The Lasso is a very well known penalized regression model, which adds an L 1 penalty with parameter λ 1 on the coecients to the squared error loss function. The Fused Lasso extends this model by also putting an L 1 penalty with parameter λ 2 on the dierence of neighboring coecients, assuming there is a natural ordering. In this paper, we develop a fast path algorithm for solving the Fused Lasso Signal Approximator that computes the solutions for all values of λ 1 and λ 2 . In the supplement, we also give an algorithm for the general Fused Lasso for the case with predictor matrix X ∈ R n×p with rank(X) = p. *

We consider the problem of approximating a sequence of data points with a "nearly-isotonic", or nearly-monotone function. This is formulated as a convex optimization problem that yields a family of solutions, with one extreme member being the standard isotonic regression fit. We devise a simple algorithm to solve for the path of solutions, which can be viewed as a modified version of the well-known pool adjacent violators algorithm, and computes the entire path in O(n log n) operations, (n being the number of data points). In practice, the intermediate fits can be used to examine the assumption of monotonicity. Nearly-isotonic regression admits a nice property in terms of its degrees of freedom: at any point along the path, the number of joined pieces in the solution is an unbiased estimate of its degrees of freedom. We also extend the ideas to provide "nearly-convex" approximations.

BackgroundDigital technologies and advanced analytics have drastically improved our ability to capture and interpret health-relevant data from patients. However, only limited data and results have been published that demonstrate accuracy in target indications, real-world feasibility, or the validity and value of these novel approaches.ObjectiveThis study aimed to establish accuracy, feasibility, and validity of continuous digital monitoring of walking speed in frail, elderly patients with sarcopenia and to create an open source repository of raw, derived, and reference data as a resource for the community.MethodsData described here were collected as a part of 2 clinical studies: an independent, noninterventional validation study and a phase 2b interventional clinical trial in older adults with sarcopenia. In both studies, participants were monitored by using a waist-worn inertial sensor. The cross-sectional, independent validation study collected data at a single site from 26 naturally slow-walking elderly subjects during a parcours course through the clinic, designed to simulate a real-world environment. In the phase 2b interventional clinical trial, 217 patients with sarcopenia were recruited across 32 sites globally, where patients were monitored over 25 weeks, both during and between visits.ResultsWe have demonstrated that our approach can capture in-clinic gait speed in frail slow-walking adults with a residual standard error of 0.08 m per second in the independent validation study and 0.08, 0.09, and 0.07 m per second for the 4 m walk test (4mWT), 6-min walk test (6MWT), and 400 m walk test (400mWT) standard gait speed assessments, respectively, in the interventional clinical trial. We demonstrated the feasibility of our approach by capturing 9668 patient-days of real-world data from 192 patients and 32 sites, as part of the interventional clinical trial. We derived inferred contextual information describing the length of a given walking bout and uncovered positive associations between the short 4mWT gait speed assessment and gait speed in bouts between 5 and 20 steps (correlation of 0.23) and longer 6MWT and 400mWT assessments with bouts of 80 to 640 steps (correlations of 0.48 and 0.59, respectively).ConclusionsThis study showed, for the first time, accurate capture of real-world gait speed in slow-walking older adults with sarcopenia. We demonstrated the feasibility of long-term digital monitoring of mobility in geriatric populations, establishing that sufficient data can be collected to allow robust monitoring of gait behaviors outside the clinic, even in the absence of feedback or incentives. Using inferred context, we demonstrated the ecological validity of in-clinic gait assessments, describing positive associations between in-clinic performance and real-world walking behavior. We make all data available as an open source resource for the community, providing a basis for further study of the relationship between standardized physical performance assessment and real-world behavior and independence.

Using networks as prior knowledge to guide model selection is a way to reach structured sparsity. In particular, the fused lasso that was originally designed to penalize differences of coefficients corresponding to successive features has been generalized to handle features whose effects are structured according to a given network. As any prior information, the network provided in the penalty may contain misleading edges that connect coefficients whose difference is not zero, and the extent to which the performance of the method depend on the suitability of the graph has never been clearly assessed. In this work we investigate the theoretical and empirical properties of the adaptive generalized fused lasso in the context of generalized linear models. In the fixed p setting, we show that, asymptotically, adding misleading edges in the graph does not prevent the adaptive generalized fused lasso from enjoying asymptotic oracle properties, while forgetting suitable edges can be more problematic. These theoretical results are complemented by an extensive simulation study that assesses the robustness of the adaptive generalized fused lasso against misspecification of the network as well as its applicability when theoretical coefficients are not exactly equal. Our contribution is also to evaluate the applicability of the generalized fused lasso for the joint modeling of multiple sparse regression functions. Illustrations are provided on two real data examples

We introduce HistoNet, a deep neural network trained on normal tissue. On 1690 slides with rat tissue samples from 6 preclinical toxicology studies, tissue regions were outlined and annotated by pathologists into 46 different tissue classes. From these annotated regions, we sampled small 224 × 224 pixels images (patches) at 6 different levels of magnification. Using 4 studies as training set and 2 studies as test set, we trained VGG-16, ResNet-50, and Inception-v3 networks separately at each magnification level. Among these model architectures, Inception-v3 and ResNet-50 outperformed VGG-16. Inception-v3 identified the tissue from query images, with an accuracy up to 83.4%. Most misclassifications occurred between histologically similar tissues. Investigation of the features learned by the model (embedding layer) using Uniform Manifold Approximation and Projection revealed not only coherent clusters associated with the individual tissues but also subclusters corresponding to histologically meaningful structures that had not been annotated or trained for. This suggests that the histological representation learned by HistoNet could be useful as the basis of other machine learning algorithms and data mining. Finally, we found that models trained on rat tissues can be used on non-human primate and minipig tissues with minimal retraining.

Background Mobile accelerometry is a powerful and promising option to capture long-term changes in gait in both clinical and real-world scenarios. Increasingly, gait parameters have demonstrated their value as clinical outcome parameters, but validation of these parameters in elderly patients is still limited. Objective The aim of this study was to implement a validation framework appropriate for elderly patients and representative of real-world settings, and to use this framework to test and improve algorithms for mobile accelerometry data in an orthogeriatric population. Methods Twenty elderly subjects wearing a 3D-accelerometer completed a parcours imitating a real-world scenario. High-definition video and mobile reference speed capture served to validate different algorithms. Results Particularly at slow gait speeds, relevant improvements in accuracy have been achieved. Compared to the reference the deviation was less than 1% in step detection and less than 0.05 m/s in gait speed measurements, even for slow walking subjects (< 0.8 m/s). Conclusion With the described setup, algorithms for step and gait speed detection have successfully been validated in an elderly population and demonstrated to have improved performance versus previously published algorithms. These results are promising that long-term and/or real-world measurements are possible with an acceptable accuracy even in elderly frail patients with slow gait speeds.

Background Friedreich’s ataxia is an inherited, progressive, neurodegenerative disease that typically begins in childhood. Disease severity is commonly assessed with rating scales, such as the modified Friedreich’s Ataxia Rating Scale, which are usually administered in the clinic by a neurology specialist. Objective This study evaluated the utility of home‐based, self‐administered digital endpoints in children with Friedreich’s ataxia and unaffected controls and their relationship to standard clinical rating scales. Methods In a cross‐sectional study with 25 participants (13 with Friedreich’s ataxia and 12 unaffected controls, aged 6–15 years), home‐based digital endpoints that reflect activities of daily living were recorded over 1 week. Domains analyzed were hand motor function with a digitized drawing, automated analysis of speech with a recorded oral diadochokinesis test, and gait and balance with wearable sensors. Results Hand‐drawing and speech tests were easy to conduct and generated high‐quality data. The sensor‐based gait and balance tests suffered from technical limitations in this study setup. Several parameters discriminated between groups or correlated strongly with modified Friedreich’s Ataxia Rating Scale total score and activities of daily living total score in the Friedreich’s ataxia group. Hand‐drawing parameters also strongly correlated with standard 9‐hole peg test scores. Interpretation Deploying digital endpoints in home settings is feasible in this population, results in meaningful and robust data collection, and may allow for frequent sampling over longer periods of time to track disease progression. Care must be taken when training participants, and investigators should consider the complexity of the tasks and equipment used.

Continuous patient activity monitoring during rehabilitation, enabled by digital technologies, will allow the objective capture of real-world mobility and aligning treatment to each individual’s recovery trajectory in real time. To explore the feasibility and added value of such approaches, we present a case study of a 36-year-old male participant monitored continuously for activity levels and gait parameters using a waist-worn inertial sensor following a tibial plateau fracture on the right side, sustained as a result of a high-energy trauma during a sporting accident. During rehabilitation, data were collected for a period of 553 days, with > 80% daytime compliance, until the participant returned to near full mobility. The participant completed a daily diary with the annotation of major events (falls, near falls, cycling periods, or physiotherapy sessions) and key dates in the patient’s recovery, including medical interventions, transitioning off crutches, and returning to work. We demonstrate the feasibility of collecting, storing, and mining of continuous digital mobility data and show that such data can detect changes in mobility and provide insights into long-term rehabilitation. We make both raw data and annotations available as a resource with the aspiration that further methods and insights will be built on this initial exploration of added value and continue to demonstrate that continuous monitoring can be deployed to aid rehabilitation.