Artificial neural networks (ANNs) have become a powerful tool for modeling complex relationships in large-scale datasets. However, their closed box nature poses trustworthiness challenges. In certain situations, ensuring trust in predictions might require following specific partial monotonicity constraints. However, certifying if an already-trained ANN is partially monotonic is challenging. Therefore, ANNs are often disregarded in some critical applications, such as credit scoring, where partial monotonicity is required. To address this challenge, this article presents a novel algorithm (LipVor) that certifies if a closed box model, such as an ANN, is positive based on a finite number of evaluations. Consequently, since partial monotonicity can be expressed as a positivity condition on partial derivatives, LipVor can certify whether an ANN is partially monotonic. To do so, for every positively evaluated point, the Lipschitzianity of the closed box model is used to construct a specific neighborhood, where the function remains positive. Next, based on the Voronoi diagram of the evaluated points, a sufficient condition is stated to certify if the function is positive in the domain. Unlike prior methods, our approach certifies partial monotonicity without constrained architectures or piecewise linear activations. Therefore, LipVor could open up the possibility of using unconstrained ANN in some critical fields. Moreover, some other properties of an ANN, such as convexity, can be posed as positivity conditions, and therefore, LipVor could also be applied.

This study suggests using wearable activity trackers to identify mobility patterns in chronic complex patients (CCPs) and investigate their relation with the Barthel index (BI) to assess functional decline. CCPs are individuals who suffer from multiple, chronic health conditions that often lead to a progressive decline in their functional capacity. As a result, CCPs frequently require the use of healthcare and social resources, placing a significant burden on the healthcare system. Evaluating mobility patterns is critical for determining a CCP’s functional capacity and prognosis. To monitor the overall activity levels of CCPs, wearable activity trackers have been proposed. Utilizing the data gathered by the wearables, time series clustering with dynamic time warping (DTW) is employed to generate synchronized mobility patterns of the mean activity and coefficient of variation profiles. The research has revealed distinct patterns in individuals’ walking habits, including the time of day they walk, whether they walk continuously or intermittently, and their relation to BI. These findings could significantly enhance CCPs’ quality of care by providing a valuable tool for personalizing treatment and care plans.

Background: Functional impairment is one of the most decisive prognostic factors in patients with complex chronic diseases. A more significant functional impairment indicates that the disease is progressing, which requires implementing diagnostic and therapeutic actions that stop the exacerbation of the disease. Objective: This study aimed to predict alterations in the clinical condition of patients with complex chronic diseases by predicting the Barthel Index (BI), to assess their clinical and functional status using an artificial intelligence model and data collected through an internet of things mobility device. Methods: A 2-phase pilot prospective single-center observational study was designed. During both phases, patients were recruited, and a wearable activity tracker was allocated to gather physical activity data. Patients were categorized into class A (BI≤20; total dependence), class B (2060; moderate or mild dependence, or independent). Data preprocessing and machine learning techniques were used to analyze mobility data. A decision tree was used to achieve a robust and interpretable model. To assess the quality of the predictions, several metrics including the mean absolute error, median absolute error, and root mean squared error were considered. Statistical analysis was performed using SPSS and Python for the machine learning modeling. Results: Overall, 90 patients with complex chronic diseases were included: 50 during phase 1 (class A: n=10; class B: n=20; and class C: n=20) and 40 during phase 2 (class B: n=20 and class C: n=20). Most patients (n=85, 94%) had a caregiver. The mean value of the BI was 58.31 (SD 24.5). Concerning mobility aids, 60% (n=52) of patients required no aids, whereas the others required walkers (n=18, 20%), wheelchairs (n=15, 17%), canes (n=4, 7%), and crutches (n=1, 1%). Regarding clinical complexity, 85% (n=76) met patient with polypathology criteria with a mean of 2.7 (SD 1.25) categories, 69% (n=61) met the frailty criteria, and 21% (n=19) met the patients with complex chronic diseases criteria. The most characteristic symptoms were dyspnea (n=73, 82%), chronic pain (n=63, 70%), asthenia (n=62, 68%), and anxiety (n=41, 46%). Polypharmacy was presented in 87% (n=78) of patients. The most important variables for predicting the BI were identified as the maximum step count during evening and morning periods and the absence of a mobility device. The model exhibited consistency in the median prediction error with a median absolute error close to 5 in the training, validation, and production-like test sets. The model accuracy for identifying the BI class was 91%, 88%, and 90% in the training, validation, and test sets, respectively. Conclusions: Using commercially available mobility recording devices makes it possible to identify different mobility patterns and relate them to functional capacity in patients with polypathology according to the BI without using clinical parameters. Trial Registration: