A connection between uniqueness of minimizers in Tikhonov-type regularization and Morozov-like discrepancy principles

Albani, Vinicius; Cezaro, Adriano De

doi:10.3934/ipi.2019012

Cited by 8 publications

(4 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To avoid the introduction of bias in the calibration process, the parameter α must be appropriately chosen. In the present set of examples, we set α = 10 −3 /2 accordingly to an a posteriori rule [ 29 ].…”

Section: Methodsmentioning

confidence: 99%

Nowcasting and forecasting COVID-19 waves: the recursive and stochastic nature of transmission

Albani

Massad

et al. 2022

R. Soc. open sci.

View full text Add to dashboard Cite

We propose a parsimonious, yet effective, susceptible–exposed–infected–removed-type model that incorporates the time change in the transmission and death rates. The model is calibrated by Tikhonov-type regularization from official reports from New York City (NYC), Chicago, the State of São Paulo, in Brazil and British Columbia, in Canada. To forecast, we propose different ways to extend the transmission parameter, considering its estimated values. The forecast accuracy is then evaluated using real data from the above referred places. All the techniques accurately provided forecast scenarios for periods 15 days long. One of the models effectively predicted the magnitude of the four waves of infections in NYC, including the one caused by the Omicron variant for periods of 45 days using out-of-sample data.

show abstract

Section: Methodsmentioning

confidence: 99%

Nowcasting and forecasting COVID-19 waves: the recursive and stochastic nature of transmission

Albani

Massad

et al. 2022

R. Soc. open sci.

View full text Add to dashboard Cite

show abstract

“…It states that the square of the Euclidean distance between the calibrated and must be minimal. However, the importance of this term in the minimization is stated by the regularization parameter, namely, , which balances the introduction of prior information and the reduction of overfitting [ 35 ].…”

Section: Methodsmentioning

confidence: 99%

On the role of financial support programs in mitigating the SARS-CoV-2 spread in Brazil

Albani

Bobko

et al. 2022

BMC Public Health

View full text Add to dashboard Cite

Background During 2020, there were no effective treatments or vaccines against SARS-CoV-2. The most common disease contention measures were social distance (social isolation), the use of face masks and lockdowns. In the beginning, numerous countries have succeeded to control and reduce COVID-19 infections at a high economic cost. Thus, to alleviate such side effects, many countries have implemented socioeconomic programs to fund individuals that lost their jobs and to help endangered businesses to survive. Methods We assess the role of a socioeconomic program, so-called “Auxilio Emergencial” (AE), during 2020 as a measure to mitigate the Coronavirus Disease 2019 (COVID-19) outbreak in Brazil. For each Brazilian State, we estimate the time-dependent reproduction number from daily reports of COVID-19 infections and deaths using a Susceptible-Exposed-Infected-Recovered-like (SEIR-like) model. Then, we analyse the correlations between the reproduction number, the amount of individuals receiving governmental aid, and the index of social isolation based on mobile phone information. Results We observed significant positive correlation values between the average values by the AE and median values of an index accounting for individual mobility. We also observed significantly negative correlation values between the reproduction number and this index on individual mobility. Using the simulations of a susceptible-exposed-infected-removed-like model, if the AE was not operational during the first wave of COVID-19 infections, the accumulated number of infections and deaths could be 6.5 (90% CI: 1.3–21) and 7.9 (90% CI: 1.5–23) times higher, respectively, in comparison with the actual implementation of AE. Conclusions Our results suggest that the AE implemented in Brazil had a significant influence on social isolation by allowing those in need to stay at home, which would reduce the expected numbers of infections and deaths.

show abstract

“…Therefore, we assume that we know y δ ∈ Y with y δ − y Y ≤ δ for a given δ ≥ 0. The most commonly adopted technique to solve problem (1) is the p -norm sparsity regularization with 1 ≤ p < 2, cf. the monographs [20,41] and the special issues [5,14,29,30] for many developments on regularization properties and minimization schemes.…”

mentioning

confidence: 99%

“…In [3], convergence rates are investigated using variational inequalities, where the regularization parameter is determined by MDP. A relation between uniqueness of minimizers in Tikhonov-type regularization and Morozov-like discrepancy principles is shown in [1].…”

mentioning

confidence: 99%

Morozov's discrepancy principle for <inline-formula><tex-math id="M1">$ \alpha\ell_1-\beta\ell_2 $</tex-math></inline-formula> sparsity regularization

Liu¹,

Huang²

2023

IPI

View full text Add to dashboard Cite

<p style='text-indent:20px;'>In this paper, Morozov's discrepancy principle is considered for the non-convex <inline-formula><tex-math id="M2">\begin{document}$ \alpha\ell_1-\beta\ell_2 $\end{document}</tex-math></inline-formula> sparsity regularization (<inline-formula><tex-math id="M3">\begin{document}$ \alpha>\beta>0 $\end{document}</tex-math></inline-formula>). It is shown that if <inline-formula><tex-math id="M4">\begin{document}$ \tau>1 $\end{document}</tex-math></inline-formula> satisfies some conditions, there exists a regularization parameter <inline-formula><tex-math id="M5">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula> such that <inline-formula><tex-math id="M6">\begin{document}$ \delta\leq \|A(x_{\alpha,\beta}^{\delta})-y^{\delta}\|_Y\leq \tau \delta $\end{document}</tex-math></inline-formula> holds. Furthermore, it is shown that <inline-formula><tex-math id="M7">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula> converges to 0 as <inline-formula><tex-math id="M8">\begin{document}$ \delta\rightarrow 0 $\end{document}</tex-math></inline-formula>. In addition, well-posedness and convergence rate results are presented for the regularized solution under Morozov's discrepancy principle. Numerical simulation results are reported to illustrate the efficiency of the proposed approach.</p>

show abstract

A connection between uniqueness of minimizers in Tikhonov-type regularization and Morozov-like discrepancy principles

Cited by 8 publications

References 24 publications

Nowcasting and forecasting COVID-19 waves: the recursive and stochastic nature of transmission

Nowcasting and forecasting COVID-19 waves: the recursive and stochastic nature of transmission

On the role of financial support programs in mitigating the SARS-CoV-2 spread in Brazil

Morozov's discrepancy principle for <inline-formula><tex-math id="M1">$ \alpha\ell_1-\beta\ell_2 $</tex-math></inline-formula> sparsity regularization

Contact Info

Product

Resources

About