Optimal data collection design in machine learning: the case of the fixed effects generalized least squares panel data model

AbstractThis work belongs to the strand of literature that combines machine learning, optimization, and econometrics. The aim is to optimize the data collection process in a specific statistical model, commonly used in econometrics, employing an optimization criterion inspired by machine learning, namely, the generalization error conditioned on the training input data. More specifically, the paper is focused on the analysis of the conditional generalization error of the Fixed Effects Generalized Least Squares (FEGLS) panel data model, i.e., a linear regression model with applications in several fields, able to represent unobserved heterogeneity in the data associated with different units, for which distinct observations related to the same unit are corrupted by correlated measurement errors. The framework considered in this work differs from the classical FEGLS model for the additional possibility of controlling the conditional variance of the output variable given the associated unit and input variables, by changing the cost per supervision of each training example. Assuming an upper bound on the total supervision cost, i.e., the cost associated with the whole training set, the trade-off between the training set size and the precision of supervision (i.e., the reciprocal of the conditional variance of the output variable) is analyzed and optimized. This is achieved by formulating and solving in closed form suitable optimization problems, based on large-sample approximations of the generalization error associated with the FEGLS estimates of the model parameters, conditioned on the training input data. The results of the analysis extend to the FEGLS case and to various large-sample approximations of its conditional generalization error the ones obtained by the authors in recent works for simpler linear regression models. They highlight the importance of how the precision of supervision scales with respect to the cost per training example in determining the optimal trade-off between training set size and precision. Numerical results confirm the validity of the theoretical findings

Design of a Switching Controller for Adaptive Disturbance Attenuation with Guaranteed Stability

In this paper, a new algorithm is proposed for the design of a family of controllers to be used within an adaptive switching control scheme. The resulting switching controller is able to attenuate the effects of disturbances having uncertain and possibly time-varying characteristics, as well as to ensure stability under arbitrary switching sequences. Specifically, the stability requirement is addressed within the synthesis of the set of controllers by imposing some constraints in LMI form. The overall synthesis algorithm is formulated in terms of convex optimization problems, which can be solved by means of standard tools. The validity of the proposed solution is underlined by showing simulation results on an adaptive optics case study

Switching Control for Adaptive Disturbance Attenuation

The problem of adaptive disturbance attenuation is addressed in this paper using a switching control approach. A finite family of stabilizing controllers is pre-designed, with the assumption that, for any possible operating condition, at least one controller is able to achieve a prescribed level of attenuation. Then, at each time instant, a supervisory unit selects the controller associated with the best potential performance on the basis of suitably defined test functionals. In the paper, we prove some important properties which are satisfied by the test functionals, and analyze the stability of the overall switched system. Simulation results are provided to show the validity of the proposed method as a solution to the problem

Searching novel therapeutic targets for scleroderma: P2X7-receptor is UP-regulated and promotes a fibrogenic phenotype in systemic sclerosis fibroblasts

Objectives: Systemic sclerosis (SSc) is a connective tissue disorder presenting fibrosis of the skin and internal organs, for which no effective treatments are currently available. Increasing evidence indicates that the P2X7 receptor (P2X7R), a nucleotide-gated ionotropic channel primarily involved in the inflammatory response, may also have a key role in the development of tissue fibrosis in different body districts. This study was aimed at investigating P2X7R expression and function in promoting a fibrogenic phenotype in dermal fibroblasts from SSc patients, also analyzing putative underlying mechanistic pathways. Methods: Fibroblasts were isolated by skin biopsy from 9 SSc patients and 8 healthy controls. P2X7R expression, and function (cytosolic free Ca2+ fluxes, α-smooth muscle actin [α-SMA] expression, cell migration, and collagen release) were studied. Moreover, the role of cytokine (interleukin-1β, interleukin-6) and connective tissue growth factor (CTGF) production, and extracellular signal-regulated kinases (ERK) activation in mediating P2X7R-dependent pro-fibrotic effects in SSc fibroblasts was evaluated. Results: P2X7R expression and Ca2+ permeability induced by the selective P2X7R agonist 2'-3'-O-(4-benzoylbenzoyl)ATP (BzATP) weremarkedly higher in SSc than control fibroblasts. Moreover, increased aSMA expression, cell migration, CTGF, and collagen release were observed in lipopolysaccharides-primed SSc fibroblasts after BzATP stimulation. While P2X7-induced cytokine changes did not affect collagen production, it was completely abrogated by inhibition of the ERK pathway. Conclusion: In SSc fibroblasts, P2X7R is overexpressed and its stimulation induces Ca2+-signaling activation and a fibrogenic phenotype characterized by increased migration and collagen production. These data point to the P2X7R as a potential, novel therapeutic target for controlling exaggerated collagen deposition and tissue fibrosis in patients with SSc