Towards Efficient Maximum Likelihood Estimation of LPV-SS Models

How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification methods proposed in the literature suffer heavily from the curse of dimensionality and/or depend on over-restrictive approximations of the measured signal behaviors. However, obtaining an SS model of the targeted system is crucial for many LPV control synthesis methods, as these synthesis tools are almost exclusively formulated for the aforementioned representation of the system dynamics. Therefore, in this paper, we tackle the problem by combining state-of-the-art LPV input-output (IO) identification methods with an LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step. The resulting modular LPV-SS identification approach achieves statical efficiency with a relatively low computational load. The method contains the following three steps: 1) estimation of the Markov coefficient sequence of the underlying system using correlation analysis or Bayesian impulse response estimation, then 2) LPV-SS realization of the estimated coefficients by using a basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate from a maximum-likelihood point of view by a gradient-based or an expectation-maximization optimization methodology. The effectiveness of the full identification scheme is demonstrated by a Monte Carlo study where our proposed method is compared to existing schemes for identifying a MIMO LPV system

Distributed regression modeling for selecting markers under data protection constraints

Data protection constraints frequently require a distributed analysis of data, i.e., individual-level data remains at many different sites, but analysis nevertheless has to be performed jointly. The corresponding aggregated data is often exchanged manually, requiring explicit permission before transfer, i.e., the number of data calls and the amount of data should be limited. Thus, only simple aggregated summary statistics are typically transferred with just a single call. This does not allow for more complex tasks such as variable selection. As an alternative, we propose a multivariable regression approach for identifying important markers by automatic variable selection based on aggregated data from different locations in iterative calls. To minimize the amount of transferred data and the number of calls, we also provide a heuristic variant of the approach. When performing a global data standardization, the proposed methods yields the same results as when pooling individual-level data. In a simulation study, the information loss introduced by a local standardization is seen to be minimal. In a typical scenario, the heuristic decreases the number of data calls from more than 10 to 3, rendering manual data releases feasible. To make our approach widely available for application, we provide an implementation on top of the DataSHIELD framework

A PAUC-based Estimation Technique for Disease Classification and Biomarker Selection.

The partial area under the receiver operating characteristic curve (PAUC) is a well-established performance measure to evaluate biomarker combinations for disease classification. Because the PAUC is defined as the area under the ROC curve within a restricted interval of false positive rates, it enables practitioners to quantify sensitivity rates within pre-specified specificity ranges. This issue is of considerable importance for the development of medical screening tests. Although many authors have highlighted the importance of PAUC, there exist only few methods that use the PAUC as an objective function for finding optimal combinations of biomarkers. In this paper, we introduce a boosting method for deriving marker combinations that is explicitly based on the PAUC criterion. The proposed method can be applied in high-dimensional settings where the number of biomarkers exceeds the number of observations. Additionally, the proposed method incorporates a recently proposed variable selection technique (stability selection) that results in sparse prediction rules incorporating only those biomarkers that make relevant contributions to predicting the outcome of interest. Using both simulated data and real data, we demonstrate that our method performs well with respect to both variable selection and prediction accuracy. Specifically, if the focus is on a limited range of specificity values, the new method results in better predictions than other established techniques for disease classification