This study investigates the potential of hybrid metaheuristic algorithms to enhance the training of Probabilistic Neural Networks (PNNs) by leveraging the complementary strengths of multiple optimisation strategies. Traditional learning methods, such as gradient-based approaches, often struggle to optimise high-dimensional and uncertain environments, while single-method metaheuristics may fail to exploit the solution space fully. To address these challenges, we propose the constrained Hybrid Metaheuristic (cHM) algorithm, a novel approach that combines multiple population-based optimisation techniques into a unified framework. The proposed procedure operates in two phases: an initial probing phase evaluates multiple metaheuristics to identify the best-performing one based on the error rate, followed by a fitting phase where the selected metaheuristic refines the PNN to achieve optimal smoothing parameters. This iterative process ensures efficient exploration and convergence, enhancing the network's generalisation and classification accuracy. cHM integrates several popular metaheuristics, such as BAT, Simulated Annealing, Flower Pollination Algorithm, Bacterial Foraging Optimization, and Particle Swarm Optimisation as internal optimisers. To evaluate cHM performance, experiments were conducted on 16 datasets with varying characteristics, including binary and multiclass classification tasks, balanced and imbalanced class distributions, and diverse feature dimensions. The results demonstrate that cHM effectively combines the strengths of individual metaheuristics, leading to faster convergence and more robust learning. By optimising the smoothing parameters of PNNs, the proposed method enhances classification performance across diverse datasets, proving its application flexibility and efficiency.

This phenomenon--often called the Rashomon effect [7], predictive multiplicity [22], or model multiplicity [5]--has wide-ranging implications for both understanding and improving fairness, as these equally accurate models often differ substantially in other properties such as fairness [21, 28] or model simplicity [29-31]. As prior work has pointed out, this multiplicity of models can be viewed as both a fairness opportunity and a concern [5, 10]. On the positive side, legal scholarship has pointed to the fact that model multiplicity is relevant to how to interpret and enforce U.S. anti-discrimination law, and specifically, can strengthen the disparate impact doctrine to more effectively combat algorithmic discrimination [3]. In a recent paper, Black et al. [3] suggest that the phenomenon of model multiplicity could support a reading of the disparate impact doctrine that requires companies to proactively search the set of equally accurate models for less discriminatory alternatives that have equivalent accuracy to a base model deemed acceptable for deployment from a model performance perspective. On the negative side, several scholars have pointed out that facially similar models, with equivalent accuracy but differences in their individual predictions, can suggest that some model decisions are arbitrary since they seem to be made on the basis of model choice that does not impact performance (e.g., a <1% change in a model's training set accuracy) [2, 17, 22]. This arbitrariness can impact model explanations and recourse as well: individuals with decisions that are unstable across small model changes may not receive reliable explanations for their model outcome, or ways to change it [4, 6, 25]. Further, if there is a group-based asymmetry of arbitrariness-e.g., if female loan applicants have more arbitrariness in their decisions than male loan applicants-- this could lead to a group-based equity concern in and of itself. Understanding the extent of the benefits and risks of model multiplicity relies upon an understanding of the properties of the Rashomon set, or the set of approximately equally accurate models for a given prediction task, i.e., equally accurate up to

Trustworthiness is essential for the precise and interpretable application of artificial intelligence (AI) in medical imaging. Traditionally, precision and interpretability have been addressed as separate tasks, namely medical image analysis and explainable AI, each developing its own models independently. In this study, for the first time, we investigate the development of a unified medical vision-language pre-training model that can achieve both accurate analysis and interpretable understanding of medical images across various modalities. To build the model, we construct MedConcept-23M, a large-scale dataset comprising 23 million medical image-text pairs extracted from 6.2 million scientific articles, enriched with concepts from the Unified Medical Language System (UMLS). Based on MedConcept-23M, we introduce ConceptCLIP, a medical AI model utilizing concept-enhanced contrastive language-image pre-training. The pre-training of ConceptCLIP involves two primary components: image-text alignment learning (IT-Align) and patch-concept alignment learning (PC-Align). This dual alignment strategy enhances the model's capability to associate specific image regions with relevant concepts, thereby improving both the precision of analysis and the interpretability of the AI system. We conducted extensive experiments on 5 diverse types of medical image analysis tasks, spanning 51 subtasks across 10 image modalities, with the broadest range of downstream tasks. The results demonstrate the effectiveness of the proposed vision-language pre-training model. Further explainability analysis across 6 modalities reveals that ConceptCLIP achieves superior performance, underscoring its robust ability to advance explainable AI in medical imaging. These findings highlight ConceptCLIP's capability in promoting trustworthy AI in the field of medicine.

As probabilistic models continue to permeate various facets of our society and contribute to scientific advancements, it becomes a necessity to go beyond traditional metrics such as predictive accuracy and error rates and assess their trustworthiness. Grounded in the competence-based theory of trust, this work formalizes I-trustworthy framework -- a novel framework for assessing the trustworthiness of probabilistic classifiers for inference tasks by linking local calibration to trustworthiness. To assess I-trustworthiness, we use the local calibration error (LCE) and develop a method of hypothesis-testing. This method utilizes a kernel-based test statistic, Kernel Local Calibration Error (KLCE), to test local calibration of a probabilistic classifier. This study provides theoretical guarantees by offering convergence bounds for an unbiased estimator of KLCE. Additionally, we present a diagnostic tool designed to identify and measure biases in cases of miscalibration. The effectiveness of the proposed test statistic is demonstrated through its application to both simulated and real-world datasets. Finally, LCE of related recalibration methods is studied, and we provide evidence of insufficiency of existing methods to achieve I-trustworthiness.

The Classical Bloom Filter (CBF) is a class of Probabilistic Data Structures (PDS) for handling Approximate Query Membership (AMQ). The Learned Bloom Filter (LBF) is a recently proposed class of PDS that combines the Classical Bloom Filter with a Learning Model while preserving the Bloom Filter's one-sided error guarantees. Bloom Filters have been used in settings where inputs are sensitive and need to be private in the presence of an adversary with access to the Bloom Filter through an API or in the presence of an adversary who has access to the internal state of the Bloom Filter. Prior work has investigated the privacy of the Classical Bloom Filter providing attacks and defenses under various privacy definitions. In this work, we formulate a stronger differential privacy-based model for the Bloom Filter. We propose constructions of the Classical and Learned Bloom Filter that satisfy $(\epsilon, 0)$-differential privacy. This is also the first work that analyses and addresses the privacy of the Learned Bloom Filter under any rigorous model, which is an open problem.

Spatial Transcriptomics (ST) allows a high-resolution measurement of RNA sequence abundance by systematically connecting cell morphology depicted in Hematoxylin and Eosin (H&E) stained histology images to spatially resolved gene expressions. ST is a time-consuming, expensive yet powerful experimental technique that provides new opportunities to understand cancer mechanisms at a fine-grained molecular level, which is critical for uncovering new approaches for disease diagnosis and treatments. Here, we present $\textbf{Stem}$ ($\textbf{S}$pa$\textbf{T}$ially resolved gene $\textbf{E}$xpression inference with diffusion $\textbf{M}$odel), a novel computational tool that leverages a conditional diffusion generative model to enable in silico gene expression inference from H&E stained images. Through better capturing the inherent stochasticity and heterogeneity in ST data, $\textbf{Stem}$ achieves state-of-the-art performance on spatial gene expression prediction and generates biologically meaningful gene profiles for new H&E stained images at test time. We evaluate the proposed algorithm on datasets with various tissue sources and sequencing platforms, where it demonstrates clear improvement over existing approaches. $\textbf{Stem}$ generates high-fidelity gene expression predictions that share similar gene variation levels as ground truth data, suggesting that our method preserves the underlying biological heterogeneity. Our proposed pipeline opens up the possibility of analyzing existing, easily accessible H&E stained histology images from a genomics point of view without physically performing gene expression profiling and empowers potential biological discovery from H&E stained histology images.

Weaknesses: I think the significance of the results (maybe because of the delivery of the result) is below the threshold of acceptance. 1) The first weakness is that there is no discussion about whether the upper bound (mentioned in the strengths) is tight and when this upper bound implies consistency, i,e., the error goes to 0 under a certain limit. Note that the norm of the true signal, the scale of the feature matrix, and the best tuning parameter need to satisfy certain order conditions such that the problem becomes meaningful. A common approach is to apply PCA and do feature selection first. Then, the authors should compare their results with prior works on the selected features. After response: I noticed corollary 1 and corollary 2. But these two corollaries together only cover the trivial case when sample size goes to infinity while the rank of feature matrix is bounded by constant.

Two reviewers agree that this submission represents an important contribution to the field. However, a third expressed significant concerns about the tightness of the presented bounds, the accommodation of matrices with growing rank, and behavior in the presence of principal component preprocessing. Please be sure to carefully review and address the concerns of all reviewers in the revision.

Correctness: Mostly correct with some misleading wording used as explained below. "But this existing ACV work is restricted to simpler models by the assumptions that (i) data are independent and (ii) an exact initial model fit is available. In structured data analyses, (i) is always untrue, and (ii) is often untrue." If we assume complete independence, there is no common model. It would be better to discuss conditional independence.

The vast repositories of Electronic Health Records (EHR) and medical claims hold untapped potential for studying rare but critical events, such as suicide attempt. Conventional setups often model suicide attempt as a univariate outcome and also exclude any ``single-record'' patients with a single documented encounter due to a lack of historical information. However, patients who were diagnosed with suicide attempts at the only encounter could, to some surprise, represent a substantial proportion of all attempt cases in the data, as high as 70--80%. We innovate a hybrid and integrative learning framework to leverage concurrent outcomes as surrogates and harness the forbidden yet precious information from single-record data. Our approach employs a supervised learning component to learn the latent variables that connect primary (e.g., suicide) and surrogate outcomes (e.g., mental disorders) to historical information. It simultaneously employs an unsupervised learning component to utilize the single-record data, through the shared latent variables. As such, our approach offers a general strategy for information integration that is crucial to modeling rare conditions and events. With hospital inpatient data from Connecticut, we demonstrate that single-record data and concurrent diagnoses indeed carry valuable information, and utilizing them can substantially improve suicide risk modeling.