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.