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Distributed lags play important roles in explaining the short-run dynamic and long-run cumulative effects of features on a response variable. Unlike the usual lag length selection, important lags with significant weights are selected in a distributed lag model (DLM). Inspired by the importance of distributed lags, this research focuses on the construction of distributed lag inspired machine learning (DLIML) for predicting vaccine-induced changes in COVID-19 hospitalization and intensive care unit (ICU) admission rates. Importance of a lagged feature in DLM is examined by hypothesis testing and a subset of important features are selected by evaluating an information criterion. Akin to the DLM, we demonstrate the selection of distributed lags in machine learning by evaluating importance scores and objective functions. Finally, we apply the DLIML with supervised learning for forecasting daily changes in COVID-19 hospitalization and ICU admission rates in United Kingdom (UK) and United States of America (USA). A sharp decline in hospitalization and ICU admission rates are observed when around 40% people are vaccinated. For one percent more vaccination, daily changes in hospitalization and ICU admission rates are expected to reduce by 4.05 and 0.74 per million after 14 days in UK, and 5.98 and 1.04 per million after 20 days in USA, respectively. Long-run cumulative effects in the DLM demonstrate that the daily changes in hospitalization and ICU admission rates are expected to jitter around the zero line in a long-run. Application of the DLIML selects fewer lagged features but provides qualitatively better forecasting outcome for data-driven healthcare service planning. [ABSTRACT FROM AUTHOR]

Remote analysis systems allow analysts to obtain statistical results without providing direct access to confidential data stored in a secure server system. An attacking analyst could send queries to a remote server to obtain outputs of statistical analyses and use those outputs for a disclosure attack. Statistical disclosure control (SDC) methods are used to modify remote analysis system (RAS) outputs in the protection of confidential information. Confidentiality protection through perturbation is one of the most commonly adopted SDC methods. In the case of generalized linear modelling, random noise is added to the estimated coefficients or to the associated estimating equation prior to getting estimates. This inflates the variances of estimators, and some efficiency and utility of estimators are lost. Thus the application of any perturbation based SDC method could result in an inefficient estimator, with the danger of producing worthless inferences. To date, little attention has been given to systematically controlling the disclosure risk and utility in SDC methods for RAS. In this paper, we develop a framework for the perturbation of estimating equations that enables an RAS to release modified generalized linear model output in such a way that the disclosure risk is not only reduced but also a good utility is maintained. Finally, we present some empirical results demonstrating the application of our framework for obtaining estimates from perturbed estimating equations of binary and count response models. [ABSTRACT FROM AUTHOR]

This paper provides an information theoretic analysis of the signal identification problem in singular spectrum analysis. We present a signal-plus-noise model based on the Karhunen-Loève expansion and use this model to motivate the construction of a minimum description length criterion that can be employed to identify the dimension (rank) of the signal component. We show that under very general regularity conditions the criterion will identify the true signal dimension with probability one as the sample size increases. A by-product of this analysis is a procedure for selecting a window length consistent with the Whitney embedding theorem. The upshot is a modeling strategy that results in a specification that yields a signal-noise reconstruction that minimises mean squared reconstruction error. Empirical results obtained using simulated and real world data series indicate that theoretical properties presented in the paper are reflected in observed behaviour, even in relatively small samples, and that the minimum description length modeling strategy provides the practitioner with an effective addition to the SSA tool box. [ABSTRACT FROM AUTHOR]