space of biological sequences. Whereas it is possible to optimize the various properties of interest jointly using a multi-objective acquisition function, such as the expected hypervolume improvement (EHVI), this approach does not account for objectives with a hierarchical dependency structure. We consider a common use case where some regions of the Pareto frontier are prioritized over others according to a specified $\textit{partial ordering}$ in the objectives. For instance, when designing antibodies, we would like to maximize the binding affinity to a target antigen only if it can be expressed in live cell culture -- modeling the experimental dependency in which affinity can only be measured for antibodies that can be expressed and thus produced in viable quantities. In general, we may want to confer a partial ordering to the properties such that each property is optimized conditioned on its parent properties satisfying some feasibility condition. To this end, we present PropertyDAG, a framework that operates on top of the traditional multi-objective BO to impose this desired ordering on the objectives, e.g. expression $\rightarrow$ affinity. We demonstrate its performance over multiple simulated active learning iterations on a penicillin production task, toy numerical problem, and a real-world antibody design task.

Variance reduction has been commonly used in stochastic optimization. It relies crucially on the assumption that the data set is finite. However, when the data are imputed with random noise as in data augmentation, the perturbed data set be- comes essentially infinite. Recently, the stochastic MISO (S-MISO) algorithm is introduced to address this expected risk minimization problem. Though it converges faster than SGD, a significant amount of memory is required. In this pa- per, we propose two SGD-like algorithms for expected risk minimization with random perturbation, namely, stochastic sample average gradient (SSAG) and stochastic SAGA (S-SAGA). The memory cost of SSAG does not depend on the sample size, while that of S-SAGA is the same as those of variance reduction methods on un- perturbed data. Theoretical analysis and experimental results on logistic regression and AUC maximization show that SSAG has faster convergence rate than SGD with comparable space requirement, while S-SAGA outperforms S-MISO in terms of both iteration complexity and storage.

We propose novel first-order stochastic approximation algorithms for canonical correlation analysis (CCA). Algorithms presented are instances of inexact matrix stochastic gradient (MSG) and inexact matrix exponentiated gradient (MEG), and achieve $\epsilon$-suboptimality in the population objective in $\operatorname{poly}(\frac{1}{\epsilon})$ iterations. We also consider practical variants of the proposed algorithms and compare them with other methods for CCA both theoretically and empirically.