Developing knowledge-driven contemporaneous health index (CHI) that can precisely reflect the underlying patient across the course of the condition's progression holds a unique value, like facilitating a range of clinical decision-making opportunities. This is particularly important for monitoring degenerative condition such as Alzheimer's disease (AD), where the condition of the patient will decay over time. Detecting early symptoms and progression sign, and continuous severity evaluation, are all essential for disease management. While a few methods have been developed in the literature, uncertainty quantification of those health index models has been largely neglected. To ensure the continuity of the care, we should be more explicit about the level of confidence in model outputs. Ideally, decision-makers should be provided with recommendations that are robust in the face of substantial uncertainty about future outcomes. In this paper, we aim at filling this gap by developing an uncertainty quantification based contemporaneous longitudinal index, named UQ-CHI, with a particular focus on continuous patient monitoring of degenerative conditions. Our method is to combine convex optimization and Bayesian learning using the maximum entropy learning (MEL) framework, integrating uncertainty on labels as well. Our methodology also provides closed-form solutions in some important decision making tasks, e.g., such as predicting the label of a new sample. Numerical studies demonstrate the effectiveness of the propose UQ-CHI method in prediction accuracy, monitoring efficacy, and unique advantages if uncertainty quantification is enabled practice.
The CHI formulation can be solved by using the block coordinate descent algorithm that is illustrated in @cite_13 . Note, the CHI formulation generalizes many existing models, such as SVM, sparse SVM, LASSO, etc.
@cite_13
2737258108 2264003244 1673797905 2032395696
Abstract In this paper, we develop a novel formulation for contemporaneous patient risk monitoring by exploiting the emerging data-rich environment in many healthcare applications, where an abundance of longitudinal data that reflect the degeneration of the health condition can be continuously collected. Our objective, and the developed formulation, is fundamentally different from many existing risk score models for different healthcare applications, which mostly focus on predicting the likelihood of a certain outcome at a pre-specified time. Rather, our formulation translates multivariate longitudinal measurements into a contemporaneous health index (CHI) that captures patient condition changes over the course of progression. Another significant feature of our formulation is that, CHI can be estimated with or without label information, different from other risk score models strictly based on supervised learning. To develop this formulation, we focus on the degenerative disease conditions, for which we could utilize the monotonic progression characteristic (either towards disease or recovery) to learn CHI. Such a domain knowledge leads us to a novel learning formulation, and on top of that, we further generalize this formulation with a capacity to incorporate label information if available. We further develop algorithms to mitigate the challenges associated with the nonsmooth convex optimization problem by first identifying its dual reformulation as a constrained smooth optimization problem, and then, using the block coordinate descent algorithm to iteratively solve the optimization with a derived efficient projection at each iteration. Extensive numerical studies are performed on both synthetic datasets and real-world applications on Alzheimer’s disease and Surgical Site Infection, which demonstrate the utility and efficacy of the proposed method on degenerative conditions that include a wide range of applications. In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, fits into the framework of RC-FDM. We prove linear convergence for both R-FDM and RC-FDM under the weak strong convexity assumption. Moreover, we show that the duality gap converges linearly for RC-FDM, which implies that the duality gap also converges linearly for SDCA applied to the SVM dual problem. One of the key steps at each iteration of a randomized block coordinate descent method consists in determining the update to a block of variables. Existing algorithms assume that in order to compute the update, a particular subproblem is solved exactly. In this work, we relax this requirement and allow for the subproblem to be solved inexactly, leading to an inexact block coordinate descent method. Our approach incorporates the best known results for exact updates as a special case. Moreover, these theoretical guarantees are complemented by practical considerations: the use of iterative techniques to determine the update and the use of preconditioning for further acceleration. In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially separable smooth convex function and a simple separable convex function. The theoretical speedup, as compared to the serial method, and referring to the number of iterations needed to approximately solve the problem with high probability, is a simple expression depending on the number of parallel processors and a natural and easily computable measure of separability of the smooth component of the objective function. In the worst case, when no degree of separability is present, there may be no speedup; in the best case, when the problem is separable, the speedup is equal to the number of processors. Our analysis also works in the mode when the number of blocks being updated at each iteration is random, which allows for modeling situations with busy or unreliable processors. We show that our algorithm is able to solve a LASSO problem involving a matrix with 20 billion nonzeros in 2 h on a large memory node with 24 cores.