ܝܘܠܦܢܐ ܕܡܟܝܢܐ ܩܐ ܒܘܨܝܐ ܟܢܫܝܐ: ܕܡܢܒܝܚ، ܠܐ ܒܣ ܕܡܦܫܩܚ

ܡܐ ܐܝܬ ܓܘ ܐܗܐ ܦܐܬܐ (On this page)

ܝܘܠܦܢܐ ܕܡܟܝܢܐ (machine learning) ܝܠܗ، ܒܬܚܘܡܐ ܕ-Géron ܟܦܬܚ ܒܝܗ ܟܬܒܐ ܕܝܠܗ، "ܝܕܥܬܐ (ܘܐܘܡܢܘܬܐ) ܕܬܘܟܢܝܬܐ ܕܡܚܫܒ̈ܢܐ ܗܕܟ ܕܡܨܝܐ ܕܝܠܦܝ ܡܢ ܝܗܝ̈ܒܬܐ"؛ ܒܢܘܣܚܐ ܩܠܐܣܝܩܝܐ ܕ-Arthur Samuel (1959) – "ܚܩܠܐ ܕܒܘܨܝܐ ܕܟܝܗܒ ܠܡܚܫܒ̈ܢܐ ܚܝܠܐ ܕܝܠܦܝ ܕܠܐ ܕܬܘܟܢܝܬܐ ܓܠܝܬܐ"؛ ܘܒܢܘܣܚܐ ܕܗܢܕܣܘܬܐ ܕ-Tom Mitchell (1997) – ܬܘܟܢܝܬܐ "ܟܝܠܦܐ ܡܢ ܢܣܝܘܢܐ E ܠܘܬ ܥܒܕܐ T ܘܡܚܘܝܢܐ ܕܥܒܕܐ P، ܐܢ ܥܒܕܐ ܕܝܠܗ̇ ܓܘ T، ܐܝܟ ܕܡܫܝܚܐ ܝܠܗ ܒ-P، ܟܡܫܬܦܪ ܥܡ ܢܣܝܘܢܐ E" (ܬܪܘܝܗܝ ܐܝܟ ܕܡܝܬܝ̈ܐ ܝܢܐ ܓܘ Géron, 2022، ܨܚܚܐ 1). ܩܐ ܒܘܨܝܬܐ ܕܐܬܝܐ ܡܢ ܣܛܐܛܝܣܛܝܩܐ ܐܢܝ ܬܚܘ̈ܡܐ ܝܕܝ̈ܥܐ ܝܢܐ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ: ܐܦ ܪܝܓܪܫܢ (regression) "ܟܝܠܦܐ" ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ (coefficients) ܡܢ ܝܗܝ̈ܒܬܐ. ܦܘܪܫܢܐ ܠܝܠܗ ܓܘ ܐܠܓܘܪܝܬܡ – ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܐܦ ܗܘ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܝܠܗ ܓܘ ܬܪܝܢ ܥܠܡ̈ܐ – ܐܠܐ ܓܘ ܢܝܫܐ ܘܡܛܠ ܗܕܐ ܓܘ ܫܘܪܪܐ: ܣܛܐܛܝܣܛܝܩܐ ܕܡܚܫܒ̈ܢܐ ܕܣܐܝܛ ܟܫܐܠܐ ܐܝܢܐ ܡܫܬܚܠܦܢܐ ܟܡܥܒܕ ܘܟܡܐ، ܘܟܡܫܪܪܐ ܐܗܐ ܒܡܢܝܢܐ ܡܫܘܬܦܐ، ܒܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܘܒܪܫܝܡܘܬܐ (significance)؛ ܝܘܠܦܢܐ ܕܡܟܝܢܐ ܟܫܐܠ ܡܐ ܦܝܫܐ ܗܘܝܐ ܠܚܙܝܬܐ (observation) ܚܕܬܐ، ܘܟܡܫܪܪ ܐܗܐ ܒܚܕ ܐܘܪܚܐ ܒܣ – ܥܠ ܝܗܝ̈ܒܬܐ ܕܡܘܕܝܠ ܠܐ ܚܙܐ ܠܗܝܢ. ܦܐܬܐ ܒܢܝܐ ܝܠܗ̇ ܚܕܪ ܟܬܒܐ ܕܝܘܠܦܢܐ ܥܒܕܢܝܐ ܕܡܦܠܚ ܣܓܝ ܓܘ ܚܩܠܐ، Hands-On Machine Learning ܕ-Aurélien Géron (ܡܦܩܬܐ ܬܠܝܬܝܬܐ، 2022)، ܘܟܡܩܪܒܐ ܥܡܗ ܓܢܒܐ ܐܚܪܢܐ ܕܐܦ ܗܝ ܙܘܙܐ – The Elements of Statistical Learning ܕ-Hastie، Tibshirani ܘ-Friedman (ܡܦܩܬܐ ܬܪܝܢܝܬܐ، 2009)، ܟܬܒܐ ܕܟܬܒܠܗ ܣܛܐܛܝܣܛܝܩ̈ܝܐ ܩܐ ܕܡܦܫܩܝ ܐܦ ܐܢܝ ܐܠܓܘܪܝ̈ܬܡܐ ܐܝܟ ܡܘܕܝ̈ܠܐ ܣܛܐܛܝܣܛܝܩ̈ܝܐ: "ܐܗܐ ܟܬܒܐ ܥܠ ܝܘܠܦܢܐ ܡܢ ܝܗܝ̈ܒܬܐ ܝܠܗ"، ܘ-"ܝܘܠܦܢܐ ܣܛܐܛܝܣܛܝܩܝܐ ܟܫܩܠ ܥܒܕܐ ܪܫܝܐ ܓܘ ܚܩ̈ܠܐ ܣܓܝ̈ܐܐ ܕܝܕܥܬܐ، ܕܙܘܙ̈ܐ ܘܕܐܘܡܢܘܬܐ" (Hastie et al., 2009, p. 1). ܘܟܬܒܐ ܬܠܝܬܝܐ، ܕ-Christopher Bishop (2006)، ܟܡܘܣܦ ܚܙܝܐ ܕܡܣܬܒܪܢܘܬܐ (probability): ܦܘܪܫܐ ܕܛܘ̈ܦܣܐ (pattern recognition) "ܡܒܘܥܐ ܕܝܠܗ ܓܘ ܗܢܕܣܘܬܐ ܝܠܗ، ܘܝܘܠܦܢܐ ܕܡܟܝܢܐ ܪܒܐ ܡܢ ܝܕܥܬܐ ܕܡܚܫܒ̈ܢܐ"، ܐܢܐ "ܡܨܝܐ ܕܚܙܝܚ ܠܗܘܢ ܐܝܟ ܬܪܝܢ ܦܐ̈ܬܐ ܕܐܦ ܗܘ ܚܩܠܐ" – ܘܓܘܗ ܐܘܪ̈ܚܬܐ Bayesian ܥܒܪܝ "ܡܢ ܩܘܪܢܬܐ ܕܡܗܝܪ̈ܐ ܠܢܗܪܐ ܪܫܝܐ" (Bishop, 2006، ܦܘܬܚܐ ܕܟܬܒܐ). ܘܪܒܝܥܝܐ، ܡܢ ܡܫܠܡܢܘܬܐ ܕܗܢܕܣܘܬܐ ܕܦܘܪܫܐ ܕܛܘ̈ܦܣܐ: ܟܬܒܐ ܕܝܘܠܦܢܐ ܕܒܝܚܕܝܘܬܐ ܕ-Ishii، Ueda، Maeda ܘ-Murase (2026) – ܕܟܬܝܒܐ ܝܠܗ "ܩܐ ܐܢܝ ܕܟܡܢܣܝ ܕܝܠܦܝ ܐܢܝ ܡ̈ܠܐ ܒܚܝܠܐ ܕܝܗܘܢ"، ܓܠܝܐܝܬ ܟܓܒܐ "ܡ̈ܠܐ ܩܠܐܣܝܩ̈ܝܐ" ܡܢ "ܛܟܢܘܠܘܓܝ̈ܐ ܚܕܬ̈ܐ ܡܢ ܟܠ"، ܡܛܠ ܕ"ܩܢܝܢܐ ܕܝܕܥܬܐ ܫܬܐܣܝܬܐ… ܦܝܫܐ ܡܫܦܪܐ ܣܓܝ ܠܚܝܠܐ ܕܝܘܠܦܢܐ ܕܛܟܢܘܠܘܓܝ̈ܐ ܚܕܬ̈ܐ"، ܘܟܡܫܠܡ ܒܡܠܟܐ ܚܕ: ܕܦܠܚܚ ܥܡ ܝܗܝ̈ܒܬܐ ܫܪܝܪ̈ܬܐ (Ishii et al., 2026، ܦܘܬܚܐ ܕܟܬܒܐ). ܘܚܡܝܫܝܐ، ܡܢ ܓܢܒܐ ܕܬܘܟܢܝܬܐ: ܟܬܒܐ ܕܝܘܠܦܢܐ ܕ-Dothang Truong (2026) ܩܐ SPSS Modeler، ܕܟܬܝܒܐ ܝܠܗ ܡܢ ܝܕܥܬܐ ܕ"ܝܠܘ̈ܦܐ ܡܢ ܚܩ̈ܠܐ ܦܪ̈ܝܫܐ، ܐܝܟ ܬܓܪܘܬܐ، ܙܒܢܘܬܐ، ܙܘܙ̈ܐ، ܛܝܣܐ، ܝܕ̈ܥܬܐ ܕܟܢܫܐ ܘܝܕ̈ܥܬܐ ܕܒܪܢܫܘܬܐ، ܡܨܝܐ ܕܪܓܫܝ ܕܦܝܫ̈ܐ ܝܢܐ ܒܣܬܪ" ܓܘ ܚܩܠܐ ܕܟܡܚܝܠ ܠܬܘܟܢ̈ܝܐ، ܘܕܐܕܝܘܡ "ܡܐܢ̈ܐ ܣܓܝ̈ܐܐ ܟܝܗܒܝ ܠܡܦܠܚ̈ܢܐ ܕܒܢܝ ܡܘܕܝ̈ܠܐ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ ܕܠܐ ܟܬܒܬܐ ܕܚܕ ܣܕܪܐ ܕܪܡܙܐ" (Truong, 2026، ܦܘܬܚܐ ܕܟܬܒܐ). Géron ܟܐܡܪ ܡܐ ܟܥܒܕܚ، Hastie ܘܚܒܪ̈ܘܗܝ ܟܐܡܪܝ ܩܐ ܡܘܕܝ ܐܗܐ ܟܦܠܚ ܘܐܝܡܢ ܠܐ، Bishop ܟܐܡܪ ܡܐ ܡܘܕܝܠ ܟܣܐܡ ܥܠ ܡܣܬܒܪܢܘ̈ܝܬܐ، Ishii ܘܚܒܪ̈ܘܗܝ ܟܐܡܪܝ ܡܐ ܗܘܐ ܝܕܝܥܐ ܩܕܡ ܕܡܠܬܐ ܗܘܝܐ ܡܘܕܐ، ܘ-Truong ܟܐܡܪ ܕܟܝ ܟܡܬܩܪܐ ܓܘ ܪܫܝܡܬܐ (Menu)؛ ܦܐܬܐ ܟܡܘܣܦܐ ܠܐܪܒܥܬܝܗܘܢ ܡܐ ܕܟܬܒ̈ܐ ܕܝܘܠܦܢܐ – ܕܟܬܝ̈ܒܐ ܝܢܐ ܩܐ ܡܗܢܕܣ̈ܐ ܘܣܛܐܛܝܣܛܝܩ̈ܝܐ – ܠܐ ܟܐܡܪܝ: ܡܐ ܟܥܒܕ ܟܠ ܐܗܐ ܠܒܘܨܝܐ ܟܢܫܝܐ (ܦܣܩܐ 1)، ܘܡܐ ܟܗܘܐ ܐܡܢ ܕܟܡܢܣܚ ܕܡܢܒܝܚ ܚܝ̈ܐ ܕܒܢܝ̈ ܐܢܫܐ (Salganik et al., 2020). ܛܟܣܐ: ܦܘܪܫܢܐ ܒܝܢܝ ܦܘܫܩܐ ܘܡܢܒܝܢܘܬܐ (prediction) (1)، ܨܘܪܬܐ ܕܙܢ̈ܐ ܕܝܘܠܦܢܐ ܘܕܥܘܩ̈ܢܐ (2)، ܦܪܘܝܩܬ ܡܢ ܪܫܐ ܗܠ ܚܪܬܐ (3)، ܟܢܘܫܝܐ ܕܫܘܪܪܐ (4) – ܡܚܘ̈ܝܢܐ، ܓܘܕܐ ܕܒܘܚܪܢܐ (test set)، ܫܘܪܪܐ ܡܚܠܦܢܐ (cross-validation)، ܡܪܕܝܬܐ ܕܝܗܝ̈ܒܬܐ ܘܬܚܘ̈ܡܐ ܕܡܢܒܝܢܘܬܐ ܦܐܬܐ ܦܪܝܫܬܐ ܝܠܗ̇، ܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ – ܡܘܕܝ̈ܠܐ ܓܢܗܘܢ (5)، neural networks (6)، ܡܐܢ̈ܐ (7)، ܛܟܣܐ ܕܥܒܕܐ (8) – ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-R (9) ܘܒ-SPSS Modeler (10). ܡܥܝܪܢܘܬܐ ܥܠ ܡܬܠܐ: ܢܘܣܚܐ ܕܝܓܝܛܠܝܐ ܕ-Géron ܠܝܬ ܓܘܗ ܡܢܝ̈ܢܐ ܕܦܐ̈ܬܐ، ܘܡܛܠ ܗܕܐ ܡܬ̈ܠܐ ܡܢܗ ܠܦܘܬ ܨܚܚܐ ܘܦܣܩܐ ܝܢܐ؛ Hastie ܘܚܒܪ̈ܘܗܝ، Bishop، Ishii ܘܚܒܪ̈ܘܗܝ ܘ-Truong – ܠܦܘܬ ܦܐܬܐ.

1. ܬܪܬܝܢ ܬܪ̈ܒܝܬܐ: ܕܡܦܫܩܚ ܝܢ ܕܡܢܒܝܚ

ܦܘܪܫܢܐ ܕܣܛܐܛܝܣܛܝܩܐ ܠܐ ܥܒܕܠܗ. Leo Breiman، ܡܫܟܚܢܐ ܕ-random forests، ܦܬܚܠܗ ܠܕܪܐ ܒܡܐܡܪܐ ܕܦܫܩܠܗ ܩܐ ܡܘܕܝ ܣܛܐܛܝܣܛܝܩ̈ܝܐ ܘܡܗܢܕܣ̈ܐ ܠܐ ܟܡܡܠܠܝ ܐܦ ܗܘ ܠܫܢܐ: "ܐܝܬ ܬܪܬܝܢ ܬܪ̈ܒܝܬܐ ܓܘ ܡܦܠܚܢܘܬܐ ܕܡܘܕܝ̈ܠܐ ܣܛܐܛܝܣܛܝܩ̈ܝܐ ܩܐ ܕܡܛܚ ܠܦܐܪ̈ܐ ܡܢ ܝܗܝ̈ܒܬܐ. ܚܕܐ ܟܣܐܡܐ ܕܝܗܝ̈ܒܬܐ ܒܪܝ̈ܐ ܝܢܐ ܒܝܕ ܡܘܕܝܠ ܕܝܗܝ̈ܒܬܐ stochastic ܝܕܝܥܐ. ܐܚܪܢܝܬܐ ܟܡܦܠܚܐ ܡܘܕܝ̈ܠܐ ܕܐܠܓܘܪܝ̈ܬܡܐ ܘܟܚܫܒܐ ܠܡܟܝܢܘܬܐ ܕܝܗܝ̈ܒܬܐ ܐܝܟ ܠܐ ܝܕܝܥܬܐ" – ܘܟܢܘܫܬܐ ܕܣܛܐܛܝܣܛܝܩ̈ܝܐ، ܐܝܟ ܕܐܡܪ، "ܐܣܝܪܐ ܝܠܗ̇ ܓܢܗ̇ ܠܡܦܠܚܢܘܬܐ ܡܩܪܒܘܬ ܝܚܝܕܝܬܐ ܕܡܘܕܝ̈ܠܐ ܕܝܗܝ̈ܒܬܐ" (Breiman, 2001a، ܟܢܘܫܝܐ). Galit Shmueli ܥܒܕܠܗ̇ ܠܦܘܪܫܢܐ ܨܘܪܬܐ ܥܒܕܢܝܬܐ: ܡܘܕܝܠ ܕܟܡܦܫܩ ܝܠܗ ܡܦܠܚܢܘܬܐ ܕܡܘܕܝܠ ܩܐ ܒܘܚܪܢܐ ܕܬܐܘܪܝܐ ܕܥܠ̈ܠܬܐ، ܘܓܘ ܝܕ̈ܥܬܐ ܕܟܢܫܐ "ܐܘܪ̈ܚܬܐ ܣܛܐܛܝܣܛܝܩ̈ܝܐ ܡܩܪܒܘܬ ܒܣ ܩܐ ܒܘܚܪܢܐ ܕܬܐܘܪܝܐ ܕܥܠ̈ܠܬܐ ܡܬܦܠܚ̈ܢܐ ܝܢܐ" – ܘܒܥܒܕܐ، ܡܩܪܒܘܬ ܟܠܝܘܡ، ܓܘ "ܡܘܕܝ̈ܠܐ ܥܠ ܫܬܐܣܐ ܕܐܣܘܪ̈ܐ ܥܠ ܝܗܝ̈ܒܬܐ ܕܚܙ̈ܝܬܐ. ܡܘܕܝ̈ܠܐ ܕܪܝܓܪܫܢ ܡܬܠܐ ܕܣܓܝ ܡܬܚܙܐ ܡܢ ܟܠ ܝܢܐ" (Shmueli, 2010, Section 1.1)؛ ܡܘܕܝܠ ܕܟܡܢܒܐ ܝܠܗ "ܐܘܪܚܐ ܕܡܦܠܚܢܘܬܐ ܕܡܘܕܝܠ ܣܛܐܛܝܣܛܝܩܝܐ ܝܢ ܐܠܓܘܪܝܬܡ ܕ-data mining ܥܠ ܝܗܝ̈ܒܬܐ ܩܐ ܡܢܒܝܢܘܬܐ ܕܚܙ̈ܝܬܐ ܚܕ̈ܬܬܐ ܝܢ ܕܐܬܝܢ" (ܦܣܩܐ 1.2). ܛܥܝܘܬܐ ܕܣܓܝ ܡܬܚܙܝܐ ܝܠܗ̇ ܣܝܡܬܐ "ܕܡܘܕܝ̈ܠܐ ܥܡ ܚܝܠܐ ܪܡܐ ܕܦܘܫܩܐ ܡܢ ܟܝܢܐ ܕܝܗܘܢ ܐܝܬ ܠܗܘܢ ܚܝܠܐ ܪܡܐ ܕܡܢܒܝܢܘܬܐ" (ܟܢܘܫܝܐ) – ܘܠܐ ܝܠܗ̇ ܫܪܝܪܬܐ: ܚܝܠܐ ܕܦܘܫܩܐ ܘܚܝܠܐ ܕܡܢܒܝܢܘܬܐ ܬܪܝܢ ܡܫܘ̈ܚܬܐ ܝܢܐ، ܠܐ ܬܪܝܢ ܪ̈ܫܐ ܕܚܕ ܣܪܛܐ (ܦܣܩܐ 4.2)؛ ܐܦ ܫܘܪܪܐ ܦܪܝܫܐ ܝܠܗ – ܓܘ ܡܘܕܝܠ ܕܟܡܦܫܩ ܟܒܚܪܚ ܕܡܘܕܝܠ ܟܡܚܘܐ ܠܬܐܘܪܝܐ ܘܕܦܐܫ ܠܝܗܝ̈ܒܬܐ، ܘܓܘ ܡܘܕܝܠ ܕܟܡܢܒܐ ܟܒܚܪܚ ܦܘܫܛܐ ܠܝܗܝ̈ܒܬܐ ܚܕ̈ܬܬܐ، ܘ"ܣܘܟܢܐ ܪܒܐ ܡܢ ܟܠ ܩܐ ܦܘܫܛܐ ܝܠܗ ܦܐܝܘܬܐ ܝܬܝܪܬܐ (overfitting) ܠܝܗܝ̈ܒܬܐ ܕܝܘܠܦܢܐ" (ܦܣܩܐ 2.6.1). Géron ܟܐܡܪ ܐܦ ܗܝ ܡܠܬܐ ܡܢ ܓܢܒܐ ܐܚܪܢܐ ܕܣܝܓܐ: ܣܓܝܐܘܬܐ ܕܥܒ̈ܕܐ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ ܥܠ ܡܢܒܝܢܘܬܐ ܝܢܐ، ܘ"ܥܒܕܐ ܛܒܐ ܥܠ ܝܗܝ̈ܒܬܐ ܕܝܘܠܦܢܐ ܛܒܐ ܝܠܗ، ܐܢܐ ܠܐ ܡܣܦܩ؛ ܢܝܫܐ ܫܪܝܪܐ ܝܠܗ ܕܦܠܚܚ ܛܒ ܥܠ ܗܘܝ̈ܐ ܚܕ̈ܬܐ" (Géron, 2022, Chapter 1, "Instance-Based Versus Model-Based Learning").

ܘܡܐ ܟܥܒܕ ܐܗܐ ܠ-psychology ܘܠ-sociology. Yarkoni ܘ-Westfall ܟܐܡܪܝ ܕܚܝܠܐ ܡܩܪܒܘܬ ܓܡܝܪܐ ܕ-psychology ܥܠ ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܫܒܩܠܗ̇ ܥܡ "ܬܐܘܪܝ̈ܐ ܡܪܟܒ̈ܬܐ ܕܡܟܝܢܘܬܐ ܕܢܦܫܐ" ܕܐܝܬ ܠܗܝܢ "ܚܝܠܐ ܙܥܘܪܐ (ܝܢ ܠܐ ܝܕܝܥܐ) ܕܡܢܒܝܢܘܬܐ ܕܬܘܪ̈ܨܐ ܕܐܬܝܢ"، ܘܟܡܩܪܒܝ ܕܫܩܠܚ ܢܡܘ̈ܣܐ ܡܢ ܝܘܠܦܢܐ ܕܡܟܝܢܐ – ܘܐܝܟ ܕܐܡܪܝ، ܚܝܠܐ ܥܠ ܡܢܒܝܢܘܬܐ ܓܢܗ ܦܝܫܐ ܡܛܝܐ ܠܦܘܗܡܐ ܛܒܐ ܒܝܫ ܕܬܘܪ̈ܨܐ (Yarkoni & Westfall, 2017، ܟܢܘܫܝܐ). Hofman، Watts ܘܚܒܪ̈ܘܗܝ – ܒܝܢܬܘܗܝ Susan Athey، Jon Kleinberg، Matthew Salganik ܘ-Tal Yarkoni – ܟܡܩܪܒܝ ܓܘ Nature ܨܘܪܬܐ ܕܬܪܝܢ ܡܫܘ̈ܚܬܐ ܩܐ ܟܠ ܒܘܨܝܐ: ܟܡܐ ܟܡܦܫܩ (ܦܘܪܫܐ ܘܫܘܥܪܐ ܕܡܥܒ̈ܕܢܘܝܬܐ ܕܥܠ̈ܠܬܐ) ܘܟܡܐ ܟܒܚܪ ܡܢܒܝ̈ܢܘܝܬܐ ܕܦܐܪ̈ܐ، ܘܟܩܪܝ ܠܝܕ̈ܥܬܐ ܕܟܢܫܐ ܒܚܘܫܒܢܐ (computational social science) ܠ"ܡܘܕܝܠ ܐܟܚܕܝܐ" ܕܬܪܘܝܗܝ (Hofman et al., 2021، ܟܢܘܫܝܐ). Molina ܘ-Garip، ܩܐ sociologists، ܟܡܢܝ ܡܦܠܚܢܘ̈ܝܬܐ: ܡܦܩܬܐ ܕܡܚܘ̈ܝܢܐ ܡܢ ܡܒܘ̈ܥܐ ܚܕ̈ܬܐ ܐܝܟ ܟܬܝܒܬܐ ܘܨܘܪ̈ܬܐ، ܬܚܘܝܬܐ ܕܦܘܪܫܢܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ (population)، ܫܘܦܪܐ ܕܡܦܩܬܐ ܕܥܠ̈ܠܬܐ، ܘܡܢܒܝ̈ܢܘܝܬܐ ܩܐ ܡܕܒܪܢܘܬܐ ܘܩܐ ܒܢܝܢܐ ܕܬܐܘܪܝܐ (Molina & Garip, 2019، ܟܢܘܫܝܐ).

ܘܡܐ ܟܗܘܐ ܐܡܢ ܕܟܡܢܣܚ. ܢܣܝܘܢܐ (experiment) ܪܒܐ ܡܢ ܟܠ ܓܘ ܡܢܒܝܢܘܬܐ ܕܚܝ̈ܐ ܕܒܢܝ̈ ܐܢܫܐ ܝܠܗ "Fragile Families Challenge": 160 ܓܘ̈ܕܐ ܕܒܘܨ̈ܝܐ ܫܩܠܠܗܘܢ ܝܗܝ̈ܒܬܐ ܥܠ 4,242 ܫܪ̈ܒܬܐ – 12,942 ܡܫܬܚܠܦ̈ܢܐ ܩܐ ܟܠ ܫܪܒܬܐ، ܕܟܢܝ̈ܫܐ ܝܢܐ ܡܢ ܡܘܠܕܐ ܕܝܠܘܕܐ ܗܠ ܥܘܡܪܐ ܕ-9 – ܘܐܡܝܪܐ ܝܠܗ ܩܐ ܕܡܢܒܝ ܐܫܬܐ ܦܐܪ̈ܐ ܓܘ ܥܘܡܪܐ ܕ-15: ܡܨܥܝܬܐ ܕܡܢܝ̈ܢܐ ܕܡܕܪܫܬܐ، "grit" (ܡܩܘܝܢܘܬܐ)، ܦܠܛܬܐ ܡܢ ܒܝܬܐ، ܥܩܬܐ ܕܡܢܝܢܐ (material hardship)، ܦܪܩܬܐ ܡܢ ܥܒܕܐ ܕܐܒܐ ܝܢ ܝܡܐ ܕܡܪܒܐ ܘܫܘܬܦܘܬܐ ܕܝܠܗ ܓܘ ܝܘܠܦܢܐ ܕܐܘܡܢܘܬܐ. ܦܐܪܐ: ܐܦ ܡܢܒܝ̈ܢܘܝܬܐ ܛܒ̈ܐ ܡܢ ܟܠ ܠܐ ܗܘܝ ܚܬܝ̈ܬܐ – R² ܥܠ ܝܗܝ̈ܒܬܐ ܕܡܬܢܛܪ̈ܢ ܝܢܐ (holdout) ܕܡܩܪܒܘܬ 0.2 ܩܐ ܥܩܬܐ ܕܡܢܝܢܐ ܘܩܐ ܡܨܥܝܬܐ ܕܡܢܝ̈ܢܐ ܘܡܩܪܒܘܬ 0.05 ܩܐ ܐܪܒܥܐ ܦܐܪ̈ܐ ܐܚܪ̈ܢܐ – ܘܗܘܝ ܒܣ ܩܠܝܠ ܛܒ̈ܐ ܒܝܫ ܡܢ ܡܘܕܝܠ ܦܫܝܛܐ ܕ-reference: ܪܝܓܪܫܢ ܣܪܛܢܝܐ ܝܢ ܠܘܓܝܣܛܝܩܝܐ ܥܠ ܐܪܒܥܐ ܡܫܬܚܠܦ̈ܢܐ ܕܓܒܝܠܗܘܢ ܡܗܝܪܐ ܓܘ ܚܩܠܐ (ܬܠܬܐ ܥܠ ܝܡܐ ܓܘ ܡܘܠܕܐ – ܫܪܒܬܐ، ܗܘܝܐ ܕܙܘܘܓܐ ܘܝܘܠܦܢܐ – ܘܡܫܘܚܬܐ ܕܐܦ ܗܘ ܦܐܪܐ، ܝܢ ܩܪܝܒܐ ܠܗ، ܓܘ ܥܘܡܪܐ ܕ-9). ܛܥܝܘܬܐ ܕܡܢܒܝܢܘܬܐ ܐܣܝܪܬܐ ܗܘܝܠܗ̇ ܚܝܠܬܢܐܝܬ ܥܡ ܫܪܒܬܐ ܕܟܡܢܒܝܚ ܥܠܗ̇ ܘܒܣ ܟܪܝܗܐܝܬ ܥܡ ܐܘܪܚܐ (Salganik et al., 2020، ܟܢܘܫܝܐ ܘܦܣܩܐ Results). ܦܐܪܐ ܕܡܟܬܒ̈ܢܐ – 112 ܒܘܨ̈ܝܐ، ܘܒܪܫܝܗܘܢ Matthew Salganik (ܡܟܬܒܢܐ ܕ-Bit by Bit ܕܐܝܬ ܓܘ ܨܘܪܬܐ ܕܡܐܢ̈ܐ) – ܝܠܗ ܕܒܘܨ̈ܝܐ ܕܐܘܪܚܐ ܕܚܝ̈ܐ ܓܪܓ "ܡܫܘܝܝ ܚܘܫܒܐ ܕܟܦܗܡܝ ܐܘܪ̈ܚܬܐ ܕܚܝ̈ܐ ܥܡ ܫܪܪܐ ܕܚܕܐ ܡܢ ܡܢܒܝ̈ܢܘܝܬܐ ܠܐ ܗܘܝܠܗ̇ ܚܬܝܬܐ ܣܓܝ" (Section Significance)، ܘܡܫܪܝ ܡܐ ܕܟܩܪܝ ܠܗ "ܦܪܕܘܟܣ ܕܦܘܗܡܐ/ܡܢܒܝܢܘܬܐ": ܐܦ ܐܢܝ ܝܗܝ̈ܒܬܐ ܝܗܒܠܗܝܢ ܝܬܝܪ ܡܢ 750 ܡܐܡܪ̈ܐ ܕܟܡܦܫܩܝ – ܘܠܐ ܟܡܢܒܝܐ (Section Discussion). ܩܐ ܒܘܨܝܬܐ: ܬܪܬܝܢ ܬܪ̈ܒܝܬܐ ܠܐ ܟܚܠܦܝ ܚܕܐ ܠܚܕܐ. ܡܘܕܝܠ ܕܟܡܦܫܩ ܘܠܐ ܟܡܢܒܐ ܡܕܡ ܚܫܝܕܐ ܝܠܗ؛ ܡܘܕܝܠ ܕܟܡܢܒܐ ܘܚܕ ܠܐ ܟܦܗܡ ܠܗ ܚܫܝܕܐ ܝܠܗ ܒܐܘܪܚܐ ܐܚܪܢܐ (ܦܣܩܐ 5، "ܩܘܦܬܐ ܚܘܪܬܐ ܘܐܘܟܡܬܐ")؛ ܘܣܓܝܐܘܬܐ ܕܙܒܢܐ ܦܘܢܝܐ ܝܠܗ ܕܬܢܚ ܬܪܘܝܗܝ.

2. ܨܘܪܬܐ ܕܚܩܠܐ: ܙܢ̈ܐ ܕܝܘܠܦܢܐ ܘܡܐ ܕܡܨܝܐ ܕܛܥܐ

Géron ܟܦܠܓ ܛܟ̈ܣܐ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ ܠܦܘܬ ܬܠܬܐ ܣܪ̈ܛܐ (Géron, 2022, Chapter 1, "Types of Machine Learning Systems"). ܩܕܡܝܐ – ܟܡܐ ܕܘܒܪܐ ܐܝܬ. ܓܘ ܝܘܠܦܢܐ ܥܡ ܡܕܒܪܢܐ (supervised) ܓܘܕܐ ܕܝܘܠܦܢܐ ܐܝܬ ܓܘܗ ܦܘܢ̈ܝܐ ܕܟܡܒܥܝܚ – ܪܘ̈ܫܡܐ (labels) – ܘܬܪܝܢ ܥܒ̈ܕܐ ܛܘܦܣܢ̈ܝܐ ܝܢܐ ܦܘܪܫܐ ܠܓܢ̈ܣܐ (spam / ܠܐ spam) ܘܪܝܓܪܫܢ (ܛܝܡܐ ܕܥܓܠܬܐ ܠܦܘܬ ܡܫܘܚܬܐ ܕܐܘܪܚܐ ܕܡܗܠܟܐ ܝܠܗ̇، ܥܘܡܪܐ ܘܡܥܡܠܢܐ)؛ ܬܚܘܡܐ ܒܝܢܬܝܗܘܢ ܦܬܝܚܐ ܝܠܗ – ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܡܘܕܝܠ ܕܪܝܓܪܫܢ ܝܠܗ ܕܟܡܬܦܠܚ ܩܐ ܦܘܪܫܐ ܠܓܢ̈ܣܐ، ܡܛܠ ܕܟܡܦܩ ܡܣܬܒܪܢܘܬܐ. ܓܘ ܝܘܠܦܢܐ ܕܠܐ ܡܕܒܪܢܐ (unsupervised) ܠܝܬ ܪܘ̈ܫܡܐ، ܘܥܒ̈ܕܐ ܝܢܐ ܥܢܩܘ̈ܕܐ (clusters) (ܓܘ̈ܕܐ ܕܡܦܠܚ̈ܢܐ ܕܡܝ̈ܐ)، visualization ܘ-dimensionality reduction (ܚܘܠܛܐ ܕ-features ܐܣܝܪ̈ܐ، ܐܝܟ ܐܘܪܚܐ ܕܡܗܠܟܐ ܝܠܗ̇ ܥܓܠܬܐ ܘܥܘܡܪܐ، ܠܚܕ feature ܕ"ܥܬܝܩܘܬܐ")، ܦܘܪܫܐ ܕܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ (anomaly detection) ܘܝܘܠܦܢܐ ܕ-association rules (ܐܝܢܐ ܕܟܙܒܢ ܡܪܩܐ barbecue ܘ-chips ܟܙܒܢ ܐܦ steak) – ܩܐ ܒܘܨܝܐ ܟܢܫܝܐ ܐܢܝ ܝܢܐ ܦܘܫܩܐ ܕܥܠ̈ܠܬܐ (factor analysis) ܘܦܘܫܩܐ ܕܥܢܩܘ̈ܕܐ ܕܝܕܥ ܠܗܘܢ، ܘܐܝܬ ܠܗܘܢ ܦܐܬܐ ܕܝܠܗܘܢ: ܝܘܠܦܢܐ ܕܠܐ ܡܕܒܪܢܐ – ܘܡܚܫܒ̈ܢܐ: ܦܘܫܩܐ ܕܥܢܩܘ̈ܕܐ ܘܦܘܫܩܐ ܕܥܠ̈ܠܬܐ ܡܒܨܝܢܐ. ܒܝܢܬܝܗܘܢ – semi-supervised learning (ܩܠܝܠ ܪܘ̈ܫܡܐ، ܣܓܝ ܝܗܝ̈ܒܬܐ ܕܠܐ ܪܘ̈ܫܡܐ)، self-supervised learning (ܡܘܕܝܠ ܟܒܪܐ ܪܘ̈ܫܡܐ ܩܐ ܓܢܗ – ܟܡܛܫܐ ܡܢܬܐ ܡܢ ܨܘܪܬܐ ܘܟܝܠܦ ܕܡܕܥܪ ܠܗ̇ – ܘܒܬܪܗ ܟܡܬܩܢܚ ܠܗ ܩܐ ܥܒܕܐ ܐܚܪܢܐ: ܐܗܐ ܝܠܗ ܢܡܘܣܐ ܕܡܘܕܝ̈ܠܐ ܕܠܫܢܐ ܕܐܝܬ ܓܘ ܦܐܬܐ ܕ-NLP)، ܘ-reinforcement learning (agent، ܥܒ̈ܕܐ، ܦܘܪ̈ܥܢܐ). ܬܪܝܢܐ – batch ܠܩܘܒܠ online: ܡܘܕܝܠ ܕܟܡܬܝܠܦ ܚܕ ܓܐܝܐ ܥܠ ܟܠ ܝܗܝ̈ܒܬܐ، ܠܩܘܒܠ ܡܘܕܝܠ ܕܟܝܠܦ ܓܘ ܢܗܪܐ ܕܝܗܝ̈ܒܬܐ؛ ܡܐ ܕܡܘܚܡܐ ܝܠܗ ܩܐ ܒܘܨܝܐ ܝܠܗ̇ ܡܥܝܪܢܘܬܐ ܥܠ "ܚܒܠܐ ܕܡܘܕܝܠ" (model rot) – ܥܒܕܐ ܕܡܘܕܝܠ ܟܒܨܪ ܥܡ ܙܒܢܐ "ܒܣ ܡܛܠ ܕܥܠܡܐ ܟܡܫܡܠܐ ܠܡܪܒܐ ܘܡܘܕܝܠ ܟܦܐܫ ܐܝܟ ܕܗܘܐ". ܬܠܝܬܝܐ – instance-based ܠܩܘܒܠ model-based: ܕܝܠܦܚ ܡܢ ܠܒܐ ܘܦܫܛܚ ܠܦܘܬ ܕܡܝܘܬܐ (ܫܒ̈ܒܐ ܩܪ̈ܝܒܐ، nearest neighbors)، ܝܢ ܕܒܢܚ ܡܘܕܝܠ ܕܡܬ̈ܠܐ. ܡܬܠܐ ܕ-Géron ܕ-sociology ܝܠܗ: ܣܒܥܘܬܐ ܡܢ ܚܝ̈ܐ ܠܦܘܬ GDP ܩܐ ܟܠ ܢܦܫܐ (ܝܗܝ̈ܒܬܐ ܕ-OECD ܘܕ-World Bank). ܣܪܛܐ ܬܪܝܨܐ ܟܝܗܒ ܠܩܘܦܪܘܣ 6.30؛ ܬܠܬܐ ܫܒ̈ܒܐ ܩܪ̈ܝܒܐ ܒ-GDP – ܐܝܣܪܐܝܠ (7.2)، ܠܬܘܐܢܝܐ ܘܣܠܘܒܢܝܐ (5.9 ܟܠ ܚܕܐ) – ܟܝܗܒܝ ܒܡܨܥܝܬܐ 6.33. ܬܪܬܝܢ ܐܘܪ̈ܚܬܐ، ܐܦ ܗܘ ܦܘܢܝܐ، ܘܚܕܐ ܡܢܝܗܝܢ ܠܐ ܚܙܠܗ̇ ܠܩܘܦܪܘܣ. ܐܢܐ "ܫܒ̈ܒܐ" ܠܐ ܟܦܝܫܝ ܩܪ̈ܝܒܐ ܐܡܢ ܕܐܝܬ ܣܓܝ ܡܫܬܚܠܦ̈ܢܐ – ܠܘܛܬܐ ܕܡܫܘ̈ܚܬܐ (curse of dimensionality): ܓܘ ܥܣܪܐ ܡܫܘ̈ܚܬܐ، ܩܐ ܕܐܚܕܚ 10% ܡܢ ܝܗܝ̈ܒܬܐ ܓܪܓ ܚܦܚ 80% ܡܢ ܦܬܝܘܬܐ (range) ܕܟܠ ܡܫܬܚܠܦܢܐ، ܗܕܟ ܕܟܠ ܫܒܒܘܬܐ "ܐܬܪܢܝܬܐ" ܒܫܪܪܐ ܣܓܝܐܘܬܐ ܕܓܘܫܡܐ ܝܠܗ̇ (Hastie et al., 2009, pp. 22-23)؛ ܘܡܛܠ ܗܕܐ ܟܠ ܐܘܪܚܐ ܕܟܡܢܣܝܐ ܕܡܦܝܐ function ܕܟܡܫܬܚܠܦܐ ܐܬܪܢܐܝܬ ܓܘ ܫܒܒܘ̈ܬܐ ܙܥܘܪ̈ܬܐ "ܦܝܫܐ ܦܓܥܐ ܒܥܘ̈ܩܢܐ ܓܘ ܡܫܘ̈ܚܬܐ ܪ̈ܡܐ" (ܦܐܬܐ 33). "ܚܘܫ̈ܒܐ ܕܓܐܘܡܛܪܝܐ ܕܝܠܢ، ܕܒܪܝ̈ܐ ܝܢܐ ܓܘ ܚܝ̈ܐ ܓܘ ܓܘܫܡܐ ܕܬܠܬܐ ܡܫܘ̈ܚܬܐ، ܡܨܝܐ ܕܦܝܫܝ ܡܚܝ̈ܐ ܣܓܝ" ܓܘ ܓܘܫ̈ܡܐ ܕܡܫܘ̈ܚܬܐ ܣܓܝ̈ܐܐ – ܓܘ ܟܘܪܐ ܕܥܣܪܝܢ ܡܫܘ̈ܚܬܐ ܡܩܪܒܘܬ ܟܠ ܚܠܐ ܝܬܝܒܐ ܝܠܗ ܓܘ ܩܠܦܬܐ ܩܛܝܢܬܐ ܩܪܝܒ ܠܣܦܬܐ (Bishop, 2006, p. 36). ܩܐ ܒܘܨܝܬܐ ܥܡ ܒܘܨܝܐ ܕܫܘܐ̈ܠܐ ܕ-80 ܦܣܘ̈ܩܐ (items) ܘ-300 ܡܫܬܘܬܦ̈ܢܐ ܐܗܐ ܠܝܠܗ ܡܠܬܐ ܛܟܢܝܩܝܬܐ – ܐܗܐ ܝܠܗ ܥܠܬܐ ܕܡܘܕܝ̈ܠܐ ܟܪ̈ܝܐ ܘ-trees (ܦܣܩܐ 5) ܟܦܠܚܝ ܬܡܢ، ܘܫܒ̈ܒܐ ܩܪ̈ܝܒܐ ܠܐ.

ܡܐ ܕܡܨܝܐ ܕܛܥܐ: ܝܗܝ̈ܒܬܐ ܒܝܫ̈ܬܐ ܘܡܘܕܝܠ ܒܝܫܐ (ibid., "Main Challenges of Machine Learning"). ܝܗܝ̈ܒܬܐ ܩܠܝܠ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ – "ܐܦ ܩܐ ܥܘ̈ܩܢܐ ܦܫܝܛ̈ܐ ܣܓܝ ܟܠܝܘܡ ܣܢܝܩܘܬܐ ܐܝܬ ܠܐܠܦ̈ܐ ܕܡܬ̈ܠܐ"؛ ܡܐܡܪܐ ܝܕܝܥܐ ܕ-Banko ܘ-Brill (2001) ܚܘܝܠܗ ܕܐܠܓܘܪܝ̈ܬܡܐ ܦܪ̈ܝܫܐ ܣܓܝ، ܥܡ ܦܫܝܛ̈ܐ، ܟܡܛܝ ܠܥܒܕܐ ܡܩܪܒܘܬ ܐܦ ܗܘ ܐܡܢ ܕܟܝܗܒܚ ܠܗܘܢ ܝܗܝ̈ܒܬܐ ܡܣܦܩ̈ܢܐ – ܐܢܐ Géron ܓܢܗ ܟܡܬܚܡܐ ܕ"ܛܟ̈ܣܐ ܕܝܗܝ̈ܒܬܐ ܙܥܘܪ̈ܐ ܘܡܨܥܝ̈ܐ ܗܠܝܐ ܣܓܝ ܡܬܚܙܝܢ ܝܢܐ"، ܘܡܛܠ ܗܕܐ "ܠܐ ܫܒܩܝܬܘܢ ܐܠܓܘܪܝ̈ܬܡܐ ܗܠܝܐ". ܝܗܝ̈ܒܬܐ ܕܠܐ ܕܡܝܢ ܠܟܢܫܐ ܟܠܢܝܐ – ܡܬܠܐ ܕܝܠܢ ܝܠܗ: ܒܘܨܝܐ ܕܫܘܐ̈ܠܐ ܕ-Literary Digest ܓܘ 1936، ܡܩܪܒܘܬ ܥܣܪܐ ܡܠܝܘܢ̈ܐ ܕܡܩܒ̈ܠܢܐ، 2.4 ܡܠܝܘܢ̈ܐ ܕܦܘܢ̈ܝܐ، ܡܢܒܝܢܘܬܐ ܕ-57% ܩܐ Landon؛ Roosevelt ܙܟܐ ܒ-62%. ܪܫܝܡ̈ܬܐ (ܡܩܒ̈ܠܢܐ ܕ-telephone، ܗܕ̈ܡܐ ܕ-clubs) ܡܨܠܝ̈ܢܐ ܗܘܝ ܠܥܬܝܪ̈ܐ، ܘܒܨܝܪ ܡܢ ܪܘܒܥܐ ܦܢܝܠܗܘܢ – ܡܣܒ ܒܐܦ̈ܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ (sampling bias) ܘܡܣܒ ܒܐܦ̈ܐ ܕܠܐ ܦܘܢܝܐ (nonresponse bias)، ܒܚܬܝܬܘܬܐ ܒܡ̈ܠܐ ܕܝܘܠܦܢܐ ܕܐܘܪ̈ܚܬܐ ܕܒܘܨܝܐ. ܝܗܝ̈ܒܬܐ ܕܓܢܣܐ ܒܝܫܐ – ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ (outliers)، noise، ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values): "ܣܓܝܐܘܬܐ ܕܡܗܝܪ̈ܐ ܕܝܗܝ̈ܒܬܐ ܟܡܥܒܪܝ ܡܢܬܐ ܪܒܬܐ ܡܢ ܙܒܢܐ ܕܝܗܘܢ" ܓܘ ܡܕܟܝܢܘܬܐ (cleaning). Features ܕܠܐ ܡܘܚ̈ܡܐ – "garbage in, garbage out"؛ feature engineering ܝܠܗ ܓܘܒܝܐ، ܡܦܩܬܐ ܘܟܢܫܐ ܕ-features ܚܕ̈ܬܐ. ܘܡܢ ܓܢܒܐ ܕܡܘܕܝܠ: ܦܐܝܘܬܐ ܝܬܝܪܬܐ – ܡܘܕܝܠ ܡܪܟܒܐ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ ܠܦܘܬ ܟܡܝܘܬܐ ܕܝܗܝ̈ܒܬܐ ܘ-noise ܕܐܝܬ ܓܘܝܗܝܢ، ܕܟܦܪܫ ܛܘ̈ܦܣܐ ܓܘ noise ܓܢܗ؛ ܡܬܠܐ: ܓܘ ܝܗܝ̈ܒܬܐ ܕܝܘܠܦܢܐ، ܟܠ ܡܬ̈ܘܬܐ ܕܐܝܬ w ܓܘ ܫܡܐ ܕܝܗܝܢ ܐܝܬ ܠܗܝܢ ܣܒܥܘܬܐ ܠܥܠ ܡܢ 7 – New Zealand (7.3)، Norway (7.6)، Sweden (7.3) ܘ-Switzerland (7.5) – "ܟܡܐ ܫܪܝܪ̈ܐ ܝܬܘܢ ܕܢܡܘܣܐ ܕ-w ܟܦܫܛ ܠ-Rwanda ܝܢ ܠ-Zimbabwe؟" ܫܪ̈ܝܐ: ܡܘܕܝܠ ܦܫܝܛܐ ܒܝܫ، ܝܬܝܪ ܝܗܝ̈ܒܬܐ، ܒܨܝܪ noise – ܘregularization: ܟܪܝܘܬܐ ܕܡܘܕܝܠ، ܡܬܠܐ ܐܠܨܐ ܕܡܨܠܝܢܘܬܐ (slope) ܦܝܫܐ ܙܥܘܪܬܐ، ܕܟܡܬܡܠܟܐ ܒܝܕ hyperparameter. Bishop ܟܡܚܘܐ ܐܦ ܗܝ ܡܠܬܐ ܓܘ polynomial: ܕܕܪܓܐ 9 ܥܠ ܥܣܪ ܢܘܩ̈ܙܐ ܟܥܒܪ ܒܚܬܝܬܘܬܐ ܒܝܕ ܟܠܗܝܢ، ܥܡ ܛܥܝܘܬܐ ܕܝܘܠܦܢܐ ܨܦܪܐ، "ܐܢܐ ܣܪܛܐ ܟܦܝܦܐ ܟܡܬܬܙܝܥ ܒܚܝܠܬܢܘܬܐ" – "ܘܐܗܐ ܬܘܪܨܐ ܝܕܝܥܐ ܝܠܗ ܐܝܟ ܦܐܝܘܬܐ ܝܬܝܪܬܐ" (ܦܐܬܐ 6)؛ "ܩܐ ܡܪܟܒܘܬܐ ܝܕܝܥܬܐ ܕܡܘܕܝܠ، ܥܘܩܢܐ ܕܦܐܝܘܬܐ ܝܬܝܪܬܐ ܟܗܘܝܐ ܒܨܝܪ ܩܫܝܐ ܐܡܢ ܕܛܟܣܐ ܕܝܗܝ̈ܒܬܐ ܟܪܒܐ"، ܘܢܡܘܣܐ ܕܨܒܥܐ ܓܫܝܡܐ ܕܟܡܝܬܐ – ܘܟܡܬܚܡܐ ܡܢܗ – ܝܠܗ ܕܡܢܝܢܐ ܕܚܙ̈ܝܬܐ (observations) ܠܐ ܦܝܫܐ ܒܨܝܪ ܡܢ 5 ܗܠ 10 ܓܐܝ̈ܐ ܡܢܝܢܐ ܕܦܪܡܝ̈ܛܪܐ ܕܡܬܛܟܣ̈ܢܐ ܕܡܘܕܝܠ (ܦܐܬܐ 9). ܥܢܫܐ ܥܠ ܪܒܘܬܐ ܕܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܟܡܬܩܪܐ ܓܘ ܣܛܐܛܝܣܛܝܩܐ "shrinkage methods"، ܗܘܝܐ ܕܡܪ̈ܒܥܐ – ridge regression، ܘܓܘ neural networks – "weight decay" (ܦܐܬܐ 10): ܬܠܬܐ ܫܡ̈ܗܐ ܩܐ ܚܕ ܚܘܫܒܐ. ܘܡܐ ܕ-Bishop ܟܡܘܣܦ ܐܝܟ ܡܐܡܪܐ ܫܬܐܣܝܐ: ܦܐܝܘܬܐ ܝܬܝܪܬܐ ܝܠܗ̇ "ܕܝܠܢܝܘܬܐ ܓܘܢܝܬܐ ܕ-maximum likelihood"، ܘܓܘ ܐܘܪܚܐ Bayesian – ܕܓܘܗ̇ "ܡܢܝܢܐ ܥܒܕܢܝܐ ܕܦܪܡܝ̈ܛܪܐ ܟܡܬܛܟܣ ܡܢ ܓܢܗ ܠܪܒܘܬܐ ܕܛܟܣܐ ܕܝܗܝ̈ܒܬܐ" – ܡܨܝܚ ܦܪܩܚ ܡܢܗ̇ ܐܦ ܓܘ ܡܘܕܝܠ ܕܡܢܝܢܐ ܕܦܪܡܝ̈ܛܪܐ ܕܝܠܗ ܣܓܝ ܝܬܝܪ ܝܠܗ ܡܢ ܡܢܝܢܐ ܕܚܙ̈ܝܬܐ (ܦܐܬܐ 9). ܘܐܦ ܗܘ ܫܘܐܠܐ – ܟܡܐ ܚܙ̈ܝܬܐ ܣܢܝܩܘܬܐ ܐܝܬ – ܦܘܪܫܐ ܕܛܘ̈ܦܣܐ ܟܫܐܠ ܡܢ ܓܢܒܐ ܕ-features: "ܒܥܩܬܐ، ܠܝܬ ܦܘܢܝܐ ܓܘܢܝܐ"، ܐܢܐ ܐܝܬ ܬܘܪܨܐ ܝܕܝܥܐ – ܬܘܪܨܐ ܕ-Hughes (Hughes phenomenon): ܐܝܡܢ ܕܡܢܝܢܐ ܕ-features d ܙܥܘܪܐ ܝܠܗ ܠܦܘܬ ܡܢܝܢܐ ܕܚܙ̈ܝܬܐ n، ܡܘܣܦܬܐ ܕ-feature ܟܡܫܦܪܐ ܠܦܘܪܫܐ ܠܓܢ̈ܣܐ؛ ܐܡܢ ܕ-d ܟܪܒܐ ܡܣܦܩ ܠܦܘܬ n، "ܫܪܝܪܘܬܐ ܣܛܐܛܝܣܛܝܩܝܬܐ ܟܢܚܬܐ، ܘܠܩܘܒܠ ܣܒܪܐ، ܥܒܕܐ ܕܦܘܪܫܐ ܠܓܢ̈ܣܐ ܟܒܨܪ" – ܥܠܬܐ ܝܠܗ̇ "ܡܘܣܦܬܐ ܕ-features ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ، ܥܡ ܛܥܝܘܬܐ ܕܡܢܝܢܐ ܕܚܙ̈ܝܬܐ ܕܝܘܠܦܢܐ ܬܚܘܡܐ ܝܠܗ" (Ishii et al., 2026, pp. 84, 86-87). ܩܐ ܒܘܨܝܬܐ: ܦܣܘܩܐ (item) ܐܚܪܢܐ ܓܘ ܣܒܠܬܐ (scale) ܠܐ ܟܠܝܘܡ ܝܠܗ ܝܕܥܬܐ ܐܚܪܬܐ ܩܐ ܡܘܕܝܠ. ܘܦܐܝܘܬܐ ܒܨܝܪܬܐ – ܡܘܕܝܠ ܦܫܝܛܐ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ ܩܐ ܒܢܝܢܐ ܕܝܗܝ̈ܒܬܐ (ܣܪܛܐ ܬܪܝܨܐ ܩܐ ܣܒܥܘܬܐ ܡܢ ܚܝ̈ܐ)، ܕܟܦܐܫ ܡܚܝܐ ܐܦ ܥܠ ܝܗܝ̈ܒܬܐ ܕܝܘܠܦܢܐ. ܒܚܪܬܐ، ܢܡܘܣܐ "No Free Lunch" (Wolpert, 1996, as cited in Géron, Chapter 1): ܐܝܢܐ ܕܠܐ ܟܣܐܡ ܡܕܡ ܥܠ ܝܗܝ̈ܒܬܐ ܠܝܬ ܠܗ ܥܠܬܐ ܕܓܒܐ ܡܘܕܝܠ ܚܕ ܡܢ ܐܚܪܢܐ؛ ܩܐ ܟܠ ܓܘܒܝܐ ܕܡܘܕܝܠ ܐܝܬ ܣܝܡܬܐ ܟܣܝܬܐ (ܣܪܛܐ ܬܪܝܨܐ = "ܪܘܚܩܐ ܡܢ ܣܪܛܐ noise ܝܠܗ")، ܘܐܘܪܚܐ ܝܚܝܕܝܬܐ ܕܝܕܥܚ ܡܢܝܐ ܛܒܐ ܝܠܗ ܒܝܫ ܝܠܗ̇ ܕܦܚܡܚ – ܥܠ ܝܗܝ̈ܒܬܐ ܕܠܐ ܡܘܦܠܚ̈ܐ ܝܢܐ ܩܐ ܝܘܠܦܢܐ.

3. ܦܪܘܝܩܬ ܡܢ ܪܫܐ ܗܠ ܚܪܬܐ: ܬܡܢܝܐ ܦܣܥ̈ܬܐ

ܨܚܚܐ 2 ܕ-Géron ܚܕ ܦܪܘܝܩܬ ܓܡܝܪܐ ܝܠܗ – ܡܢܒܝܢܘܬܐ ܕܛܝܡܐ ܡܨܥܝܐ (median) ܕܒܝܬܐ ܓܘ 20,640 ܦܢܝ̈ܬܐ ܕܡܟܬܒܬ ܥܡܐ (census) ܓܘ California (census ܕ-1990) – ܘܬܘܣܦܬܐ ܐ ܕܟܬܒܐ ܟܥܒܕܐ ܠܗ ܪܫܝܡܬܐ ܕܒܘܚܪܢܐ ܕܬܡܢܝܐ ܦܣܥ̈ܬܐ: ܬܚܘܡܐ ܕܥܘܩܢܐ، ܫܩܠܬܐ ܕܝܗܝ̈ܒܬܐ، ܒܘܨܝܐ ܕܝܗܝ̈ܒܬܐ، ܡܛܝܒܘܬܐ ܕܝܗܝ̈ܒܬܐ، ܪܫܝܡܬܐ ܩܨܝܪܬܐ ܕܡܘܕܝ̈ܠܐ ܕܐܝܬ ܠܗܘܢ ܣܒܪܐ، fine-tuning، ܡܚܘܝܢܘܬܐ ܕܫܪܝܐ، ܘܡܫܪܝܬܐ ܘܢܛܪܬܐ (Géron, 2022، ܬܘܣܦܬܐ ܐ). ܡܐ ܕܟܦܪܫ ܐܗܐ ܨܢܘܪܐ (pipeline) ܡܢ ܦܘܫܩܐ ܣܛܐܛܝܣܛܝܩܝܐ ܥܡܝܐ ܠܝܠܗ ܐܠܓܘܪܝܬܡ ܐܠܐ ܐܪܒܥܐ ܦܣ̈ܩܐ ܕܟܡܬܥܒܕܝ ܩܕܡ ܕܚܙܝܚ ܠܝܗܝ̈ܒܬܐ.

ܐ. ܬܚܘܡܐ: ܡܘܢܐ ܝܠܗ ܢܝܫܐ، ܡܘܢܐ ܝܠܗ ܡܚܘܝܢܐ، ܡܐ ܐܝܬ ܐܕܝܘܡ. ܫܘܐܠܐ ܩܕܡܝܐ ܝܠܗ ܡܘܢܐ ܝܠܗ ܢܝܫܐ – "ܒܢܝܢܐ ܕܡܘܕܝܠ ܡܨܝܐ ܕܗܘܝܐ ܠܐ ܝܠܗ ܢܝܫܐ ܐܚܪܝܐ" – ܡܛܠ ܕܐܗܘ ܟܦܣܩ ܠܬܚܘܡܐ (ܥܡ ܡܕܒܪܢܐ؟ ܪܝܓܪܫܢ؟ batch؟)، ܠܐܠܓܘܪܝܬܡ ܘܠܡܚܘܝܢܐ ܕܥܒܕܐ؛ ܬܪܝܢܐ ܝܠܗ ܡܘܢܐ ܝܠܗ ܫܪܝܐ ܕܗܫܐ – ܓܘ ܡܬܠܐ، ܡܗܝܪ̈ܐ ܕܟܫܥܪܝ ܒܐܝܕܐ ܘܛܥܝܝ "ܝܬܝܪ ܡܢ 30%": ܐܗܐ ܝܠܗ ܣܪܛܐ ܕ-baseline ܕܡܘܕܝܠ ܓܪܓ ܥܒܪ ܡܢܗ. ܘܒܬܪܗ ܟܒܚܪܚ ܣܝ̈ܡܬܐ: ܐܢ ܛܟܣܐ ܕܦܝܫܐ ܫܩܠܐ ܠܡܢܒܝܢܘܬܐ ܟܡܫܚܠܦ ܛܝ̈ܡܐ ܠܓܢ̈ܣܐ ("ܙܘܠ / ܡܨܥܝܐ / ܝܩܝܪ")، ܥܘܩܢܐ ܦܘܪܫܐ ܠܓܢ̈ܣܐ ܝܠܗ ܘܠܐ ܪܝܓܪܫܢ – "ܠܐ ܦܝܫܐ ܨܒܝܬܘܢ ܕܝܕܥܝܬܘܢ ܐܗܐ ܒܬܪ ܝܪ̈ܚܐ ܕܥܒܕܐ ܥܠ ܛܟܣܐ ܕܪܝܓܪܫܢ" (Chapter 2, "Frame the Problem", "Check the Assumptions"). ܡܚܘܝܢܐ ܕܥܒܕܐ ܟܡܬܓܒܐ ܗܫܐ، ܠܐ ܒܚܪܬܐ: ܩܐ ܪܝܓܪܫܢ – RMSE، ܕܟܡܥܢܫ ܛܥܝ̈ܘܬܐ ܪ̈ܒܐ، ܝܢ MAE ܐܡܢ ܕܐܝܬ ܣܓܝ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ؛ ܩܐ ܦܘܪܫܐ ܠܓܢ̈ܣܐ – ܠܦܘܬ ܛܝܡܐ ܕܛܥܝܘܬܐ (ܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ، ܦܣܩܐ 1 ܘܠܘܚܐ 1 ܬܡܢ).

ܒ. ܓܘܕܐ ܕܒܘܚܪܢܐ – ܩܕܡ ܒܘܨܝܐ ܕܝܗܝ̈ܒܬܐ، ܠܐ ܒܬܪܗ. "ܡܨܝܐ ܕܡܬܚܙܐ ܢܘܟܪܝܐ ܕܡܢܛܪܚ ܠܓܢܒ ܡܢܬܐ ܡܢ ܝܗܝ̈ܒܬܐ ܓܘ ܐܗܐ ܕܪܓܐ"، ܟܟܬܒ Géron، ܐܢܐ "ܡܘܚܐ ܕܝܘܟܘܢ ܛܟܣܐ ܬܡܝܗܐ ܝܠܗ ܩܐ ܦܘܪܫܐ ܕܛܘ̈ܦܣܐ، ܘܐܗܐ ܐܦ ܟܡܥܢܐ ܕܣܓܝ ܡܨܠܝܢܐ ܝܠܗ ܠܦܐܝܘܬܐ ܝܬܝܪܬܐ" – ܡܣܒ ܒܐܦ̈ܐ ܕܚܝܪܬܐ ܡܢ ܩܕܡ (data snooping bias; Chapter 2, "Create a Test Set"). ܡܩܪܒܘܬ 20% ܩܐ ܒܘܚܪܢܐ، ܒܦܘܠܓܐ ܩܝܡܐ ܘ-stratified؛ ܦܪ̈ܝܫܘܝܬܐ – ܩܐ ܡܘܕܝ ܬܠܬܐ ܓܘ̈ܕܐ ܘܠܐ ܬܪܝܢ، ܘܠܦܘܬ ܐܝܢܐ ܚܕܝܘܬܐ ܟܦܠܓܚ – ܓܘ ܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ، ܦܣܩ̈ܐ 2 ܘ-6.

ܓ. ܒܘܨܝܐ ܘܡܛܝܒܘܬܐ – ܥܠ ܓܘܕܐ ܕܝܘܠܦܢܐ ܒܣ، ܘܒ-functions. ܒܘܨܝܐ ܝܕܝܥܐ ܝܠܗ: ܦܘ̈ܠܓܐ (distributions)، ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܕ-Pearson ܥܡ ܢܝܫܐ (ܓܘ ܡܬܠܐ، ܡܥܠܬܐ ܡܨܥܝܬܐ (median) ܐܣܝܪܬܐ ܝܠܗ̇ 0.69 ܥܡ ܛܝܡܐ ܕܒܝܬܐ)، ܨܘܪ̈ܬܐ ܕܒܕܪܐ، ܘܚܘ̈ܠܛܐ ܕ-features (ܐܘܬܩ̈ܐ ܩܐ ܟܠ ܒܝܬܐ ܒܕܘܟܬܐ ܕܓܘܡܪܐ ܕܐܘܬܩ̈ܐ). ܡܛܝܒܘܬܐ – ܒܪܡܙܐ، ܠܐ ܒܐܝܕܐ، ܡܛܠ ܐܪܒܥܐ ܥܠ̈ܠܬܐ: ܥܒܕܐ ܡܢ ܪܝܫ ܥܠ ܝܗܝ̈ܒܬܐ ܚܕ̈ܬܬܐ، ܡܦܠܚܢܘܬܐ ܡܢ ܪܝܫ ܓܘ ܦܪܘܝ̈ܩܛܐ ܕܐܬܝܢ، ܪܗܛܐ ܓܘ ܛܟܣܐ ܚܝܐ، ܘܢܣܝܘܢܐ ܦܫܝܩܐ ܕܚܠܦ̈ܬܐ (Chapter 2, "Prepare the Data"). ܬܠܬܐ ܦܣܥ̈ܬܐ: ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ – ܫܩܠܬܐ ܕܣܕܪ̈ܐ، ܫܩܠܬܐ ܕܡܫܬܚܠܦܢܐ، ܝܢ ܡܠܝܐ (impute) ܕܛܝܡܐ – ܛܝܡܐ ܡܨܥܝܐ، ܡܨܥܝܬܐ، ܛܝܡܐ ܕܣܓܝ ܡܬܚܙܐ – ܘܢܡܘܣܐ ܕܟܦܪܫ ܝܘܠܦܢܐ ܕܡܟܝܢܐ ܡܢ ܥܝܕ̈ܐ ܕ-SPSS: ܛܝܡܐ ܡܨܥܝܐ ܟܚܫܒܚ ܠܗ ܥܠ ܓܘܕܐ ܕܝܘܠܦܢܐ ܘܟܢܛܪܚ ܠܗ، ܩܐ ܕܡܦܠܚܚ ܠܗ ܥܠ ܓܘܕܐ ܕܫܘܪܪܐ، ܥܠ ܓܘܕܐ ܕܒܘܚܪܢܐ ܘܥܠ ܟܠ ܝܗܒܬܐ ܚܕܬܐ؛ ܡܫܬܚܠܦ̈ܢܐ ܕܓܢ̈ܣܐ (categorical) – ܪܡܙܢܘܬܐ one-hot (one-hot، ܡܫܬܚܠܦ̈ܢܐ dummy)؛ ܘscaling – "ܠܒܪ ܡܢ ܚܕܟܡܐ ܓܢ̈ܣܐ ܙܥܘܪ̈ܐ، ܐܠܓܘܪܝ̈ܬܡܐ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ ܠܐ ܟܦܠܚܝ ܛܒ ܐܡܢ ܕ-features ܡܢܝܢܝ̈ܐ ܐܝܬ ܠܗܘܢ ܡܫܘ̈ܚܬܐ ܦܪ̈ܝܫܐ ܣܓܝ" (ܓܘܡܪܐ ܕܐܘܬܩ̈ܐ ܡܢ 6 ܗܠ 39,320، ܡܥܠܬܐ ܡܢ 0 ܗܠ 15): min-max ܠܦܬܝܘܬܐ 0-1، ܝܢ standardization (ܡܨܥܝܬܐ 0، ܣܛܝܘܬܐ ܬܩܝܢܬܐ (SD) 1)، ܕܒܨܝܪ ܪܓܝܫܐ ܝܠܗ̇ ܠܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ. ܘܙܘܗܪܐ، ܒܐܬ̈ܘܬܐ ܕ-Géron: "ܡܢ ܡܬܘܡ ܠܐ ܦܠܚܝܬܘܢ ܒ-fit() ܝܢ ܒ-fit_transform() ܩܐ ܚܕ ܡܕܡ ܠܒܪ ܡܢ ܓܘܕܐ ܕܝܘܠܦܢܐ" (Chapter 2, "Feature Scaling and Transformation") – ܦܣܩܐ 4 ܟܡܦܫܩ ܩܐ ܡܘܕܝ ܐܗܐ ܠܝܠܗ ܙܥܘܪܘܬ ܢܦܫܐ. decision trees ܝܢܐ ܦܪܝܫܘܬܐ ܦܫܝܩܬܐ: ܠܐ ܣܢܝܩܝ ܠ-scaling ܡܢ ܟܠ (ܨܚܚܐ 6).

ܕ. ܝܘܠܦܢܐ، ܦܘܚܡܐ – ܒ-k folds – ܘ-tuning. ܪܝܓܪܫܢ ܣܪܛܢܝܐ ܥܠ ܝܗܝ̈ܒܬܐ ܕܝܘܠܦܢܐ ܟܝܗܒ RMSE ܕܡܩܪܒܘܬ 68,600 dollars ܐܡܢ ܕܣܓܝܐܘܬܐ ܕܛܝ̈ܡܐ ܒܝܢܝ 120 ܘ-265 ܐܠܦ̈ܐ ܝܢܐ – ܦܐܝܘܬܐ ܒܨܝܪܬܐ (underfitting). decision tree ܟܝܗܒ RMSE ܕ-0.0 – "ܟܘܪ، ܡܐ!؟ ܕܠܐ ܛܥܝܘܬܐ ܡܢ ܟܠ؟" – ܦܐܝܘܬܐ ܝܬܝܪܬܐ ܓܡܝܪܬܐ، ܕܠܐ ܡܨܝܐ ܕܚܙܝܚ ܠܗ̇ ܕܠܐ ܝܗܝ̈ܒܬܐ ܕܡܘܕܝܠ ܠܐ ܚܙܐ ܠܗܝܢ. ܡܐܢܐ ܝܠܗ ܫܘܪܪܐ ܡܚܠܦܢܐ (k-fold cross-validation): ܟܦܠܓܚ ܠܓܘܕܐ ܕܝܘܠܦܢܐ ܠ-10 folds، ܟܡܠܦܚ 10 ܓܐܝ̈ܐ ܥܠ 9 ܘܟܒܚܪܚ ܥܠ ܥܣܝܪܝܐ، ܘܟܫܩܠܚ ܠܐ ܒܣ ܫܘܥܪܐ ܐܠܐ ܐܦ ܚܬܝܬܘܬܐ ܕܝܠܗ – ܡܨܥܝܬܐ ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ. tree ܟܢܚܬ ܠ-66,868 (±2,061)، ܡܩܪܒܘܬ ܐܝܟ ܪܝܓܪܫܢ (69,858 ±4,182)؛ random forest ܟܝܗܒ 47,019 (±1,034) – ܐܢܐ ܥܠ ܓܘܕܐ ܕܝܘܠܦܢܐ ܓܢܗ ܡܩܪܒܘܬ 17,474، ܝܢܝ ܗܠܝܐ ܐܝܬ ܦܐܝܘܬܐ ܝܬܝܪܬܐ ܓܠܝܬܐ (Chapter 2, "Better Evaluation Using Cross-Validation"). ܟܡܐ folds، ܢܡܘܣܐ ܕ-one standard error، ܘܡܐ ܟܥܒܕܚ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ – ܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ، ܦܣܩܐ 3. ܦܘܩܕܢܐ: ܕܢܣܚ ܡܘܕܝ̈ܠܐ ܡܢ ܚܕܟܡܐ ܫܪ̈ܒܬܐ ܕܠܐ tuning، ܕܩܨܪܚ ܠ-2-5 ܕܐܝܬ ܠܗܘܢ ܣܒܪܐ – ܘܒܬܪܗ ܒܣ ܕܥܒܕܚ tuning ܕ-hyperparameters، ܒ-grid search (ܟܠ ܚܘ̈ܠܛܐ) ܝܢ، ܐܡܢ ܕܓܘܫܡܐ ܕܚܘ̈ܠܛܐ ܪܒܐ ܝܠܗ، ܒ-random search (ܡܢܝܢܐ ܩܝܡܐ ܕܚܘ̈ܠܛܐ؛ ܬܘܣܦܬܐ ܐ: ܛܒܐ ܝܠܗ random ܐܠܐ ܐܢ ܐܝܬ ܩܠܝܠ ܛܝ̈ܡܐ). ܒܬܪ tuning ܟܚܙܝܚ ܓܘ ܡܘܕܝܠ: random forest ܟܬܢܐ feature importance – ܓܘ ܡܬܠܐ، ܡܥܠܬܐ ܡܨܥܝܬܐ ܩܕܡܝܬܐ ܝܠܗ̇ (0.19) – ܘܟܦܫܩܚ ܠܛܥܝ̈ܘܬܐ؛ ܘ-Géron ܟܡܘܣܦ ܣܢܝܩܘܬܐ ܕܟܠ ܒܘܨܝܐ ܟܢܫܝܐ ܦܝܫܐ ܡܢܟܪ ܠܗ̇: ܕܫܪܪܚ ܕܡܘܕܝܠ ܟܦܠܚ ܠܐ ܒܣ ܒܡܨܥܝܬܐ ܐܠܐ "ܥܠ ܟܠ ܓܢ̈ܣܐ ܕܦܢܝ̈ܬܐ، ܕܩܘܪ̈ܝܐ ܝܢ ܕܡܕܝ̈ܢܬܐ، ܥܬܝܪ̈ܐ ܝܢ ܡܣܟܢ̈ܐ، ܕܓܪܒܝܐ ܝܢ ܕܬܝܡܢܐ، ܙܥܘܪܘܬܐ ܝܢ ܠܐ" – ܘܐܢ ܟܦܐܫ ܡܚܝܐ ܥܠ ܓܢܣܐ ܓܡܝܪܐ، ܠܐ ܦܪܣܚ ܠܗ ܩܐ ܐܗܝ، "ܡܛܠ ܕܡܨܝܐ ܕܡܚܒܠ ܝܬܝܪ ܡܢ ܕܡܘܬܪ" (Chapter 2, "Analyzing the Best Models and Their Errors").

ܗ. ܓܘܕܐ ܕܒܘܚܪܢܐ – ܚܕ ܓܐܝܐ، ܘܒܬܪܗ ܠܐ ܟܡܩܪܒܚ. ܡܘܕܝܠ ܐܚܪܝܐ ܟܡܬܡܫܚ ܥܠ ܓܘܕܐ ܕܒܘܚܪܢܐ ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval)، ܘܒܬܪܗ: "ܓܪܓ ܩܝܡܝܬܘܢ ܠܩܘܒܠ ܢܣܝܘܢܐ ܕ-tuning ܕ-hyperparameters ܩܐ ܕܡܢܝ̈ܢܐ ܡܬܚܙܝ ܛܒ̈ܐ ܥܠ ܓܘܕܐ ܕܒܘܚܪܢܐ؛ ܫܘܦܪ̈ܐ ܠܐ ܡܣܟܝ ܝܢܐ ܕܦܫܛܝ ܠܝܗܝ̈ܒܬܐ ܚܕ̈ܬܬܐ" (Chapter 2, "Evaluate Your System on the Test Set"). ܡܚܘܝܢܘܬܐ – ܡܐ ܝܠܦܠܢ، ܡܐ ܦܠܚܠܗ ܘܡܐ ܠܐ، ܐܝܢܝ ܣܝ̈ܡܬܐ، ܡܘܢܐ ܝܢܐ ܟܪ̈ܝܘܝܬܐ؛ ܘܓܘ ܡܬܠܐ، ܒܫܪܝܪܘܬܐ: ܛܟܣܐ "ܠܐ ܝܠܗ ܛܒܐ ܣܓܝ ܝܬܝܪ" ܡܢ ܡܗܝܪ̈ܐ ܕܛܥܝܠܗܘܢ ܒ-30%. ܬܪܬܝܢ ܦܣܥ̈ܬܐ ܐܚܪ̈ܝܬܐ – ܡܫܪܝܬܐ، ܢܛܪܬܐ ܘܝܘܠܦܢܐ ܡܢ ܪܝܫ – ܕܛܟ̈ܣܐ ܚܝ̈ܐ ܝܢܐ؛ ܩܐ ܒܘܨܝܐ ܟܦܝܫܐ ܡܢܝܗܝܢ ܒܣ ܡܥܝܪܢܘܬܐ ܥܠ ܚܒܠܐ ܕܡܘܕܝܠ: ܡܘܕܝܠ ܐܣܝܪܐ ܝܠܗ ܥܡ ܝܗܝ̈ܒܬܐ ܕܙܒܢܗ.

4. ܕܟܝ ܝܕܥܚ ܕܡܘܕܝܠ ܛܒܐ ܝܠܗ – ܒܩܘܪܒܐ

ܓܡܝܪܐ – ܓܘ ܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ؛ ܐܟܐ ܐܪܒܥܐ ܣܕܪ̈ܐ ܕܟܠ ܫܪܟܐ ܟܣܡܟ ܥܠܝܗܝ. ܡܚܘܝܢܐ ܠܦܘܬ ܛܝܡܐ ܕܛܥܝܘܬܐ: ܚܬܝܬܘܬܐ ܟܠܢܝܬܐ (accuracy) ܟܡܛܥܝܐ ܓܘ ܓܢܣܐ ܙܥܘܪܐ – classifier dummy ܕܟܐܡܪ "ܠܐ" ܥܠ ܟܠ ܡܕܡ ܟܫܩܠ 90% ܐܡܢ ܕܚܕ ܡܢ ܥܣܪܐ ܡܢ ܚܙ̈ܝܬܐ ܕܙܘܕܐ ܝܢܐ، "ܟܙܟܐ ܠ-Nostradamus" (Géron, 2022, Chapter 3)؛ ܟܬܢܚ confusion matrix، precision ܘܪܓܝܫܘܬܐ (sensitivity)، ܘܬܚܘܡܐ ܕܦܘܪܫܐ (cutoff). ܝܗܝ̈ܒܬܐ ܕܡܘܕܝܠ ܠܐ ܚܙܐ ܠܗܝܢ: ܛܥܝܘܬܐ ܕܝܘܠܦܢܐ ܟܢܚܬܐ ܗܠ ܨܦܪܐ ܥܡ ܡܪܟܒܘܬܐ، "ܐܢܐ ܡܘܕܝܠ ܥܡ ܛܥܝܘܬܐ ܕܝܘܠܦܢܐ ܨܦܪܐ ܦܐܝܐ ܝܠܗ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ ܠܝܗܝ̈ܒܬܐ ܕܝܘܠܦܢܐ ܘܟܠܝܘܡ ܦܝܫܐ ܦܫܛ ܒܝܫܐܝܬ" (Hastie et al., 2009, pp. 220-221) – ܘܡܛܠ ܗܕܐ ܝܘܠܦܢܐ، ܫܘܪܪܐ ܘܒܘܚܪܢܐ، ܘܫܘܪܪܐ ܡܚܠܦܢܐ ܕܟܝܗܒ ܡܨܥܝܬܐ ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ. ܡܣܒ ܒܐܦ̈ܐ (bias) ܘܫܘܚܠܦܐ (variance): ܛܥܝܘܬܐ ܕܦܘܫܛܐ = ܡܣܒ ܒܐܦ̈ܐ² + ܫܘܚܠܦܐ + noise؛ ܡܪܟܒܘܬܐ ܟܡܒܨܪܐ ܠܡܣܒ ܒܐܦ̈ܐ ܘܟܡܪܒܝܐ ܠܫܘܚܠܦܐ – "ܘܡܛܠ ܗܕܐ ܟܡܬܩܪܐ trade-off" (Géron, Chapter 4). ܡܪܕܝܬܐ ܘܬܚܘܡܐ: Kapoor ܘ-Narayanan ܡܫܟܚܠܗܘܢ ܡܪܕܝܬܐ ܕܝܗܝ̈ܒܬܐ (data leakage) ܓܘ 294 ܡܐܡܪ̈ܐ ܓܘ 17 ܚܩ̈ܠܐ، ܘܓܘ ܡܢܒܝܢܘܬܐ ܕܩܪ̈ܒܐ ܕܡܕܝܢ̈ܝܐ، "ܐܡܢ ܕܛܥܝ̈ܘܬܐ ܡܬܘܪܨ̈ܐ ܗܘܝ، ܡܘܕܝ̈ܠܐ ܡܪܟܒ̈ܐ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ ܠܐ ܟܦܠܚܝ ܛܒ ܒܝܫ ܡܢ ܥܩܪܐ ܡܢ ܡܘܕܝ̈ܠܐ LR ܕܥܣܪ̈ܐ ܕܫܢ̈ܐ" (Kapoor & Narayanan, 2023, Section Summary)؛ ܘܠܥܠ ܡܢ ܟܠ ܝܬܝܒܐ ܝܠܗ̇ Bayes error – "ܛܥܝܘܬܐ ܕܠܐ ܡܨܝܐ ܕܦܪܩܚ ܡܢܗ̇" ܕܛܟܣܐ ܕ-features (Ishii et al., 2026, p. 101)، ܬܚܘܡܐ ܕ-160 ܓܘ̈ܕܐ ܕ-Salganik ܘܚܒܪ̈ܘܗܝ ܦܓܥܠܗܘܢ ܒܝܗ ܓܘ R² = 0.2. ܦܐܪܐ ܪܡܐ ܣܓܝ ܡܢ ܣܪܛܐ ܕ-baseline ܘܡܢ ܣܦܪܝܘܬܐ ܐܬܐ ܝܠܗ ܕܡܪܕܝܬܐ ܩܕܡ ܕܗܘܝܐ ܐܬܐ ܕܬܒܪܬܐ ܕܐܘܪܚܐ.

5. ܡܘܕܝ̈ܠܐ: ܡܢ ܣܪܛܐ ܬܪܝܨܐ ܠ-random forest

Géron ܟܡܫܠܡ ܠܦܪܘܝܩܬ ܕܡܬܠܐ ܒܡܠܟܐ ܕ"ܡܨܝܐ ܕܗܘܝܐ ܛܒܐ ܝܠܗ ܕܪܓܫܝܬܘܢ ܒܦܫܝܩܘܬܐ ܥܡ ܐܘܪܚܐ ܟܠܢܝܬܐ ܘܝܕܥܝܬܘܢ ܛܒ ܬܠܬܐ-ܐܪܒܥܐ ܐܠܓܘܪܝ̈ܬܡܐ، ܝܬܝܪ ܡܢ ܕܡܥܒܪܝܬܘܢ ܟܠܗ ܙܒܢܐ ܒܒܘܨܝܐ ܕܐܠܓܘܪܝ̈ܬܡܐ ܡܬܩܕ̈ܡܐ" (Chapter 2, "Try It Out!"). ܠܘܚܐ 1 ܟܡܛܟܣ ܠܫܪ̈ܒܬܐ ܕܛܒܐ ܝܠܗ ܕܡܢܟܪܚ ܠܗܝܢ، ܘܡܐ ܕܐܝܬ ܩܕܡܗ ܟܡܦܫܩ ܬܠܬܐ ܡܘܚ̈ܡܐ ܡܢ ܟܠ ܩܐ ܒܘܨܝܐ ܟܢܫܝܐ – ܪܝܓܪ̈ܫܢܐ ܕܐܝܬ ܠܗ ܡܢ ܩܕܡ، tree، ܘ-forest.

ܪܝܓܪ̈ܫܢܐ – ܐܦ ܐܢܝ ܢܘ̈ܣܚܐ، ܚܕܐ ܬܘܣܦܬܐ. ܪܝܓܪܫܢ ܣܪܛܢܝܐ ܘܠܘܓܝܣܛܝܩܝܐ ܓܘ Géron (ܨܚܚܐ 4) ܒܚܬܝܬܘܬܐ ܐܝܟ ܕܐܝܬܝܗܘܢ ܓܘ ܦܐܬܐ ܕܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܕܣܐܝܛ ܝܢܐ – ܓܘܡܪܐ ܕܡܬܩܠܢܘܬܐ (weighting) ܕ-features، ܘܓܘ ܠܘܓܝܣܛܝܩܝܐ – logistic ܕܝܠܗ ܐܝܟ ܡܣܬܒܪܢܘܬܐ (probability)، ܘܬܚܘܡܐ ܕܦܘܪܫܐ (ܟܠܝܘܡ 50%) ܕܟܥܒܕܐ ܠܗ̇ classifier؛ ܪܘܚܬܐ ܠܚܕܟܡܐ ܓܢ̈ܣܐ ܝܠܗ̇ softmax regression. ܡܐ ܕܟܬܒܐ ܟܡܘܣܦ ܝܠܗ regularization: ridge regression (ridge؛ ܥܢܫܐ ܥܠ ܓܘܡܪܐ ܕܡܪ̈ܒܥܐ ܕܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ – ܟܡܒܨܪ ܠܗܘܢ)، lasso (lasso؛ ܥܢܫܐ ܥܠ ܓܘܡܪܐ ܕܛܝ̈ܡܐ ܓܡܝܪ̈ܐ ܕܝܗܘܢ – ܟܥܒܕ ܚܕܟܡܐ ܡܢܝܗܘܢ ܨܦܪܐ، ܝܢܝ ܟܓܒܐ features)، elastic net (ܚܘܠܛܐ)، ܘ-early stopping. Hastie ܘܚܒܪ̈ܘܗܝ – Tibshirani ܝܠܗ ܡܫܟܚܢܐ ܕ-lasso – ܟܡܢܣܚܝ ܡܐ ܕܟܥܒܕ ܒܚܬܝܬܘܬܐ: ܐܡܢ ܕܟܡܒܨܪܚ ܠܬܚܘܡܐ ܕܓܘܡܪܐ ܕܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ، "ܚܕܟܡܐ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܦܝܫܝ ܨܦܪܐ ܒܚܬܝܬܘܬܐ. ܗܕܟ lasso ܟܥܒܕ ܐܝܟ ܓܘܒܝܐ ܡܬܡܫܚܢܐ (continuous) ܕܡܢܬܐ ܕܡܫܬܚܠܦ̈ܢܐ" (Hastie et al., 2009, p. 69). ܩܐ ܒܘܨܝܬܐ ܕܝܠܝܦܬܐ ܝܠܗ̇ ܠܪܝܓܪܫܢ "ܐܝܟ ܕܐܝܬܘܗܝ": ܐܡܢ ܕܢܝܫܐ ܡܢܒܝܢܘܬܐ (prediction) ܝܠܗ̇، ܡܘܕܝܠ ܥܡ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܒܨܝܪ̈ܐ ܘ"ܛܥܝ̈ܐ" ܐܚܪܢܝ ܙܒܢ̈ܐ ܟܡܢܒܐ ܛܒ ܒܝܫ ܡܢ ܡܘܕܝܠ ܥܡ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܕܠܐ ܡܣܒ ܒܐܦ̈ܐ (unbiased) – ܐܗܐ ܝܠܗ trade-off ܕܦܣܩܐ 4 ܓܘ ܥܒܕܐ، ܘܡܢܝܢܐ ܡܫܘܬܦܐ ܟܪܝܐ ܠܝܠܗ ܡܢܝܢܐ ܕܡܨܝܚ ܡܦܫܩܚ ܠܗ ܐܝܟ ܡܥܒܕܢܘܬܐ.

Decision tree – ܩܘܦܬܐ ܚܘܪܬܐ. tree (ܨܚܚܐ 6) ܣܕܪܐ ܕܫܘܐ̈ܠܐ ܝܠܗ: ܐܘܪܟܐ ܕ-petal ܙܥܘܪܐ ܝܠܗ ܡܢ 2.45 cm؟ – ܐܢ ܐܝܢ، Iris setosa؛ ܐܢ ܠܐ، ܦܬܝܘܬܗ ܙܥܘܪܬܐ ܝܠܗ̇ ܡܢ 1.75؟ – versicolor، ܐܢ ܠܐ virginica. ܐܠܓܘܪܝܬܡ (CART) ܓܘ ܟܠ node ܟܓܒܐ ܚܕ feature ܘܚܕ ܬܚܘܡܐ ܕܟܦܠܓܝ ܠܓܘܕܐ ܠܬܪܬܝܢ ܓܘ̈ܕܐ ܙܥܘܪ̈ܐ ܕܟܝ̈ܐ ܡܢ ܟܠ (ܡܬܩ̈ܠܐ ܠܦܘܬ ܪܒܘܬܐ ܕܝܗܘܢ)، ܒܡܚܘܝܢܐ ܕ-Gini ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ ܝܢ ܒ-entropy – "ܣܓܝܐܘܬܐ ܕܙܒܢܐ ܐܗܐ ܠܐ ܟܡܫܚܠܦ ܣܓܝ"، Gini ܡܣܪܗܒ ܝܠܗ ܒܝܫ. ܡܣܬܒܪܢܘܬܐ ܕܓܢܣܐ ܓܘ ܛܪܦܐ (leaf) ܝܠܗ̇ ܡܢܬܐ ܕܚܙ̈ܝܬܐ ܡܢ ܓܢܣܐ ܓܘܗ (49 ܡܢ 54 = 90.7%). ܝܘܬܪ̈ܢܐ: ܡܩܪܒܘܬ ܕܠܐ ܡܛܝܒܘܬܐ ܕܝܗܝ̈ܒܬܐ، ܕܠܐ scaling، ܘܦܘܫܩܐ – "ܢܡܘ̈ܣܐ ܕܦܘܪܫܐ ܠܓܢ̈ܣܐ ܫܦܝܪ̈ܐ ܘܦܫܝܛ̈ܐ ܕܡܨܝܚ ܐܦ ܡܦܠܚܚ ܠܗܘܢ ܒܐܝܕܐ" – ܘܡܛܠ ܗܕܐ "ܡܘܕܝܠ ܕܩܘܦܬܐ ܚܘܪܬܐ"، ܠܩܘܒܠ forests ܘ-networks، ܕܟܡܬܚܫܒܝ "ܩܘܦܬܐ ܐܘܟܡܬܐ": ܟܡܢܒܝ ܛܒ ܣܓܝ، ܘܡܨܝܚ ܒܚܪܚ ܟܠ ܚܘܫܒܢܐ ܕܥܒܕܠܗܘܢ، "ܘܥܡ ܐܗܐ ܟܠܝܘܡ ܩܫܝܐ ܝܠܗ ܕܡܦܫܩܚ ܒܡ̈ܠܐ ܦܫܝܛ̈ܐ ܩܐ ܡܘܕܝ ܡܢܒܝ̈ܢܘܝܬܐ ܥܒܝ̈ܕܐ ܝܢܐ". ܚܘܣܪ̈ܢܐ: tree ܡܘܕܝܠ ܠܐ ܦܪܡܝܛܪܝܐ (nonparametric) ܝܠܗ – ܡܢܝܢܐ ܕܦܪܡܝ̈ܛܪܐ ܠܐ ܝܠܗ ܩܝܡܐ ܡܢ ܩܕܡ، ܘܦܝܫܐ ܕܒܝܩܐ ܠܝܗܝ̈ܒܬܐ ܗܠ ܦܐܝܘܬܐ ܝܬܝܪܬܐ (overfitting) ܐܢ ܠܐ ܟܡܟܪܚ ܠܗ (ܥܘܡܩܐ ܪܒܐ ܡܢ ܟܠ – ܓܘܒܝܐ ܡܩܕܡܐ: ܕܠܐ ܬܚܘܡܐ – ܡܢܝܢܐ ܕܛܪ̈ܦܐ، ܡܢܝܢܐ ܬܚܬܝܐ ܕܚܙ̈ܝܬܐ ܓܘ ܛܪܦܐ)؛ ܪܚܡ ܠܬܚܘ̈ܡܐ ܙܩܝܦ̈ܐ ܥܠ ܣܪ̈ܛܐ، ܘܡܛܠ ܗܕܐ ܪܓܝܫܐ ܝܠܗ ܠܚܘܕܪܐ ܕܝܗܝ̈ܒܬܐ؛ ܘܒܝܬܪܘܬܐ – ܫܘܚܠܦܐ (variance) ܪܡܐ: ܫܘܚܠܦܐ ܙܥܘܪܐ ܓܘ ܝܗܝ̈ܒܬܐ ܝܢ ܓܘ hyperparameters ܟܝܗܒ tree ܦܪܝܫܐ ܣܓܝ، ܘܐܦ ܝܘܠܦܢܐ ܡܢ ܪܝܫ ܥܠ ܐܦ ܐܢܝ ܝܗܝ̈ܒܬܐ ܒܚܬܝܬܘܬܐ ܡܨܝܐ ܕܝܗܒ tree ܐܚܪܢܐ، ܡܛܠ ܕܐܠܓܘܪܝܬܡ ܓܕܫܐܝܬ ܟܓܒܐ ܕܘܡܝܐ ܕ-features ܕܟܒܚܪ ܓܘ ܟܠ node (ܐܠܐ ܐܢ ܟܦܣܩܚ ܙܪܥܐ (random seed)؛ ܨܚܚܐ 6، "Decision Trees Have a High Variance"). ܣܛܐܛܝܣܛܝܩ̈ܝܐ ܟܡܫܠܡܝ ܡܢ ܬܪܝܢ ܓܢܒ̈ܐ: "ܚܕ ܥܘܩܢܐ ܪܫܝܐ ܕ-trees ܝܠܗ ܫܘܚܠܦܐ ܪܡܐ ܕܝܗܘܢ. ܣܓܝ ܓܐܝ̈ܐ ܫܘܚܠܦܐ ܙܥܘܪܐ ܓܘ ܝܗܝ̈ܒܬܐ ܡܨܝܐ ܕܡܬܐ ܠܣܕܪܐ ܕ-splits ܦܪܝܫܐ ܣܓܝ، ܡܐ ܕܟܥܒܕ ܠܦܘܫܩܐ ܩܠܝܠ ܠܐ ܫܪܝܪܐ" – ܡܛܠ ܒܢܝܢܐ ܕܕܪ̈ܓܐ، ܛܥܝܘܬܐ ܓܘ split ܥܠܝܐ ܟܡܬܦܪܣܐ ܠܟܠ ܡܐ ܕܐܝܬ ܬܚܘܬܗ (Hastie et al., 2009, p. 312)؛ ܘܥܡ ܐܗܐ، "ܡܢ ܟܠ ܐܘܪ̈ܚܬܐ ܝܕܝ̈ܥܬܐ ܕܝܘܠܦܢܐ، decision trees ܩܪ̈ܝܒܐ ܝܢܐ ܡܢ ܟܠ ܠܣܢܝܩܘ̈ܝܬܐ" ܕܐܘܪܚܐ "ܡܢ ܪܦܐ" (off-the-shelf) ܩܐ data mining – ܡܣܪ̈ܗܒܐ، ܕܡܨܝܐ ܕܡܬܦܫܩܝ (ܐܡܢ ܕ-tree ܙܥܘܪܐ ܝܠܗ)، ܟܦܠܚܝ ܥܡ ܚܘܠܛܐ ܕܡܫܬܚܠܦ̈ܢܐ ܡܢܝܢܝ̈ܐ ܘܕܓܢ̈ܣܐ ܘܥܡ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ، ܘܠܐ ܟܡܬܥܒܕܝ ܡܢ transformations monotonic ܘܡܢ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ (outliers) ܓܘ ܡܢܒ̈ܝܢܐ (ܦܐܬܐ 352). ܓܘ ܐܦ ܗܝ ܦܐܬܐ ܐܝܬ ܐܦ ܡܥܝܪܢܘܬܐ ܕܒܘܨ̈ܝܐ ܣܢܝܩܝ ܠܗ̇: ܡܦܠܚܢܘ̈ܝܬܐ ܕ-data mining "ܟܠܝܘܡ ܣܢܝܩܝ ܠܡܘܕܝ̈ܠܐ ܕܡܨܝܐ ܕܡܬܦܫܩܝ. ܠܐ ܡܣܦܩ ܕܝܗܒܚ ܡܢܒܝ̈ܢܘܝܬܐ" – ܘܡܛܠ ܗܕܐ "ܐܘܪ̈ܚܬܐ ܕܩܘܦܬܐ ܐܘܟܡܬܐ ܐܝܟ neural networks" ܣܓܝ ܒܨܝܪ ܡܘܚ̈ܡܐ ܝܢܐ ܬܡܢ (ܦܐܬܐ 351-352). ܐܝܢܐ ܕܟܬܢܐ "tree ܡܫܟܚܠܗ ܕ…" ܟܬܢܐ ܥܠ ܚܕ tree ܡܢ ܣܓܝ̈ܐܐ ܕܡܨܝܐ ܕܗܘܝ.

Random forest – ܚܟܡܬܐ ܕܥܡܐ، ܒܛܝܡܐ ܕܦܘܫܩܐ. ܫܪܝܐ ܩܐ ܫܘܚܠܦܐ ܝܠܗ ܕܫܩܠܚ ܡܨܥܝܬܐ: "ensemble" ܕܡܢܒ̈ܝܢܐ (ܨܚܚܐ 7). ܚܘܫܒܐ ܕ-Géron ܝܠܗ ܙܘܙܐ ܥܡ ܡܣܒ ܒܐܦ̈ܐ ܕܟܢܦܠ ܥܠ "ܐܝܠܢܐ" ܒܡܣܬܒܪܢܘܬܐ ܕ-51% – ܒܚܕ ܫܕܝܬܐ ܡܩܪܒܘܬ ܓܕܫܢܝܐ، ܐܢܐ ܒ-1,000 ܫܕܝ̈ܬܐ ܡܣܬܒܪܢܘܬܐ ܕܣܓܝܐܘܬܐ ܕ"ܐܝܠܢܐ" ܡܩܪܒܘܬ 75% ܝܠܗ̇، ܘܒ-10,000 ܠܥܠ ܡܢ 97%: ܢܡܘܣܐ ܕܡܢܝ̈ܢܐ ܪ̈ܒܐ – ܥܡ ܫܪܛܐ ܕܡܢܒ̈ܝܢܐ ܣܓܝ̈ܐܐ ܝܢܐ ܡܣܦܩ ܘܦܪ̈ܝܫܐ ܡܣܦܩ. ܦܘܪܫܢܐ ܟܡܛܐ ܒܬܪܬܝܢ ܐܘܪ̈ܚܬܐ: bagging (bagging, "bootstrap aggregating"; Breiman, 1996, as cited in Géron) – ܟܠ tree ܡܠܦܐ ܝܠܗ ܥܠ ܕܘܡܝܐ ܥܡ ܕܥܪܬܐ ܡܢ ܓܘܕܐ ܕܝܘܠܦܢܐ (ܒܡܨܥܝܬܐ ܡܩܪܒܘܬ 63% ܡܢ ܚܙ̈ܝܬܐ؛ 37% ܕܦܝܫܝ، "ܠܒܪ ܡܢ ܟܝܣܐ"، ܟܡܬܦܠܚܝ ܩܐ ܫܘܪܪܐ ܡܓܢ – out-of-bag evaluation – ܕܠܐ ܓܘܕܐ ܦܪܝܫܬܐ ܕܫܘܪܪܐ)؛ ܘܝܬܝܪ ܡܢ ܐܗܐ، ܓܘ random forest، ܓܘ ܟܠ node ܐܝܠܢܐ ܟܓܒܐ split ܛܒܐ ܡܢ ܟܠ ܒܣ ܡܢ ܡܢܬܐ ܓܕܫܢܝܬܐ ܕ-features (ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ ܫܪܫܐ ܕ-n ܡܢ n) – "ܡܐ ܕܟܡܚܠܦ، ܬܘܒ، ܡܣܒ ܒܐܦ̈ܐ ܪܡܐ ܒܝܫ ܒܫܘܚܠܦܐ ܒܨܝܪܐ ܒܝܫ، ܘܟܠܝܘܡ ܟܝܗܒ ܡܘܕܝܠ ܛܒܐ ܒܝܫ ܒܓܘܡܪܐ" (Chapter 7, "Random Forests"). ܡܒܘܥܐ ܪܫܡܝܐ ܝܠܗ Breiman (2001b): ܚܘܠܛܐ ܕ-trees ܕܟܠ ܚܕ ܬܠܐ ܝܠܗ ܒ-vector ܓܕܫܢܝܐ ܕܓܒܝܐ ܝܠܗ ܕܠܐ ܬܠܝܘܬܐ، ܘܛܥܝܘܬܐ ܕܦܘܫܛܐ ܕܝܠܗ ܟܡܬܟܢܫܐ ܠܬܚܘܡܐ ܐܝܟ ܕܡܢܝܢܐ ܕ-trees ܟܪܒܐ (ܟܢܘܫܝܐ) – ܝܢܝ، ܡܘܣܦܬܐ ܕ-trees ܠܐ ܟܒܪܝܐ ܦܐܝܘܬܐ ܝܬܝܪܬܐ. Hastie ܘܚܒܪ̈ܘܗܝ ܟܡܚܬܬܝ ܠܐܗܐ ܡܐܡܪܐ: ܫܪܝܪܐ ܝܠܗ ܕ"ܡܪܒܝܬܐ ܕ-B ܠܐ ܟܥܒܕܐ ܠܣܕܪܐ ܕ-random forests ܕܦܐܐ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ"، ܐܢܐ ܬܚܘܡܐ ܕܟܡܬܟܢܫ ܠܗ "ܡܨܝܐ ܕܦܐܐ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ ܠܝܗܝ̈ܒܬܐ" – ܡܨܥܝܬܐ ܕ-trees ܓܡܝܪ̈ܐ ܡܨܝܐ ܕܗܘܝܐ ܡܘܕܝܠ ܥܬܝܪܐ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ؛ ܡܢ ܢܣܝܘܢܐ ܕܝܗܘܢ، ܡܪܒܝܬܐ ܕ-trees ܓܡܝܪ̈ܐ "ܚܕ ܚܕ ܓܐܝ̈ܐ ܟܡܟܠܦܐ ܣܓܝ" ܘܟܦܪܩ ܦܪܡܝܛܪ ܕ-tuning (Hastie et al., 2009, p. 596). ܘܫܘܥܪܐ ܟܠܢܝܐ ܕܝܗܘܢ، ܕܟܡܦܫܩ ܩܐ ܡܘܕܝ forest ܝܠܗ ܣܪܛܐ ܕ-baseline ܕܦܣܩܐ 8: "ܓܘ ܥܘ̈ܩܢܐ ܣܓܝ̈ܐܐ ܥܒܕܐ ܕ-random forests ܕܡܐ ܝܠܗ ܣܓܝ ܠܕ-boosting، ܘܦܫܝܛ̈ܐ ܝܢܐ ܒܝܫ ܩܐ ܝܘܠܦܢܐ ܘܩܐ tuning" (ܦܐܬܐ 587)؛ ܫܘܥܪܐ ܕܛܥܝܘܬܐ out-of-bag "ܡܩܪܒܘܬ ܐܦ ܗܘ ܝܠܗ" ܐܝܟ ܫܘܪܪܐ ܡܚܠܦܢܐ (cross-validation) ܕ-N folds (ܦܐܬܐ 593). forest ܐܦ ܟܡܫܚ feature importance: ܟܡܐ ܟܠ feature ܟܡܒܨܪ ܠܠܐ ܕܟܝܘܬܐ (impurity) ܒܡܨܥܝܬܐ ܥܠ ܟܠ nodes ܕܟܡܦܠܚܝ ܒܝܗ، ܡܬܩܠܐ ܒܡܢܝܢܐ ܕܚܙ̈ܝܬܐ، ܘܓܘܡܪܐ ܕܝܠܗ 1 (ܓܘ Iris: ܐܘܪܟܐ ܕ-petal 44%، ܦܬܝܘܬܗ 42%، sepals 11% ܘ-2%). ܡܐ ܕ-forest ܠܐ ܟܝܗܒ ܝܠܗ ܐܘܪܚܐ: importance ܠܝܠܗ̇ ܡܢܝܢܐ ܡܫܘܬܦܐ (coefficient)، ܘܠܐ ܟܐܡܪܐ ܐܢ feature ܟܡܪܒܐ ܝܢ ܟܡܒܨܪ ܠܡܣܬܒܪܢܘܬܐ. ܫܪܒܬܐ ܚܬܐ: boosting – "ܚܕ ܡܢ ܚܘܫ̈ܒܐ ܕܝܘܠܦܢܐ ܚܝܠܬܢ̈ܐ ܡܢ ܟܠ ܕܚܘܝ̈ܐ ܝܢܐ ܓܘ ܥܣܪܝܢ ܫܢ̈ܐ ܐܚܪ̈ܝܐ" (Hastie et al., 2009, p. 337)؛ Breiman ܩܪܐܠܗ ܠ-AdaBoost ܥܡ trees "classifier ܛܒܐ ܡܢ ܟܠ ܡܢ ܪܦܐ ܓܘ ܥܠܡܐ" (ܐܝܟ ܕܡܝܬܝܐ ܝܠܗ ܬܡܢ، ܦܐܬܐ 340) – trees ܒܣܕܪܐ، ܟܠ ܚܕ ܟܡܬܪܨ ܠܕܩܕܡܗ (AdaBoost ܟܡܬܩܠ ܡܢ ܪܝܫ ܚܙ̈ܝܬܐ ܕܦܪܝ̈ܫܐ ܝܢܐ ܛܥܝܐܝܬ؛ gradient boosting ܟܡܦܐܐ ܟܠ tree ܠܫܪ̈ܟܐ (residuals) ܕܕܩܕܡܗ؛ ܡܫܡܠܝܢܘܬܐ ܥܠ ܫܬܐܣܐ ܕ-bins ܩܐ ܝܗܝ̈ܒܬܐ ܪ̈ܒܬܐ – ܡܐܐ ܓܐܝ̈ܐ ܡܣܪܗܒ؛ XGBoost، LightGBM ܘ-CatBoost ܠܒܪ ܡܢ scikit-learn)؛ ܘstacking (stacking) – ܡܘܕܝܠ ܕܟܝܠܦ ܕܡܬܩܠ ܠܡܢܒܝ̈ܢܘܝܬܐ ܕܐܚܪ̈ܢܐ.

ܩܘܦܬܐ ܚܘܪܬܐ ܘܐܘܟܡܬܐ – ܘܐܝܡܢ ܐܘܟܡܬܐ ܠܐ ܫܪܝܐ ܝܠܗ̇. Cynthia Rudin ܟܐܡܪܐ ܕ"ܐܗܐ ܬܫܥܝܬܐ (myth) ܝܠܗ̇ ܕܐܝܬ ܡܢ ܐܠܨܘܬܐ trade-off ܒܝܢܝ ܚܬܝܬܘܬܐ (accuracy) ܘܦܘܫܩܐ": ܗܝܡܢܘܬܐ ܕܡܘܕܝ̈ܠܐ ܡܪܟܒ̈ܐ ܒܝܫ ܚܬܝ̈ܬܐ ܝܢܐ ܒܝܫ "ܣܓܝ ܓܐܝ̈ܐ ܠܐ ܝܠܗ̇ ܫܪܝܪܬܐ، ܒܝܬܪܘܬܐ ܐܡܢ ܕܝܗܝ̈ܒܬܐ ܒܢܝ̈ܬܐ ܝܢܐ، ܥܡ ܡܚܘܝܢܘܬܐ ܛܒܬܐ ܒܡ̈ܠܐ ܕ-features ܕܐܝܬ ܠܗܘܢ ܣܘܟܠܐ ܛܒܝܥܝܐ" – ܘܝܗܝ̈ܒܬܐ ܕܒܘܨܝܐ ܕܫܘܐ̈ܠܐ ܒܚܬܝܬܘܬܐ ܐܗܐ ܝܢܐ. ܦܘܫܩ̈ܐ ܕܟܡܠܒܫܚ ܥܠ ܩܘܦܬܐ ܐܘܟܡܬܐ ܒܬܪ ܥܒܕܐ (ܡܘܕܝܠ ܬܪܝܢܐ ܕܟܡܕܡܐ ܠܩܕܡܝܐ) "ܡܢ ܐܠܨܘܬܐ ܛܥܝ̈ܐ ܝܢܐ": ܐܢ ܗܘܝ ܫܪܝܪ̈ܐ ܓܡܝܪܐܝܬ ܠܡܘܕܝܠ ܩܕܡܝܐ، ܦܘܫܩܐ ܗܘܐ ܗܘܐ ܐܝܟ ܡܘܕܝܠ ܘܠܐ ܗܘܬ ܣܢܝܩܘܬܐ ܠܡܒܘܥܐ؛ ܡܬܠܐ ܕܝܠܗ̇ ܝܠܗ COMPAS – ܡܘܕܝܠ ܕܡܪܘܬܐ ܩܐ ܡܢܒܝܢܘܬܐ ܕܕܥܪܬܐ ܠܚܛܝܬܐ (recidivism) ܓܘ ܒ̈ܬܐ ܕܕܝܢܐ ܓܘ ܐܡܪܝܟܐ، ܕ-ProPublica ܐܟܠܗ̇ ܩܪܨܐ ܕܡܣܒ ܒܐܦ̈ܐ ܕܓܢܣܐ ܕܒܢܝ̈ ܐܢܫܐ (racial bias) ܥܠ ܫܬܐܣܐ ܕܡܘܕܝܠ ܣܪܛܢܝܐ ܕܦܘܫܩܐ ܕܒܢܝܠܗ̇ ܩܐ ܕܝܠܗ، ܟܕ ܡܘܕܝܠ ܓܢܗ ܡܨܝܐ ܕܗܘܝܐ ܠܐ ܣܪܛܢܝܐ ܝܠܗ (Rudin, 2019, Section 2). ܦܐܪܐ ܕܝܠܗ̇: ܩܐ ܦܣ̈ܩܐ ܕܐܝܬ ܠܗܘܢ ܣܘܟܢܐ ܪܒܐ ܥܠ ܒܢܝ̈ ܐܢܫܐ – ܕܝܢܐ، ܚܘܠܡܢܐ، ܫܝܢܐ ܕܟܢܫܐ – ܓܪܓ ܒܢܚ ܡܘܕܝ̈ܠܐ ܕܡܨܝܐ ܕܡܬܦܫܩܝ ܡܢ ܫܘܪܝܐ، ܠܐ ܕܡܦܫܩܚ ܩܘ̈ܦܝܬܐ ܐܘܟ̈ܡܬܐ. ܩܐ ܒܘܨܝܬܐ: ܥܠ ܝܗܝ̈ܒܬܐ ܕܒܘܨܝܐ ܕܫܘܐ̈ܠܐ ܕܚܕܟܡܐ ܡܐܐ ܡܫܬܘܬܦ̈ܢܐ، ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܟܪܝܐ ܝܢ tree ܠܐ ܥܡܝܩܐ ܟܠܝܘܡ ܦܝܫܝ ܡܢܒܝܐ ܐܝܟ forest – ܘܦܝܫܝ ܐܡܪܝ ܐܦ ܩܐ ܡܘܕܝ. forest ܟܡܪܗܛܚ ܠܗ ܐܝܟ ܣܪܛܐ ܕ-baseline: ܐܢ ܛܒܐ ܝܠܗ ܣܓܝ ܝܬܝܪ، ܐܝܬ ܓܘ ܝܗܝ̈ܒܬܐ ܠܐ ܣܪܛܢܝܘܬܐ ܝܢ ܥܒ̈ܕܐ ܕܚܕ̈ܕܐ (interactions) ܕܡܘܕܝܠ ܕܡܬܦܫܩ ܠܐ ܟܚܙܐ ܠܗܘܢ – ܘܐܗܐ ܟܬܢܚ.

6. Neural networks – ܐܝܡܢ ܐܝܢ ܘܐܝܡܢ ܠܐ

neural network ܥܒܝܕܬܐ (ܨܚܚܐ 10) ܫܩܠܠܗ̇ ܡܘܚܒܬܐ ܡܢ ܡܘܚܐ، ܐܢܐ "ܐܝܟ ܕܛܝ̈ܣܬܐ ܫܩܠܠܗܝܢ ܡܘܚܒܬܐ ܡܢ ܦܪ̈ܚܬܐ، ܠܐ ܣܢܝܩܝ ܕܡܬܦܦܝ ܓܦ̈ܐ ܩܐ ܕܛܝܣܝ"؛ ܡܘܕܝܠ ܩܕܡܝܐ ܕ-McCulloch ܘ-Pitts ܝܠܗ (1943)، ܘܒܬܪܗ ܬܪܝܢ "ܣܬܘ̈ܝܐ" – ܫܢ̈ܐ ܕ-60 ܘܫܢ̈ܐ ܕ-90، ܐܡܢ ܕ-support vector machines ܡܬܚܙܝ ܗܘܝ ܕܐܝܬ ܠܗܘܢ ܣܒܪܐ ܒܝܫ. ܓܠܠܐ ܕܗܫܐ ܦܪܝܫܐ ܝܠܗ، ܐܝܟ ܕܐܡܪ Géron، ܡܛܠ ܐܪܒܥܐ ܥܠ̈ܠܬܐ: ܟܡܝܘܬܐ ܕܝܗܝ̈ܒܬܐ، ܚܝܠܐ ܕܚܘܫܒܢܐ (ܢܡܘܣܐ ܕ-Moore، ܟܪ̈ܛܐ GPU ܕܐܘܡܢܘܬܐ ܕܓܡ̈ܐ ܒܪܝܠܗܘܢ ܒܡܠܝܘܢ̈ܐ، cloud)، ܫܘܦܪ̈ܐ ܙܥܘܪ̈ܐ ܐܢܐ ܦܣܘܩ̈ܐ ܓܘ ܐܠܓܘܪܝ̈ܬܡܐ ܕܝܘܠܦܢܐ، ܘܓܠܝܘܬܐ ܕܟܪܝܘ̈ܝܬܐ ܕܬܐܘܪܝܐ – ܐܝܟ local optima – ܠܐ ܟܡܚܒܠܝ ܒܥܒܕܐ. ܘܡܐ ܝܠܗ̇ network ܡܢ ܓܢܒܐ ܣܛܐܛܝܣܛܝܩܝܐ: "ܗܘܐ ܣܓܝ hype ܚܕܪ neural networks، ܕܥܒܕܠܗܘܢ ܕܡܬܚܙܝ ܚܪ̈ܫܐ ܘܟܣ̈ܝܐ. ܐܝܟ ܕܟܡܓܠܚ ܓܘ ܐܗܐ ܦܣܩܐ، ܐܢܝ ܒܣ ܡܘܕܝ̈ܠܐ ܣܛܐܛܝܣܛܝܩ̈ܝܐ ܠܐ ܣܪܛܢ̈ܝܐ ܝܢܐ" – ܡܘܕܝܠ ܕܪܝܓܪܫܢ ܝܢ ܕܦܘܪܫܐ ܠܓܢ̈ܣܐ ܒܬܪܝܢ ܕܪ̈ܓܐ (Hastie et al., 2009, p. 392). architecture ܫܬܐܣܝܬܐ، multilayer perceptron، ܝܠܗ̇ layer ܕܡܥܠܢܐ، ܚܕ ܝܢ ܝܬܝܪ hidden layers، ܘ-layer ܕܡܦܩܢܐ (output) – ܘ-Bishop ܟܡܥܝܪ ܕܫܡܐ "ܒܫܪܪܐ ܫܡܐ ܛܥܝܐ ܝܠܗ، ܡܛܠ ܕܡܘܕܝܠ ܡܪܟܒܐ ܝܠܗ ܡܢ layers ܣܓܝ̈ܐܐ ܕܡܘܕܝ̈ܠܐ ܕܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ" (ܥܡ ܠܐ ܣܪܛܢܝܘܬܐ ܡܬܡܫܚܢܝܬܐ) ܘܠܐ ܡܢ perceptrons (Bishop, 2006, p. 226): ܩܐ ܒܘܨܝܬܐ ܕܝܕܥܐ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ، network ܝܠܗ̇ ܪܝܓܪ̈ܫܢܐ ܠܘܓܝܣܛܝܩ̈ܝܐ ܕܟܡܬܝܗܒܝ ܚܕ ܠܚܕ؛ "ܥܡܝܩܬܐ" ܝܠܗ̇ network ܥܡ ܛܐܦܐ ܥܡܝܩܐ ܕ-hidden layers، ܐܦܢ "ܣܓܝ̈ܐܐ ܟܡܡܠܠܝ ܥܠ deep learning ܟܠ ܓܐܝܐ ܕ-neural networks ܐܝܬ ܓܘ ܡܠܬܐ (ܐܦ ܠܐ ܥܡܝܩ̈ܬܐ)". ܝܘܠܦܢܐ – backpropagation (backpropagation): automatic differentiation ܒ-reverse mode (Linnainmaa، 1970) ܕܟܚܫܒ ܒܬܪܝܢ ܥܒܘ̈ܪܐ – ܠܩܕܡ ܘܠܒܣܬܪ – ܕܟܝ ܓܪܓ ܡܫܚܠܦܚ ܟܠ ܡܬܩܠܐ (weight) ܩܐ ܕܒܨܪܚ ܛܥܝܘܬܐ، ܘܒܬܪܗ ܦܣܥܬܐ ܕ-gradient descent؛ ܘܬܘܒ ܡܢ ܪܝܫ. ܚܕ hidden layer ܡܨܝܐ، ܒܬܐܘܪܝܐ، ܕܥܒܕ ܡܘܕܝܠ ܩܐ ܟܠ function ܐܢ ܐܝܬ ܚܕܝܘ̈ܬܐ ܡܣܦܩ̈ܢܐ، ܐܢܐ networks ܥܡܝܩ̈ܬܐ ܣܓܝ ܒܨܝܪ ܦܪܡܝ̈ܛܪܐ ܣܢܝܩܝ، ܡܛܠ ܕܟܡܦܠܚܝ ܒܛܟܣܐ ܕܕܪ̈ܓܐ ܕܐܝܬ ܓܘ ܝܗܝ̈ܒܬܐ – ܣܪ̈ܛܐ، ܘܒܬܪܗ ܐܣܟܝ̈ܡܐ، ܘܒܬܪܗ ܦܐ̈ܬܐ – ܘܐܗܐ ܐܦ ܝܠܗ ܕܟܡܨܝܐ transfer learning (transfer learning): ܕܫܩܠܚ layers ܬܚܬ̈ܝܐ ܕ-network ܡܠܦܬܐ ܘܡܠܦܚ ܒܣ ܠܥܠ̈ܝܐ ܩܐ ܥܒܕܐ ܚܕܬܐ. "ܚܕ ܚܕ ܓܐܝ̈ܐ ܦܝܫܐ ܣܢܝܩܝܬܘܢ ܕܡܠܦܝܬܘܢ networks ܐܝܟ ܐܢܝ ܡܢ ܨܦܪܐ" (Chapter 10, "Number of Hidden Layers").

ܘܐܝܡܢ ܠܐ. ܙܘܗܪܐ ܐܝܬ ܡܢ ܩܕܡ ܓܘ ܦܘܬܚܐ ܕܟܬܒܐ: "ܠܐ ܫܘܪܝܬܘܢ ܠܓܘ ܡ̈ܝܐ ܥܡܝܩ̈ܐ ܒܥܓܠܘܬܐ… ܣܓܝܐܘܬܐ ܕܥܘ̈ܩܢܐ ܡܨܝܐ ܕܡܬܫܪܝ ܛܒ ܒܐܘܡܢ̈ܘܝܬܐ ܦܫܝܛ̈ܐ ܒܝܫ ܐܝܟ random forests ܘܐܘܪ̈ܚܬܐ ensemble… deep learning ܦܐܫ ܡܢ ܟܠ ܠܥܘ̈ܩܢܐ ܡܪܟܒ̈ܐ ܐܝܟ ܦܘܪܫܐ ܕܨܘܪ̈ܬܐ، ܦܘܪܫܐ ܕܡܡܠܠܐ ܝܢ ܦܘܠܚܢܐ ܕܠܫܢܐ ܛܒܝܥܝܐ، ܘܣܢܝܩܐ ܝܠܗ ܠܣܓܝ ܝܗܝ̈ܒܬܐ، ܚܝܠܐ ܕܚܘܫܒܢܐ ܘܡܓܪܬ ܪܘܚܐ (ܐܠܐ ܐܢ ܡܨܝܚ ܫܩܠܚ ܥܘܕܪܢܐ ܡܢ neural network ܡܠܦܬܐ ܡܢ ܩܕܡ)" (Géron, 2022، ܦܘܬܚܐ ܕܟܬܒܐ، "Roadmap"). ܩܐ ܒܘܨܝܐ ܟܢܫܝܐ ܦܐܪܐ ܚܪܝܦܐ ܝܠܗ: ܥܠ ܠܘܚܐ ܕܒܘܨܝܐ ܕܫܘܐ̈ܠܐ – ܠܐ؛ ܥܠ ܟܬܝ̈ܒܬܐ ܕܡܫܐܠܬ̈ܐ، posts، ܨܘܪ̈ܬܐ ܘܩܠ̈ܐ ܪܫܝܡ̈ܐ – ܐܝܢ، ܐܢܐ ܡܩܪܒܘܬ ܟܠܝܘܡ ܒܝܕ ܡܘܕܝܠ ܡܠܦܐ ܡܢ ܩܕܡ ܕܚܕ ܐܚܪܢܐ ܡܠܦܠܗ ܥܠ ܡܠܝܘܢ̈ܐ ܕܡܬ̈ܠܐ، ܘܕܟܡܬܩܢܚ ܠܗ (fine-tuning) ܝܢ ܒܣ ܟܡܦܠܚܚ ܠܗ: DictaBERT، HeBERT ܘ-BEREL ܕܐܝܬ ܓܘ ܦܐܬܐ ܕ-NLP ܒܚܬܝܬܘܬܐ networks ܐܝܟ ܐܢܝ ܝܢܐ، ܘܦܘܩܕܢܐ ܬܡܢ – ܕܘܡܝܐ (sample) ܒܐܝܕܐ ܕ-100-200 ܦܣܘ̈ܩܐ (items) ܘܫܠܡܘܬܐ (agreement) ܒܝܢܝ ܪܡܙ̈ܢܐ (coders) ܩܕܡ ܕܬܟܝܚ ܥܠ ܡܦܩܢܐ – ܝܠܗ ܦܣܩܐ 4 ܕܐܗܐ ܦܐܬܐ ܒܡ̈ܠܐ ܐܚܪ̈ܢܐ. ܡܐܢܐ ܩܐ ܟܬܝܒܬܐ ܕ-networks ܝܠܗ Keras (ܠܘܚܐ 2) – "ܡܨܥܬܐ ܒܪܡܐ ܪܡܐ، ܫܦܝܪܐ ܘܦܫܝܛܐ" ܠܥܠ ܡܢ TensorFlow، ܘܣܓܝܐܘܬܐ ܕܣܢܝܩܘ̈ܝܬܐ ܦܝܫܐ ܡܫܘܡܠܝܐ ܒܝܗ.

7. ܡܐܢ̈ܐ

ܟܬܒܐ ܟܠܗ ܟܦܠܚ ܒ-Python، ܘܡܢܬܐ ܩܕܡܝܬܐ ܕܝܠܗ ܒ-scikit-learn – ܟܬܒܘܬܐ ܕ-Géron ܟܡܫܒܚ ܠܬܘܩܢܐ ܕ-API ܕܝܠܗ̇: ܟܠ object ܫܥܘܪܐ (estimator) ܝܠܗ ܥܡ fit()، ܚܕܟܡܐ ܡܢܝܗܘܢ ܡܫܚܠܦ̈ܢܐ (transformers) ܥܡ transform() ܘܚܕܟܡܐ ܡܢܒ̈ܝܢܐ (predictors) ܥܡ predict()؛ hyperparameters ܓܠܝ̈ܐ ܝܢܐ، ܦܪܡܝ̈ܛܪܐ ܕܡܬܝܠܦ̈ܐ ܝܢܐ ܡܛܝ̈ܢܐ ܝܢܐ (ܥܡ underscore ܒܚܪܬܐ ܕܝܗܘܢ)، ܝܗܝ̈ܒܬܐ arrays ܕ-NumPy ܝܢܐ ܘܠܐ classes ܕܝܠܢ̈ܝܐ، ܘܟܠ ܡܕܡ ܡܨܝܚ ܡܐܣܪܚ ܠܗ ܓܘ ܨܢܘܪܐ (Pipeline) – ܕܐܦ ܐܗܘ ܝܠܗ ܡܟܝܢܘܬܐ ܕܟܟܠܝܐ ܠܡܪܕܝܬܐ ܕܦܣܩܐ 4، ܡܛܠ ܕܨܢܘܪܐ ܟܠܗ ܟܡܬܦܐܐ ܥܠ ܝܘܠܦܢܐ ܘܟܡܬܦܠܚ ܥܠ ܫܪܟܐ (Chapter 2, "Scikit-Learn Design", "Transformation Pipelines"). ܠܘܚܐ 2 ܟܡܛܟܣ ܠܡܐܢ̈ܐ ܠܦܘܬ ܣܢܝܩܘܬܐ؛ ܐܝܢܐ ܕܠܐ ܟܟܬܒ ܪܡܙܐ ܦܝܫܐ ܡܫܟܚ ܓܘܗ ܬܠܬܐ ܡܐܢ̈ܐ ܓܪܦܝ̈ܐ – ܬܪܝܢ ܪܡܙܐ ܦܬܝܚܐ (open source) ܘܚܕ ܒܦܪܥܢܐ، ܕܦܣܩܐ 10 ܩܐ ܕܝܠܗ ܝܠܗ. ܫܪܟܐ ܕܡܐܢ̈ܐ ܣܛܐܛܝܣܛܝܩ̈ܝܐ – R، PSPP، JASP، jamovi – ܓܘ ܨܘܪܬܐ ܕܡܐܢ̈ܐ، ܦܣܩܐ 8.

8. ܛܟܣܐ ܕܥܒܕܐ: ܝܘܠܦܢܐ ܕܡܟܝܢܐ ܓܘ ܒܘܨܝܐ ܟܢܫܝܐ

ܗܘܝܐ ܛܘܦܣܢܝܐ: ܒܘܨܝܐ ܕܫܘܐ̈ܠܐ (survey) ܕܚܕܟܡܐ ܡܐܐ ܡܫܬܘܬܦ̈ܢܐ ܥܡ ܦܐܪܐ ܕܬܪܝܢ ܛܝ̈ܡܐ (ܫܒܩܬܐ ܕܡܕܪܫܬܐ، ܝܗܒܬܐ ܕܩܠܐ، ܒܥܬܐ ܕܥܘܕܪܢܐ)، ܝܢ ܦܐܝܠ ܕܡܕܒܪܢܘܬܐ ܕܐܠܦ̈ܐ. ܫܘܐܠܐ: ܡܨܝܐ ܕܡܢܒܝܚ ܠܦܐܪܐ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܕܪܩܥܐ – ܘܟܡܐ ܛܒ، ܒܦܘܚܡܐ ܥܡ ܡܐ ܕܝܕܥܚ ܡܢ ܩܕܡ. ܫܒܥܐ ܦܣܥ̈ܬܐ، ܘܟܠ ܚܕܐ ܡܢܝܗܝܢ ܟܬܝܒܬܐ ܝܠܗ̇؛ ܦܐܝܠ – ܓܘ ܛܘܦܣܐ ܬܩܝܢܐ (the standard data template) ܕܣܐܝܛ، ܣܕܪܐ = ܡܫܬܘܬܦܢܐ، ܥܡܘܕܐ = ܡܫܬܚܠܦܢܐ، ܘܡܢ SPSS – ܒܝܕ ܡܢ SPSS ܠܐܩܣܠ.

9. ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-R

ܛܟܣܐ ܕܦܣܩܐ 8، ܐܝܟ ܚܕ ܣܩܪܝܦܬ (script (R)) ܕܟܦܠܚ ܡܢ ܫܘܪܝܐ ܗܠ ܚܪܬܐ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (sample data file) ܕܦܐܬܐ – DATA_ml_example_eng.xlsx (ܘܢܘܣܚܐ ܥܡ ܫܡ̈ܗܐ ܥܒܪ̈ܝܐ، DATA_ml_example_heb.xlsx): 320 ܬܠܡܝ̈ܕܐ ܓܘ ܬܡܢܝܐ ܡܕܪ̈ܫܝܬܐ، ܫܒܥܐ ܡܫܬܚܠܦ̈ܢܐ ܕܪܩܥܐ ܘܦܐܪܐ ܕܬܪܝܢ ܛܝ̈ܡܐ – ܫܒܩܬܐ ܕܡܕܪܫܬܐ (11.6%) – ܥܡ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ ܓܘ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ، ܓܘ ܛܘܦܣܐ ܬܩܝܢܐ ܕܣܐܝܛ. ܓܘܒ̈ܝܐ ܕܡܐܢ̈ܐ ܟܐܙܠܝ ܒܬܪ ܟܬܒܐ ܕܡܕܒܪܢܘܬܐ ܕ-Gutierrez، ܕܟܬܝܒܐ ܝܠܗ ܚܕܪ ܐܦ ܗܘ ܫܘܐܠܐ – ܕܟܝ ܦܪܘܝܩܬ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ ܟܡܬܚܙܐ ܓܘ R، ܡܢ ܩܪܝܢܐ ܕܦܐܝܠ ܗܠ ܫܘܥܪܐ ܕܡܘܕܝܠ: glm ܥܡ family = binomial ܩܐ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ، randomForest ܥܡ ntree ܘ-mtry، ܘ-importance() ܩܐ feature importance (Gutierrez, 2015, Chapter 6, "Logistic Regression", "Random Forests")؛ ܦܘܠܓܐ ܠܝܘܠܦܢܐ، ܠܫܘܪܪܐ ܘܠܒܘܚܪܢܐ – "60% ܝܘܠܦܢܐ، 20% ܫܘܪܪܐ ܡܚܠܦܢܐ ܘ-20% ܒܘܚܪܢܐ" ܒܢܘܣܚܐ ܕܝܠܗ – ܘܠܓܘܕܐ ܕܒܘܚܪܢܐ "ܟܫܒܩܚ ܠܗ ܒܝܚܕܝܘܬܗ ܓܡܝܪܐܝܬ، ܡܛܠ ܕܡܢ ܡܬܘܡ ܠܐ ܟܡܬܦܠܚ ܓܘ ܐܘܪܚܐ" ܕܓܘܒܝܐ ܕܡܘܕܝܠ (Gutierrez, 2015, Chapter 7, "Bias and Variance", "Cross Validation")؛ ܘܩܐ regularization – glmnet، ܕܓܘܗ alpha = 0 ܟܝܗܒ ridge ܘ-alpha = 1 lasso، ܘ-lambda ܟܡܠܟ ܠܚܝܠܐ (Chapter 7, "Overfitting"). ܡܐ ܕܣܩܪܝܦܬ ܟܡܘܣܦ ܥܠ ܟܬܒܐ ܝܠܗ ܨܪܪܐ caret (Kuhn, 2008): ܦܘܠܓܐ stratified، ܫܘܪܪܐ ܡܚܠܦܢܐ، tuning ܘܡܛܝܒܘܬܐ ܓܘ folds – imputation ܕܛܝ̈ܡܐ ܚܣܝ̈ܪܐ ܘ-standardization ܓܘ preProcess، ܕܟܡܬܦܐܝܝ ܥܠ fold ܕܝܘܠܦܢܐ ܒܣ – ܓܘ ܚܕ ܡܨܥܬܐ ܩܐ ܟܠ ܡܘܕܝ̈ܠܐ، ܘܗܕܟ ܠܐ ܡܨܝܐ ܕܗܘܝܐ ܡܪܕܝܬܐ ܒܛܥܝܘܬܐ (ܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ، ܦܣܩܐ 5). ܫܒܝܠܐ C:\Rdata\ – ܐܦ ܗܘ ܥܝܕܐ ܕܣܐܝܛ (site convention) ܕܦܣ̈ܩܐ ܕ-R ܓܘ ܦܐ̈ܬܐ ܕܡܚܫܒ̈ܢܐ.

# machine_learning.R - machine learning in social research: the seven-step recipe in R
# Data: DATA_ml_example_eng.xlsx - 320 students in 8 schools; outcome dropout (0/1).
library(readxl)        # read Excel
library(caret)         # split, cross-validation, tuning, confusion matrix
library(randomForest)  # random forest
library(pROC)          # ROC curve and AUC confidence interval

d <- read_excel("C:/Rdata/DATA_ml_example_eng.xlsx")
d$dropout <- factor(d$dropout, levels = c(0, 1), labels = c("no", "yes"))
d$gender  <- factor(d$gender, levels = c(1, 2), labels = c("male", "female"))
d$id <- NULL                      # the id column is not a variable

# --- Step 1: goal, metric, baseline ------------------------------------------
# Metric: AUC (no threshold) and sensitivity at the chosen threshold. First baseline - the dummy classifier:
prop.table(table(d$dropout))      # majority-class rate = accuracy of "always no"

# --- Step 2: the split - first, stratified by outcome, fixed seed -----------
set.seed(20260920)
idx   <- createDataPartition(d$dropout, p = 0.8, list = FALSE)
train <- d[idx, ]
test  <- d[-idx, ]                # test set - untouched until step 6

# --- Step 3: preparation inside the pipeline - imputation and scaling within folds ---
ctrl <- trainControl(method = "cv", number = 10, classProbs = TRUE,
                     summaryFunction = twoClassSummary, savePredictions = "final")
prep <- c("medianImpute", "center", "scale")   # caret fits these on the training fold only (na.action = na.pass: NAs imputed in the pipeline)

# --- Step 4: compare models by cross-validation - same folds for all ---------
set.seed(1)
m_base <- train(dropout ~ age + gender + ses, data = train, method = "glm",
                family = binomial, metric = "ROC", trControl = ctrl)           # baseline: background variables
set.seed(1)
m_glm  <- train(dropout ~ . - school_id, data = train, method = "glm",
                family = binomial, metric = "ROC", trControl = ctrl, preProcess = prep, na.action = na.pass)
set.seed(1)
m_tree <- train(dropout ~ . - school_id, data = train, method = "rpart",
                metric = "ROC", trControl = ctrl, preProcess = prep, na.action = na.pass)
set.seed(1)
m_rf   <- train(dropout ~ . - school_id, data = train, method = "rf",
                metric = "ROC", trControl = ctrl, preProcess = prep, ntree = 500, na.action = na.pass)
res <- resamples(list(baseline = m_base, logistic = m_glm, tree = m_tree, forest = m_rf))
t(sapply(res$values[, grep("~ROC$", names(res$values))],
         function(x) c(mean = mean(x), sd = sd(x))))   # mean and SD of AUC over the 10 folds

# --- Step 5: tuning - candidates only ----------------------------------------
set.seed(1)
m_rf_t <- train(dropout ~ . - school_id, data = train, method = "rf",
                metric = "ROC", trControl = ctrl, preProcess = prep, ntree = 500, na.action = na.pass,
                tuneGrid = data.frame(mtry = c(2, 3, 4, 6)))
m_rf_t$results[, c("mtry", "ROC", "ROCSD")]

# --- Step 6: the test set - once -----------------------------------------------
final <- if (max(m_rf_t$results$ROC) - max(m_glm$results$ROC) > m_glm$results$ROCSD) m_rf_t else m_glm
# threshold chosen on the training set's cross-validated predictions (savePredictions) - not on the test set
roc_cv <- roc(final$pred$obs, final$pred$yes, levels = c("no", "yes"), direction = "<")
thr    <- coords(roc_cv, "best", best.method = "youden", ret = "threshold")$threshold
thr                                                          # the threshold to apply to the test set
p_test <- predict(final, test, type = "prob", na.action = na.pass)[, "yes"]
roc_t  <- roc(test$dropout, p_test, levels = c("no", "yes"), direction = "<")
auc(roc_t); ci.auc(roc_t)                                    # AUC and 95% CI on the test set
pred_t <- factor(ifelse(p_test >= thr, "yes", "no"), levels = c("no", "yes"))
confusionMatrix(pred_t, test$dropout, positive = "yes", mode = "everything")   # at the chosen threshold
confusionMatrix(predict(final, test, na.action = na.pass), test$dropout, positive = "yes")$byClass[c("Sensitivity", "Specificity")]  # and at 0.5, for comparison

# --- Step 7: report - plus feature importance (no direction) ----------------
varImp(final)

# --- Dependent data: folds by school instead of by student -----------------
folds_g <- groupKFold(train$school_id, k = 5)
ctrl_g  <- trainControl(method = "cv", index = folds_g, classProbs = TRUE,
                        summaryFunction = twoClassSummary)
set.seed(1)
m_rf_g <- train(dropout ~ . - school_id, data = train, method = "rf",
                metric = "ROC", trControl = ctrl_g, preProcess = prep, ntree = 500, na.action = na.pass)
m_rf_g$results[, c("mtry", "ROC", "ROCSD")]    # compare with m_rf: the gap is what the dependence "contributed"

ܡܐ ܦܠܛܠܗ (R 4.3.3, caret 6.0-94, randomForest 4.7-1.1, pROC 1.18.5؛ ܡܦܩܢܐ ܓܡܝܪܐ – qa/ml/ml_out.txt). classifier dummy: 88.4% ܚܬܝܬܘܬܐ ܟܠܢܝܬܐ – ܐܗܐ ܝܠܗ ܣܪܛܐ ܕܐܪܥܐ. ܓܘ ܫܘܪܪܐ ܡܚܠܦܢܐ ܕܥܣܪܐ folds، AUC ܡܨܥܝܐ: ܣܪܛܐ ܕ-baseline (ܥܘܡܪܐ، ܓܢܣܐ ܕܒܪܢܫܐ، ܕܪܓܐ ܕܟܢܫܐ) .59 (ܣܛܝܘܬܐ ܬܩܝܢܬܐ .21)، ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܥܠ ܟܠ ܡܫܬܚܠܦ̈ܢܐ .66 (.22)، tree .64 (.14)، random forest .64 (.21)؛ tuning ܕ-forest (mtry 2-6) ܡܛܠܗ ܒܝܬܪ ܡܢ ܟܠ ܠ-.65. ܢܡܘܣܐ ܕܦܣܥܬܐ 5 ܓܒܐܠܗ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ: forest ܠܐ ܥܒܪܠܗ ܡܢܗ ܒܦܘܪܫܢܐ ܕܥܒܪ ܡܢ ܣܛܝܘܬܐ ܬܩܝܢܬܐ – ܘ"forest ܠܐ ܝܠܗ ܛܒܐ ܡܢ ܪܝܓܪܫܢ" ܡܫܟܚܢܘܬܐ ܝܠܗ̇، ܠܐ ܡܚܝܘܬܐ. ܥܠ ܓܘܕܐ ܕܒܘܚܪܢܐ (63 ܬܠܡܝ̈ܕܐ، 7 ܕܫܒܩܠܗܘܢ): AUC = .74، ܬܚܘܡܐ ܕܬܘܟܠܢܐ 95% [.50, .97] – ܦܬܝܐ، ܡܛܠ ܕܫܒܥܐ ܗܘܝ̈ܐ ܕܙܘܕܐ ܫܒܥܐ ܝܢܐ. ܘܬܚܘܡܐ ܕܦܘܪܫܐ: ܒܬܚܘܡܐ 0.5 ܡܘܕܝܠ ܠܐ ܟܦܪܫ ܐܦ ܚܕ ܕܫܒܩܠܗ (ܪܓܝܫܘܬܐ 0، ܝܚܝܕܝܘܬܐ (specificity) 1 – "ܟܙܟܐ ܠ-Nostradamus")؛ ܬܚܘܡܐ ܕܓܒܝܐ ܝܠܗ ܥܠ ܡܢܒܝ̈ܢܘܝܬܐ ܕܫܘܪܪܐ ܡܚܠܦܢܐ ܕܓܘܕܐ ܕܝܘܠܦܢܐ، ܠܐ ܥܠ ܒܘܚܪܢܐ، ܝܠܗ .12 – ܘܓܘܗ ܪܓܝܫܘܬܐ .71، ܝܚܝܕܝܘܬܐ .73، precision .25: ܡܘܕܝܠ ܟܐܚܕ ܚܡܫܐ ܡܢ ܫܒܥܐ ܕܫܒܩܠܗܘܢ ܒܛܝܡܐ ܕ-15 ܙܘܗܪ̈ܐ ܛܥܝ̈ܐ. feature importance – ܡܢܝ̈ܢܐ ܕܡܕܪܫܬܐ، ܕܪܓܐ ܕܟܢܫܐ، ܠܐ ܐܬܝܬܐ – ܕܠܐ ܐܘܪܚܐ. ܘܒܚܪܬܐ ܦܘܠܓܐ ܠܦܘܬ ܡܕܪܫܬܐ ܒܕܘܟܬܐ ܕܠܦܘܬ ܬܠܡܝܕܐ: AUC ܕ-forest ܟܢܚܬ ܡܢ .64 ܠ-.60 – ܐܗܐ ܦܘܪܫܢܐ ܙܥܘܪܐ ܝܠܗ ܡܐ ܕܬܠܝܘܬܐ ܒܝܢܝ ܬܠܡܝ̈ܕܐ ܕܐܦ ܗܝ ܡܕܪܫܬܐ "ܝܗܒܠܗ̇" ܠܡܢܝܢܐ ܩܕܡܝܐ (ܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ، ܦܣܩܐ 6). ܝܗܝ̈ܒܬܐ ܥܒܝ̈ܕܬܐ ܝܢܐ، ܘܐܗܐ ܒܚܬܝܬܘܬܐ ܝܠܗ ܡܠܬܐ: ܗܕܟ ܟܡܬܚܙܐ ܦܪܘܝܩܬ ܫܪܝܪܐ ܥܠ 320 ܡܫܬܘܬܦ̈ܢܐ – ܠܐ AUC = .95.

10. ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-SPSS Modeler

ܩܐ ܐܝܗܝ ܕܒܘܨܝܐ ܕܝܠܗ̇ ܚܝܐ ܓܘ SPSS، ܐܘܪܚܐ ܩܨܝܪܬܐ ܠܝܘܠܦܢܐ ܕܡܟܝܢܐ ܠܝܠܗ̇ Python ܐܠܐ ܬܘܟܢܝܬܐ ܚܬܐ: SPSS Modeler، ܕܓܘܗ̇ "data mining ܐܣܝܪܐ ܝܠܗ ܒܥܒܪܬܐ ܕܝܗܝ̈ܒܬܐ ܒܝܕ ܣܕܪܐ ܕ-nodes، ܕܟܡܬܩܪܐ 'stream'. ܟܠ node ܟܡܚܘܐ ܥܒܕܐ ܝܚܝܕܝܐ ܕܟܡܬܦܠܚ ܥܠ ܝܗܝ̈ܒܬܐ، ܘܐܣܘܪ̈ܐ ܒܝܢܝ nodes ܟܡܬܚܡܝ ܠܢܗܪܐ ܕܝܗܝ̈ܒܬܐ" (Truong, 2026, p. 56). ܐܗܐ ܦܣܩܐ ܟܐܙܠ ܒܬܪ ܟܬܒܐ ܕܝܘܠܦܢܐ ܕ-Truong ܘܟܡܬܪܓܡ ܫܒܥܐ ܦܣܥ̈ܬܐ ܕܛܟܣܐ ܕܥܒܕܐ ܕܦܣܩܐ 8 – ܘܣܩܪܝܦܬ ܕ-R ܕܦܣܩܐ 9 – ܠ-nodes. ܚܕܐ ܬܚܡܘܬܐ، ܠܩܘܒܠ ܦܣܩܐ 9: Modeler ܠܐ ܡܬܩܢܐ ܝܠܗ ܓܘ ܐܬܪܐ ܕܒܘܚܪܢܐ ܕܣܐܝܛ، ܘܡܛܠ ܗܕܐ ܡܐ ܕܟܬܝܒܐ ܝܠܗ ܐܟܐ ܬܚܘܝܬܐ ܝܠܗ̇ ܠܦܘܬ ܟܬܒܐ، ܠܐ ܪܗܛܐ؛ ܐܝܗܝ ܕܟܡܪܗܛܐ ܠܗ – ܟܟܬܒܐ ܠ-stream (ܦܐܝܠ str) ܐܝܟ ܕܟܡܩܪܒܚ notebook.

ܐܘܪܚܐ. Modeler ܒܢܝܐ ܝܠܗ ܚܕܪ CRISP-DM – "ܬܩܢܐ ܕܥܒܪ ܡܢ ܫܪ̈ܒܬܐ ܕܐܘܡܢܘܬܐ ܩܐ ܐܘܪܚܐ ܕ-data mining"، ܐܫܬܐ ܕܪ̈ܓܐ: ܦܘܗܡܐ ܕܬܓܪܘܬܐ (business understanding)، ܦܘܗܡܐ ܕܝܗܝ̈ܒܬܐ، ܡܛܝܒܘܬܐ ܕܝܗܝ̈ܒܬܐ، ܒܢܝܢܐ ܕܡܘܕܝܠ، ܫܘܥܪܐ ܘܡܫܪܝܬܐ؛ "ܡܫܡܗܐ ܝܠܗ ܓܘ ܐܘܡܢܘܬܐ ܝܬܝܪ ܡܢ ܓܘ ܥܠܡܐ ܝܘܠܦܢܝܐ، ܘ-IBM ܫܩܠܠܗ̇ ܠܗ ܘܡܫܡܠܝܠܗ̇ ܠܗ ܓܘ ܬܘܟܢܝܬܐ" (ܦܐܬܐ 32). ܓܘ ܡܕܒܪܢܐ ܕܡܦܠܚܢܐ ܕܢܘܣܚܐ 19.0: "ܦܘܗܡܐ ܕܬܓܪܘܬܐ. ܐܗܐ ܡܨܝܐ ܕܗܘܝܐ ܕܪܓܐ ܡܘܚܡܐ ܡܢ ܟܠ ܓܘ data mining" (IBM Corporation, 2025, p. 23)، ܘ-stream – "ܣܕܪܐ ܕ-nodes… ܕܟܡܚܘܐ ܥܒ̈ܕܐ ܕܦܝܫܝ ܥܒܝ̈ܕܐ ܥܠ ܝܗܝ̈ܒܬܐ، ܟܕ ܐܣܘܪ̈ܐ ܒܝܢܝ nodes ܟܡܚܘܝ ܐܘܪܚܐ ܕܢܗܪܐ ܕܝܗܝ̈ܒܬܐ" (ܦܐܬܐ 31). ܩܐ ܒܘܨܝܬܐ، "ܦܘܗܡܐ ܕܬܓܪܘܬܐ" ܝܠܗ ܦܣܥܬܐ 1 ܕܦܣܩܐ 8 – ܢܝܫܐ، ܡܚܘܝܢܐ، ܣܪܛܐ ܕ-baseline – ܘܟܡܬܥܒܕ ܩܕܡ ܕܦܬܚܚ ܠܬܘܟܢܝܬܐ.

Stream، node ܒܬܪ node. Statistics File – ܟܩܪܐ ܦܐܝܠ sav ܬܪܝܨܐܝܬ (ܘܩܐ ܦܐܝܠ ܕܐܩܣܠ ܓܘ ܛܘܦܣܐ ܕܣܐܝܛ – node ܕ-Excel). Type – "ܩܐ ܚܙܝܐ ܘܫܘܚܠܦܐ ܕܕܪ̈ܓܐ ܕܡܫܘܚܬܐ (levels/scales of measurement) ܘܕܥܒ̈ܕܐ ܕ-fields": ܐܟܐ ܟܪܫܡܚ ܢܝܫܐ (Target)، ܡܢܒ̈ܝܢܐ (Input)، ܘܡܐ ܕܠܐ ܦܝܫܐ ܥܠܝܠܐ ܓܘ ܡܘܕܝܠ – ܡܢܝܢܐ ܡܦܪܫܢܐ (ID) ܕܡܫܬܘܬܦܢܐ، ܡܫܬܚܠܦܢܐ ܕܐܝܬܘܗܝ ܢܝܫܐ ܒܠܒܘܫܐ ܐܚܪܢܐ – ܐܝܟ None؛ ܐܗܐ ܝܠܗ ܦܣܥܬܐ 3 ܕܦܣܩܐ 8، ܘܐܗܐ ܝܠܗ ܕܘܟܬܐ ܕܓܘܗ̇ ܡܪܕܝܬܐ L2 ܟܡܬܟܠܝܐ ܝܢ ܟܥܠܠܐ. Partition – "ܝܘܠܦܢܐ، ܒܘܚܪܢܐ ܘܫܘܪܪܐ" ܒܡ̈ܢܘܬܐ ܕܟܡܥܠܚ (ܦܐܬܐ 87-88)، ܘܒܠܫܢܐ ܕܟܬܝ̈ܒܬܐ ܕ-IBM: "ܕܡܠܦܚ ܠܡܘܕܝܠ ܓܘ ܚܕ ܕܘܡܝܐ، ܕܒܚܪܚ ܘܡܬܩܢܚ ܠܡܘܕܝܠ ܓܘ ܕܘܡܝܐ ܬܪܝܢܐ، ܘܕܫܪܪܚ ܠܦܐܪ̈ܐ ܓܘ ܬܠܝܬܝܐ" (IBM Corporation, 2016b, p. 157)؛ ܚܙܝܡܘܢ (Note) ܠܫܡ̈ܗܐ: ܓܘ Modeler "ܒܘܚܪܢܐ" ܝܠܗ̇ ܓܘܕܐ ܬܪܝܢܝܬܐ، ܩܐ ܦܘܚܡܐ ܕܡܘܕܝ̈ܠܐ، ܘ"ܫܘܪܪܐ" – ܬܠܝܬܝܬܐ، ܩܐ ܡܫܘܚܬܐ ܐܚܪܝܬܐ، ܗܦܟܐ ܡܢ ܥܝܕܐ ܕ-Géron ܘܕܐܗܐ ܦܐܬܐ (ܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ، ܦܣܩܐ 2؛ ܠܘܚܐ 3.8 ܓܘ Truong، ܦܐܬܐ 85). ܩܐ ܕܘܡܝܐ ܕܚܕܟܡܐ ܡܐܐ، ܡܠܟܐ ܕ-Truong ܓܢܗ ܝܠܗ ܬܪܬܝܢ ܓܘ̈ܕܐ ܒܣ، 60-40 (ܦܐܬܐ 87) – ܘܫܘܪܪܐ ܡܚܠܦܢܐ، ܕܐܝܬܘܗܝ ܠܒܐ ܕܦܣܩܐ 9، ܠܝܠܗ ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-Modeler: ܓܘ Truong ܡܠܟܐ ܝܠܗ ܩܐ tuning ܕ-hyperparameters (ܦܐܬܐ 522)، ܐܢܐ ܟܠ ܡܬ̈ܠܐ ܓܘ ܟܬܒܐ ܟܡܬܡܫܚܝ ܥܠ ܚܕ ܦܘܠܓܐ. Nodes ܕܡܘܕܝ̈ܠܐ – ܡܢ ܓܘܕܐ Modeling: Logistic (ܣܪܛܐ ܕ-baseline ܘܐܦ ܡܬܩܪܒܢܐ)، C&R Tree ܘ-CHAID (tree؛ CHAID ܟܦܠܓ ܠܦܘܬ ܒܘܚܪܢܐ χ² ܘܟܡܨܐ split ܕܠܐ ܬܪܝܢ ܓܢ̈ܒܐ)، Neural Net، Random Forest ܘ-XGBoost Tree (forest ܘ-boosting – nodes ܕ-Python، ܕܣܢܝܩܝ ܠ-extension)، ܘ-Auto Classifier، ܕܟܡܪܗܛ ܚܕܟܡܐ ܐܠܓܘܪܝ̈ܬܡܐ ܘܟܡܛܟܣ ܠܗܘܢ – ܦܫܝܩܐ، ܥܡ ܫܪܛܐ ܕܡܐ ܕܟܡܛܟܣ ܠܦܘܬܗ ܡܚܘܝܢܐ ܕܦܣܥܬܐ 1 ܝܠܗ. ܩܐ node ܕ-forest ܐܝܬ "hyperparameter optimization، ܕܟܒܨܐ ܡܢ ܓܢܗ ܚܘܠܛܐ ܛܒܐ ܡܢ ܟܠ ܕܦܪܡܝ̈ܛܪܐ ܩܐ ܕܒܨܪ ܡܢܬܐ ܕܛܥܝܘܬܐ ܥܠ ܕܘ̈ܡܝܐ" (ܦܐܬܐ 499) – ܐܗܐ ܝܠܗ ܦܣܥܬܐ 5، ܐܢܐ ܚܙܝܡܘܢ ܥܠ ܐܝܢܝ ܕܘ̈ܡܝܐ: ܐܢ ܥܠ ܓܘܕܐ ܕ"ܒܘܚܪܢܐ" ܕ-Modeler، ܐܗܝ ܗܘܝܠܗ̇ ܓܘܕܐ ܕܫܘܪܪܐ (validation set)، ܘܐܗܐ ܛܒܐ ܝܠܗ – ܐܝܡܢ ܕܡܫܘܚܬܐ ܐܚܪܝܬܐ ܥܠ "ܫܘܪܪܐ" ܝܠܗ̇. ܟܬܒܐ ܕܝܘܠܦܢܐ ܝܘܠܦܢܝܐ ܕ-Modeler ܟܡܠܟ "70-80% ܡܢ ܝܗܝ̈ܒܬܐ ܩܐ ܓܘܕܐ ܕܝܘܠܦܢܐ ܘܫܪܟܐ ܩܐ ܓܘܕܐ ܕܒܘܚܪܢܐ" ܘܕܦܣܩܚ ܠܙܪܥܐ ܓܘ node ܕ-Partition "ܩܐ ܕܫܩܠܚ ܐܦ ܗܘ ܡܘܕܝܠ ܓܘ ܟܠ ܪܗܛܐ" (Wendler & Gröttrup, 2021, p. 826) – ܘܥܠ ܓܘܒܝܐ ܕܡܘܕܝܠ، ܡܐ ܕܐܗܐ ܦܐܬܐ ܟܐܡܪܐ ܓܘ ܦܣܩܐ 5: "ܠܝܬ ܐܘܪܚܐ ܕܛܒܬܐ ܝܠܗ̇ ܡܢ ܟܠ ܡܘܕܝܠ ܐܚܪܢܐ ܩܐ ܟܠ ܙܢܐ ܕܝܗܝ̈ܒܬܐ ܘܥܘܩܢܐ ܕܦܘܪܫܐ ܠܓܢ̈ܣܐ… ܣܓܝ ܟܡܠܟܚ ܕܢܣܝܬܘܢ ܐܘܪ̈ܚܬܐ ܦܪ̈ܝܫܬܐ ܥܠ ܟܠ ܛܟܣܐ ܕܝܗܝ̈ܒܬܐ" (ܦܐܬܐ 760). ܟܠ node ܕܡܘܕܝܠ ܟܦܠܛ "nugget" (nugget) – ܡܘܕܝܠ ܡܠܦܐ – ܕܟܐܣܪܚ ܠܗ ܥܡ ܝܗܝ̈ܒܬܐ. Analysis (ܡܢ ܓܘܕܐ Output) – "ܟܡܨܐ ܕܫܥܪܚ ܚܝܠܐ ܕܡܘܕܝܠ ܕܝܗܒ ܡܢܒܝ̈ܢܘܝܬܐ ܚܬܝ̈ܬܐ" ܒܦܘܚܡܐ "ܒܝܢܝ ܛܝ̈ܡܐ ܡܢܒ̈ܝܐ ܘܛܝ̈ܡܐ ܫܪܝܪ̈ܐ" (IBM Corporation, 2016b, p. 276)، ܓܘ Truong "ܟܦܚܡ ܥܒܕܐ ܕܡܘܕܝܠ ܒܝܢܝ ܕܘܡܝܐ ܕܝܘܠܦܢܐ ܘܕܘܡܝܐ ܕܒܘܚܪܢܐ" (ܦܐܬܐ 231): ܟܪܫܡܚ Coincidence matrices (confusion matrix)، Performance evaluation، Evaluation metric (AUC and Gini) ܘ-Separate by partition (ܦܐܬܐ 377)، ܘܡܢܗ ܟܫܩܠܚ ܚܬܝܬܘܬܐ، ܡܢܬܐ ܕܦܘܪܫܐ ܛܥܝܐ، Gini ܘ-AUC ܩܐ ܟܠ ܓܘܕܐ؛ "ܪܓܝܫܘܬܐ، ܝܚܝܕܝܘܬܐ ܘ-F1 ܡܨܝܚ ܚܫܒܚ ܠܗܘܢ ܡܢ confusion matrix" (ܦܐܬܐ 300) – ܒܝܚܕܝܘܬܘܟܘܢ، ܓܘ ܡܚܫܒܢܐ (calculator). ܘ-Evaluation (ܡܢ ܓܘܕܐ Graphs) – "ROC curves ܘ-Lift curves ܩܐ ܟܠ ܡܘܕܝ̈ܠܐ" ܚܕ ܥܠ ܚܕ (ܦܐܬܐ 502). ܐܡܢ ܕܟܠ nuggets ܐܣܝܪ̈ܐ ܝܢܐ ܒܫܫܠܬܐ ܥܡ ܐܦ ܐܢܝ ܝܗܝ̈ܒܬܐ، ܚܕ node ܕ-Analysis ܟܦܚܡ ܟܠܗܘܢ – ܐܗܐ ܝܠܗ ܠܘܚܐ ܕܦܣܥܬܐ 4 ܕܦܣܩܐ 8.

ܘܡܐ ܕܪܫܝܡܬܐ (Menu) ܠܐ ܟܥܒܕܐ ܩܐ ܕܝܘܟܘܢ. ܬܚܘܡܐ ܕܦܘܪܫܐ: ܓܘܒܝܐ ܡܩܕܡܐ ܕ-nugget 0.5 ܝܠܗ، ܘܡܐ ܕܦܣܩܐ 9 ܥܒܕܠܗ ܒܚܕ ܣܕܪܐ ܕ-pROC ܐܟܐ ܟܡܬܥܒܕ ܓܘ node Derive ܥܠ field ܕܡܣܬܒܪܢܘܬܐ ܕ-nugget ܟܡܘܣܦ ܓܢܒ ܡܢܒܝܢܘܬܐ – ܝܢ ܓܘ cost matrix ܓܘ ܬܘܩ̈ܢܐ ܕ-node ܕܡܘܕܝܠ، ܕܐܝܬܘܗܝ cost-sensitive learning ܕ-Truong (ܦܐܬܐ 203-204). ܓܢܣܐ ܙܥܘܪܐ: ܐܝܬ node SMOTE ܘܐܝܬ Balance، ܘܬܪܘܝܗܝ ܟܐܬܝ ܒܬܪ Partition، ܠܐ ܩܕܡܗ – ܘܛܒܐ ܝܠܗ ܕܠܐ ܐܢܝ (ܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ، ܦܣܩܐ 1). ܬܠܝܘܬܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ: ܠܝܬ ܓܘ Partition ܦܘܠܓܐ ܠܦܘܬ ܓܘܕܐ؛ ܓܘ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ ܝܢ ܓܘ ܡܕܪ̈ܫܝܬܐ ܟܦܠܓܝܬܘܢ ܒܝܚܕܝܘܬܘܟܘܢ (node Derive ܥܠ ܡܢܝܢܐ ܡܦܪܫܢܐ ܕܓܘܕܐ، ܘܒܬܪܗ Select)، ܝܢ ܟܐܙܠܝܬܘܢ ܠܦܣܩܐ 9. ܘܬܘܢܝܐ: node Analysis ܟܝܗܒ ܡܢܝ̈ܢܐ؛ ܡܐ ܟܬܢܚ ܘܡܐ ܠܐ – ܬܡܢ، ܦܣܩܐ 7، ܥܡ ܠܘܚܐ ܕ-configurations ܕܨܚܚܐ 11 ܓܘ Truong، ܕܐܝܬܘܗܝ ܐܘܪܚܐ ܕܟܬܒܚ stream ܕܠܝܬ ܠܗ ܪܡܙܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܛܥܝ̈ܘܬܐ ܕܫܘܪܪܐ – ܚܬܝܬܘܬܐ ܟܠܢܝܬܐ ܥܠ ܓܢܣܐ ܙܥܘܪܐ، ܡܛܝܒܘܬܐ ܥܠ ܟܠ ܝܗܝ̈ܒܬܐ ܩܕܡ ܦܘܠܓܐ، ܦܘܠܓܐ ܠܦܘܬ ܣܕܪܐ ܒܕܘܟܬܐ ܕܠܦܘܬ ܡܫܬܘܬܦܢܐ، tuning ܥܠ ܓܘܕܐ ܕܒܘܚܪܢܐ، ܡܢܝܢܐ ܕܠܐ ܦܪܣܐ ܘܕܠܐ ܣܪܛܐ ܕ-baseline – ܓܘ ܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ. ܐܟܐ – ܛܥܝ̈ܘܬܐ ܕܡܘܕܝ̈ܠܐ ܓܢܗܘܢ.

ܕܩܪܝܬܘܢ feature importance ܐܝܟ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ. "ܡܥܠܬܐ ܝܠܗ̇ ܡܢܒܝܢܐ ܡܘܚܡܐ ܡܢ ܟܠ" – ܐܝܢ؛ "ܡܥܠܬܐ ܟܡܪܒܝܐ ܠܣܟܘܝܐ" – forest ܠܐ ܐܡܪܠܗ. importance ܠܝܠܗ̇ ܐܘܪܚܐ ܘܠܝܠܗ̇ ܥܠܬܐ؛ ܘܡܢܝܢܐ ܡܫܘܬܦܐ ܟܪܝܐ ܓܘ lasso regression ܠܝܠܗ ܫܘܥܪܐ ܕܠܐ ܡܣܒ ܒܐܦ̈ܐ (unbiased) ܕܡܥܒܕܢܘܬܐ.

ܕܬܢܝܬܘܢ ܚܕ tree ܐܝܟ ܡܫܟܚܢܘܬܐ. ܝܘܠܦܢܐ ܡܢ ܪܝܫ ܥܠ ܐܦ ܐܢܝ ܝܗܝ̈ܒܬܐ ܡܨܝܐ ܕܝܗܒ tree ܐܚܪܢܐ (ܨܚܚܐ 6). tree ܨܘܪܬܐ ܝܠܗ̇ ܕܡܘܕܝܠ، ܠܐ ܕܫܪܪܐ؛ ܩܝܡܐ ܝܠܗ forest – ܘܐܗܘ ܠܐ ܝܠܗ ܨܝܪܐ.

ܕܓܒܝܬܘܢ k ܠܦܘܬ inertia. ܓܘ ܥܢܩܘ̈ܕܐ (clusters)، inertia ܟܠܝܘܡ ܟܢܚܬܐ ܐܡܢ ܕܟܡܘܣܦܚ ܥܢܩܘ̈ܕܐ؛ k ܟܡܬܓܒܐ ܒ-"elbow"، ܒ-silhouette score، ܒ-gap statistic (ܝܘܠܦܢܐ ܕܠܐ ܡܕܒܪܢܐ، ܦܣܩܐ 5) – ܘܒܩܪܝܢܐ ܕܥܢܩܘ̈ܕܐ ܓܢܗܘܢ. ܘܕܠܐ standardization ܩܕܡ ܥܢܩܘ̈ܕܐ "ܟܡܬܡܬܚܝ" ܘ-k-means ܟܦܠܚ ܒܝܫܐܝܬ (ܨܚܚܐ 9).

ܪܫܝܡܬܐ ܕܒܘܚܪܢܐ (checklist) – ܩܕܡ ܕܬܢܚ ܦܐܪܐ ܕܡܢܒܝܢܘܬܐ

ܡܒܘ̈ܥܐ

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