.jpg)
Perbandingan Metode Optimasi Coordinate Descent dan Stochastic Gradient Descent pada Regresi LASSO Kasus TBC di Jawa Barat Tahun 2022
Abstract
Tuberkulosis (TBC) merupakan penyakit menular yang masih menjadi masalah kesehatan masyarakat utama di Indonesia, dengan jumlah kasus tertinggi terdapat di Provinsi Jawa Barat. Kasus TBC dipengaruhi oleh berbagai faktor, seperti kepadatan penduduk, akses terhadap layanan kesehatan, kondisi lingkungan, dan status sosial ekonomi. Namun, adanya keterkaitan antarpeubah tersebut dapat menimbulkan masalah multikolinearitas sehingga menyulitkan analisis regresi konvensional. Regresi LASSO dapat mengatasi masalah tersebut melalui seleksi peubah dan regularisasi secara otomatis, tetapi kinerjanya dipengaruhi oleh metode optimasi yang digunakan. Penelitian ini bertujuan membandingkan metode optimasi coordinate descent (CD) dan stochastic gradient descent (SGD) dalam pembentukan model regresi LASSO serta mengidentifikasi faktor-faktor yang memengaruhi kasus TBC di Jawa Barat. Hasil analisis menunjukkan bahwa model LASSO dengan optimasi CD menghasilkan RMSE sebesar 808,421 dan adjusted R² sebesar 87,665% dengan lima peubah penjelas yang terpilih. Sementara itu, model LASSO dengan optimasi SGD menghasilkan RMSE sebesar 819,481 dan adjusted R² sebesar 85,089% dengan tujuh peubah penjelas yang terpilih. Model terbaik adalah LASSO dengan optimasi CD karena memiliki RMSE terendah dan adjusted R² tertinggi. Seluruh peubah terpilih pada model tersebut memiliki hubungan positif terhadap kejadian TB. Hasil penelitian menunjukkan bahwa regresi LASSO dengan optimasi CD efektif digunakan untuk mendukung kebijakan pengendalian TB di wilayah berisiko tinggi seperti Jawa Barat.
Tuberculosis (TB) is a contagious disease that remains a major public health concern in Indonesia, with the highest number of cases found in West Java Province. Various factors influence TB incidence, including population density, access to healthcare services, environmental conditions, and socioeconomic status. However, the intercorrelation among these factors often leads to multicollinearity problems, complicating conventional regression analysis. LASSO regression addresses this issue by performing automatic variable selection and regularization, yet its performance depends on the optimization method used. Coordinate Descent (CD) is known for its stability in updating coefficients one at a time, while Stochastic Gradient Descent (SGD) offers computational efficiency through updates based on randomly selected data, although it is sensitive to parameter tuning. This study aims to compare the two optimization methods in building LASSO regression models and to identify factors affecting TB cases in West Java. The analysis shows that the LASSO model using Coordinate Descent achieved an RMSE of 808.421 and an adjusted R² of 87.665% with five selected variables, whereas the model using Stochastic Gradient Descent resulted in an RMSE of 819.481 and an adjusted R² of 85.089% with seven selected variables. The best-performing model is the LASSO with Coordinate Descent optimization, as it yields the lowest RMSE and highest adjusted R², and all five variables in the model have a positive relationship with TB incidence. These findings suggest that LASSO regression with Coordinate Descent optimization can be an effective approach to support TB control policies in high-burden areas such as West Java.
Kata Kunci: Coordinate descent, multikolinearitas, regresi LASSO, stochastic gradient descent, tuberkulosis
Keywords: Coordinate descent, multicollinearity, LASSO regression, stochastic gradient descent, tuberculosis
Full Text:
PDFReferences
World Health Organization, “Global tuberculosis report 2022.” [Online]. Available: https://www.who.int/publications/i/item/9789240061729.
R. Kemenkes, “Tuberkulosis.” [Online]. Available: https://www.tbindonesia.or.id/.
I. Onozaki, I. Law, C. Sismanidis, M. Zignol, P. Glaziou, and K. Floyd, “National tuberculosis prevalence surveys in Asia, 1990-2012: An overview of results and lessons learned,” Trop. Med. Int. Heal., vol. 20, no. 9, pp. 1128–1145, 2015, doi: https://doi.org/10.1111/tmi.12534.
S. F. Febrilia, B. Lapau, K. Zaman, M. Mitra, and M. Rustam, “Hubungan faktor manusia dan lingkungan rumah terhadap kejadian tuberkulosis di wilayah kerja Puskesmas Rejosari Kota Pekanbaru,” J. Kesehat. Komunitas, vol. 8, no. 3, pp. 436–442, 2022, doi: https://doi.org/10.25311/keskom.vol8.iss3.618.
T. Kyriazos and M. Poga, “Dealing with multicollinearity in factor analysis: the problem, detections, and solutions,” Open J. Stat., vol. 13, no. 03, pp. 404–424, 2023, doi: https://doi.org/10.4236/ojs.2023.133020.
M. H. Kutner, C. J. Nachtsheim, J. Neter, and W. Li, Applied Linear Statistical Models, 5th ed. New York: McGraw-Hill/Irwin, 2005.
T. Ullmann, G. Heinze, L. Hafermann, C. Schilhart-, Wallisch, and D. Dunkler, “Evaluating variable selection methods for multivariable regression models : A simulation study protocol,” PLoS One, pp. 1–19, 2024, doi: https://doi.org/10.1371/journal.pone.0308543.
G. A. Kesse, “Variable selection using Lasso Regression,” Stat. Methodol. data Sci., 2025.
H. M. Nayem, S. Aziz, and B. M. G. Kibria, “Evaluating estimator performance under multicollinearity : a trade-off between mse and accuracy in Logistic , Lasso , Elastic Net , and Ridge Regression with varying penalty parameters,” stats, vol. 8, pp. 4–19, 2025, doi:
https://doi.org/10.3390/stats8020045.
C. J. Hsieh and I. S. Dhillon, “Fast coordinate descent methods with variable selection for non-negative matrix factorization,” Proc. ACM SIGKDD Int. Conf. Knowl. Discov. Data Min., pp. 1064–1072, 2011, doi: https://doi.org/10.1145/2020408.2020577.
J. Yang and G. Yang, “Modified convolutional neural network based on dropout and the stochastic gradient descent optimizer,” Algorithms, vol. 11, no. 3, 2018, doi: https://doi.org/10.3390/a11030028.
A. Banapon, M. L. P. Putra, and E. Widodo, “Penerapan regresi binomial negatif untuk mengatasi pelanggaran overdispersi pada regresi poisson (studi kasus penderita tuberculosis di Provinsi Jawa Barat tahun 2017),” J. Stat. dan Apl., vol. 14, no. 1, pp. 39–52, 2020. [Online]. Available https://biastatistics.statistics.unpad.ac.id/?journal=biastatistics&page=article&op=view&path%5B%5D=95.
S. Chen, K. A. Notodiputro, and S. Rahardiantoro, “Penerapan analisis Lasso dan group Lasso dalam mengidentifikasi faktor-faktor yang berhubungan dengan tuberkulosis di Jawa Barat,” Indones. J. Stat. Its Appl., vol. 4, no. 1, pp. 39–54, 2020.
N. D. Ovalingga, N. Amalita, Y. Kurniawati, and Z. Martha, “Regularized ordinal regression with Lasso : identifying factors in students ’ public speaking anxiety at Universitas Negeri Padang,” UNP Journal of Statistics and Data Science, vol. 2, no. 1999, pp. 475–482, 2024.
R. Tibshirani, “Regression shrinkage and selection via the Lasso,” J. R. Stat. Soc. Ser. B Methodol., vol. 58, no. 1, pp. 267–288, 1996, doi: https://doi.org/10.1111/j.2517-6161.1996.tb02080.x.
F. K. H. Prabowo, Y. Wilandari, and A. Rusgiyono, “Pemodelan pertumbuhan ekonomi Jawa Tengah menggunakan pendekatan least absolute shrinkage and selection operator (LASSO),” J. Gaussian, vol. 4, no. 1996, pp. 855–864, 2015, [Online]. Available: https://ejournal3.undip.ac.id/index.php/gaussian/article/view/10220.
Y. A. Mait, D. Tineke Salaki, and H. A. H. Komalig, “Kajian model prediksi metode least absolute shrinkage and selection operator (LASSO) pada data mengandung multikolinearitas,” J. Mat. dan Apl., vol. 10, no. 2, pp. 69–75, 2021, [Online]. Available: https://ejournal.unsrat.ac.id/v3/index.php/decartesian/article/view/34909.
H.-J. M. Shi, S. Tu, Y. Xu, and W. Yin, A Primer on Coordinate Descent Algorithms. Chicago, 2016, doi: http://arxiv.org/abs/1610.00040
J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” J. Stat. Softw., vol. 33, no. 1, pp. 1–22, 2010, doi: https://doi.org/10.18637/jss.v033.i01.
Y. Tsuruoka, J. Tsujii, and S. Ananiadou, “Stochastic Gradient Descent training for L1-regularized log-linear models with cumulative penalty,” ACL-IJCNLP 2009 - Jt. Conf. 47th Annu. Meet. Assoc. Comput. Linguist. 4th Int. Jt. Conf. Nat. Lang. Process. AFNLP, Proc. Conf., pp. 477–485, 2009, doi: https://doi.org/10.3115/1687878.1687946.
A. Géron, Hands-on Machine Learning whith Scikit-Learing, Keras and Tensorfow. 2019.
L. Bottou, “Large-scale machine learning with Stochastic Gradient Descent,” Proc. COMPSTAT 2010 - 19th Int. Conf. Comput. Stat. Keynote, Invit. Contrib. Pap., pp. 177–186, 2010, doi: https://doi.org/10.1007/978-3-7908-2604-3_16.
Nurhayati, I. Soekarno, I. K. Hadihardaja, and M. Cahyono, “A study of hold-out k-fold validation for accuracy of groundwater modeling in tidal lowland reclamation using extreme learning machine,” 2014 2nd Int. Conf. Technol. Informatics, Manag. Eng. Environ., pp. 228–233, 2014, doi: https://doi.org/10.1109/TIME-E.2014.7011623.
Y. Widyaningsih, G. P. Arum, and K. Prawira, “Aplikasi k-fold cross validation dalam penentuan model regresi binomial negatif terbaik,” BAREKENG J. Ilmu Mat. dan Terap., vol. 15, no. 2, pp. 315–322, 2021, doi: https://doi.org/10.30598/barekengvol15iss2pp315-322.
J. F. S. Berek and R. D. Guntur, “Pemodelan generalized poisson regression (GPR) terhadap jumlah kasus penyakit tuberculosis di Provinsi Nusa Tenggara Timur,” JSMS, vol. 11, no. 1, pp. 127–139, 2025, doi: https://dx.doi.org/10.24014/jsms.v11i1.30743.
W. Kusuma, C. F. Utomo, S. Tervia, and R. N. S. Setiawan, “Pemodelan kasus tuberkulosis (tb) di Nusa Tenggara Barat menggunakan model regresi binomial negatif,” J. Serunai Mat., vol. 14, no. 2, 2022, doi: https://doi.org/10.37755/jsm.v14i2.652.
A. H. Baun, I. Picauly, R. Paun, F. K. Masyarakat, and U. N. Cendana, “Analisis faktor risiko kejadian tuberkulosis pada anak di wilayah Kota Kupang,” PHRAJ, vol. 1, no. 1, pp. 56–73, 2023, doi: https://doi.org/10.61511/phraj.v1i1.2023.66.
V. M. Santi, A. N. Mutia, and Q. Meidianingsih, “Geographically Weighted Regression dalam menganalisis faktor-faktor yang mempengaruhi kasus tuberkulosis di Sumatera Utara,” Sainmatika, vol. 19, no. 2, pp. 107–116, 2022, doi: https://doi.org/10.31851/sainmatika.v19i2.9020.
M. Yusuf, A. Habsy, N. Rachmawati, and P. H. Khotimah, “Multiscale Geographically and Temporally Weighted Regression with Lasso and Adaptive Lasso for tuberculosis incidence mapping in West Java,” COMMUN, BIOMATH, vol. 8, no. 1, pp. 79–92, 2025, doi: https://doi.org/10.5614/cbms.2025.8.1.6.
S. M. Sholihah, N. Y. Aditiya, E. S. Evani, and S. Maghfiroh, “Konsep uji asumsi klasik pada Regresi Linier Berganda,” J. Ris. Akunt. Soedirman, vol. 2, no. 2, pp. 102–110, 2023, doi: https://doi.org/10.32424/1.jras.2023.2.2.10792.
A. Axmalia and S. A. Mulasari, “Dampak tempat pembuangan akhir sampah (tpa) terhadap gangguan kesehatan masyarakat,” J. Kesehat. Komunitas, vol. 6, no. 2, pp. 171–176, 2020, doi: https://doi.org/10.25311/keskom.vol6.iss2.536.
Refbacks
- There are currently no refbacks.
