In this paper we provide a generalization of the concept of cohesion as introduced recently by Berenhaut, Moore and Melvin [Proceedings of the National Academy of Sciences, 119 (4) (2022)]. The formulation presented builds on the technique of partitioned local depth by distilling two key probabilistic concepts: local relevance and support division. Earlier results are extended within the new context, and examples of applications to revealing communities in data with uncertainty are included. The work sheds light on the foundations of partitioned local depth, and extends the original ideas to enable probabilistic consideration of uncertain, variable and potentially conflicting information.

Many studies employ the analysis of time-to-event data that incorporates competing risks and right censoring. Most methods and software packages are geared towards analyzing data that comes from a continuous failure time distribution. However, failure-time data may sometimes be discrete either because time is inherently discrete or due to imprecise measurement. This paper introduces a novel estimation procedure for discrete-time survival analysis with competing events. The proposed approach offers two key advantages over existing procedures: first, it expedites the estimation process for a large number of unique failure time points; second, it allows for straightforward integration and application of widely used regularized regression and screening methods. We illustrate the benefits of our proposed approach by conducting a comprehensive simulation study. Additionally, we showcase the utility of our procedure by estimating a survival model for the length of stay of patients hospitalized in the intensive care unit, considering three competing events: discharge to home, transfer to another medical facility, and in-hospital death.

Artificial intelligence experienced a technological breakthrough in science, industry, and everyday life in the recent few decades. The advancements can be credited to the ever-increasing availability and miniaturization of computational resources that resulted in exponential data growth. However, because of the insufficient amount of data in some cases, employing machine learning in solving complex tasks is not straightforward or even possible. As a result, machine learning with small data experiences rising importance in data science and application in several fields. The authors focus on interpreting the general term of "small data" and their engineering and industrial application role. They give a brief overview of the most important industrial applications of machine learning and small data. Small data is defined in terms of various characteristics compared to big data, and a machine learning formalism was introduced. Five critical challenges of machine learning with small data in industrial applications are presented: unlabeled data, imbalanced data, missing data, insufficient data, and rare events. Based on those definitions, an overview of the considerations in domain representation and data acquisition is given along with a taxonomy of machine learning approaches in the context of small data.

Mobile health programs are becoming an increasingly popular medium for dissemination of health information among beneficiaries in less privileged communities. Kilkari is one of the world's largest mobile health programs which delivers time sensitive audio-messages to pregnant women and new mothers. We have been collaborating with ARMMAN, a non-profit in India which operates the Kilkari program, to identify bottlenecks to improve the efficiency of the program. In particular, we provide an initial analysis of the trajectories of beneficiaries' interaction with the mHealth program and examine elements of the program that can be potentially enhanced to boost its success. We cluster the cohort into different buckets based on listenership so as to analyze listenership patterns for each group that could help boost program success. We also demonstrate preliminary results on using historical data in a time-series prediction to identify beneficiary dropouts and enable NGOs in devising timely interventions to strengthen beneficiary retention.

Non-alcoholic fatty liver disease (NAFLD) is a prevalent chronic liver disorder characterized by the excessive accumulation of fat in the liver in individuals who do not consume significant amounts of alcohol, including risk factors like obesity, insulin resistance, type 2 diabetes, etc. We aim to identify subgroups of NAFLD patients based on demographic, clinical, and genetic characteristics for precision medicine. The genomic and phenotypic data (3,408 cases and 4,739 controls) for this study were gathered from participants in Mayo Clinic Tapestry Study (IRB#19-000001) and their electric health records, including their demographic, clinical, and comorbidity data, and the genotype information through whole exome sequencing performed at Helix using the Exome+$^\circledR$ Assay according to standard procedure (www$.$helix$.$com). Factors highly relevant to NAFLD were determined by the chi-square test and stepwise backward-forward regression model. Latent class analysis (LCA) was performed on NAFLD cases using significant indicator variables to identify subgroups. The optimal clustering revealed 5 latent subgroups from 2,013 NAFLD patients (mean age 60.6 years and 62.1% women), while a polygenic risk score based on 6 single-nucleotide polymorphism (SNP) variants and disease outcomes were used to analyze the subgroups. The groups are characterized by metabolic syndrome, obesity, different comorbidities, psychoneurological factors, and genetic factors. Odds ratios were utilized to compare the risk of complex diseases, such as fibrosis, cirrhosis, and hepatocellular carcinoma (HCC), as well as liver failure between the clusters. Cluster 2 has a significantly higher complex disease outcome compared to other clusters. Keywords: Fatty liver disease; Polygenic risk score; Precision medicine; Deep phenotyping; NAFLD comorbidities; Latent class analysis.

Neural Collapse refers to the curious phenomenon in the end of training of a neural network, where feature vectors and classification weights converge to a very simple geometrical arrangement (a simplex). While it has been observed empirically in various cases and has been theoretically motivated, its connection with crucial properties of neural networks, like their generalization and robustness, remains unclear. In this work, we study the stability properties of these simplices. We find that the simplex structure disappears under small adversarial attacks, and that perturbed examples "leap" between simplex vertices. We further analyze the geometry of networks that are optimized to be robust against adversarial perturbations of the input, and find that Neural Collapse is a pervasive phenomenon in these cases as well, with clean and perturbed representations forming aligned simplices, and giving rise to a robust simple nearest-neighbor classifier. By studying the propagation of the amount of collapse inside the network, we identify novel properties of both robust and non-robust machine learning models, and show that earlier, unlike later layers maintain reliable simplices on perturbed data.

Machine learning as a data-driven solution has been widely applied in the field of fatigue lifetime prediction. In this paper, three models for wideband fatigue life prediction are built based on three machine learning models, i.e. support vector machine (SVM), Gaussian process regression (GPR) and artificial neural network (ANN). The generalization ability of the models is enhanced by employing numerous power spectra samples with different bandwidth parameters and a variety of material properties related to fatigue life. Sufficient Monte Carlo numerical simulations demonstrate that the newly developed machine learning models are superior to the traditional frequency-domain models in terms of life prediction accuracy and the ANN model has the best overall performance among the three developed machine learning models.

This paper presents a novel fast machine learning method that leverages two techniques: Vector Embedding on Orthonormal Basis (VEOB) and Spectral Transform (ST). The VEOB converts the original data encoding into a vector embedding with coordinates projected onto orthonormal bases. The Singular Value Decomposition (SVD) technique is used to calculate the vector basis and projection coordinates, leading to an enhanced distance measurement in the embedding space and facilitating data compression by preserving the projection vectors associated with the largest singular values. On the other hand, ST transforms sequence of vector data into spectral space. By applying the Discrete Cosine Transform (DCT) and selecting the most significant components, it streamlines the handling of lengthy vector sequences. The paper provides examples of word embedding, text chunk embedding, and image embedding, implemented in Julia language with a vector database. It also investigates unsupervised learning and supervised learning using this method, along with strategies for handling large data volumes.

Autonomous systems, such as self-driving cars and drones, have made significant strides in recent years by leveraging visual inputs and machine learning for decision-making and control. Despite their impressive performance, these vision-based controllers can make erroneous predictions when faced with novel or out-of-distribution inputs. Such errors can cascade to catastrophic system failures and compromise system safety. In this work, we introduce a run-time anomaly monitor to detect and mitigate such closed-loop, system-level failures. Specifically, we leverage a reachability-based framework to stress-test the vision-based controller offline and mine its system-level failures. This data is then used to train a classifier that is leveraged online to flag inputs that might cause system breakdowns. The anomaly detector highlights issues that transcend individual modules and pertain to the safety of the overall system. We also design a fallback controller that robustly handles these detected anomalies to preserve system safety. We validate the proposed approach on an autonomous aircraft taxiing system that uses a vision-based controller for taxiing. Our results show the efficacy of the proposed approach in identifying and handling system-level anomalies, outperforming methods such as prediction error-based detection, and ensembling, thereby enhancing the overall safety and robustness of autonomous systems.

The Tanimoto coefficient is commonly used to measure the similarity between molecules represented as discrete fingerprints, either as a distance metric or a positive definite kernel. While many kernel methods can be accelerated using random feature approximations, at present there is a lack of such approximations for the Tanimoto kernel. In this paper we propose two kinds of novel random features to allow this kernel to scale to large datasets, and in the process discover a novel extension of the kernel to real-valued vectors. We theoretically characterize these random features, and provide error bounds on the spectral norm of the Gram matrix. Experimentally, we show that these random features are effective at approximating the Tanimoto coefficient of real-world datasets and are useful for molecular property prediction and optimization tasks.