ܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ: ܐܝܟܢ ܟܝܕܥܚ ܕܡܘܕܝܠ ܛܒܐ ܝܠܗ

ܡܕܒܪܢܐ (guide)

ܡܐ ܐܝܬ ܓܘ ܐܗܐ ܦܐܬܐ (On this page)

ܡܘܕܝܠ ܕܡܢܒܝܢܘܬܐ (prediction model) ܟܫܪܪ ܒܚܕ ܐܘܪܚܐ ܒܣ – ܥܠ ܝܗܝ̈ܒܬܐ ܕܠܐ ܚܙܐ. ܦܐܬܐ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ ܟܡܦܫܩܐ ܡܘܕܝ ܝܠܗ ܦܘܪܫܢܐ ܒܝܢܝ ܡܘܕܝܠ ܕܟܡܦܫܩ ܘܡܘܕܝܠ ܕܟܡܢܒܐ، ܡܘܕܝ ܝܢܐ ܡܘܕ̈ܝܠܐ ܘܐܝܟܢ ܟܒܢܚ ܦܪܘܝܩܛ؛ ܐܗܐ ܦܐܬܐ ܥܣܝܩܐ ܝܠܗ ܒܚܕ ܫܘܐܠܐ ܕܟܠ ܬܘܢܝܐ ܥܠ ܡܘܕܝܠ ܕܐܗܐ ܙܢܐ ܟܩܐܡ ܝܢ ܟܢܦܠ ܥܠܘܗܝ: ܡܢ ܐܝܟܐ ܝܠܗ ܡܢܝܢܐ. ܐܪܒܥܐ ܫܘ̈ܐܠܐ ܙܥܘܪ̈ܐ، ܒܛܟܣܐ ܕܟܩܝܡܝ: ܐܝܢܐ ܡܚܘܝܢܐ (1) – ܡܛܠ ܕ"ܚܬܝܬܘܬܐ" (accuracy) ܣܓܝ ܓܗ̈ܐ ܝܠܗ̇ ܡܚܘܝܢܐ ܠܐ ܬܪܝܨܐ؛ ܥܠ ܐܝܢܐ ܝܗܝ̈ܒܬܐ (2) – ܝܘܠܦܢܐ (training)، ܫܘܪܪܐ (validation) ܘܒܘܚܪܢܐ (test)، ܘܩܐ ܡܘܕܝ ܓܘܕܐ ܕܒܘܚܪܢܐ ܦܪܝܫܬܐ ܝܠܗ̇ ܩܕܡ ܟܠ ܡܕܡ؛ ܐܝܟܢ ܟܫܩܠܚ ܠܐ ܒܣ ܡܢܝܢܐ ܐܠܐ ܨܐ ܚܬܝܬܘܬܐ ܕܝܠܗ (3) – ܫܘܪܪܐ ܡܚܠܦܢܐ (cross-validation)؛ ܘܡܘܕܝ ܡܨܐ ܕܗܘܐ ܡܢܝܢܐ ܒܟܠܗ (4) – ܡܣܒ ܒܐܦ̈ܐ (bias)، ܫܘܚܠܦܐ (variance)، ܘܛܥܝܘܬܐ ܕ-Bayes، ܬܚܘܡܐ ܕܚܕ ܡܘܕܝܠ ܠܐ ܢܚܬ ܠܬܚܬܗ. ܘܒܬܪܟܐ ܬܪܬܝܢ ܐܘܪ̈ܚܬܐ ܕܒܓܘܝܗܝ ܡܢܝܢܐ ܟܗܘܐ ܕܓܠܬܐ ܕܠܐ ܕܚܕ ܢܟܠ: ܡܪܕܝܬܐ ܕܝܗܝ̈ܒܬܐ (data leakage) (5)، ܘܡܫܬܘܬܦ̈ܢܐ ܕܠܐ ܝܢܐ ܠܐ ܬܠܝ̈ܐ ܚܕ ܒܚܕ – ܒ̈ܢܝܐ ܕܒܝܬܐ، ܣܕܪ̈ܐ ܕܡܕܪܫܬܐ، ܡܨܝ̈ܕܬܐ – ܕܦܘܠܓܐ ܫܚܝܡܐ ܠܝܘܠܦܢܐ ܘܠܒܘܚܪܢܐ ܠܐ ܟܚܫܒ ܠܗܘܢ (6). ܦܣܩܐ 7 ܟܡܗܦܟ ܟܠ ܡܕܡ ܠܦܣܩܐ ܕܬܘܢܝܐ. ܡܒܘ̈ܥܐ ܝܢܐ ܐܪܒܥܐ ܟܬ̈ܒܐ ܕܝܘܠܦܢܐ ܕܦܐܬܐ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ – Géron (2022)، Hastie، Tibshirani ܘ-Friedman (2009)، Bishop (2006)، Ishii ܘܚܒܪ̈ܘܗܝ (2026) – ܘܬܠܬܐ ܡܐܡܪ̈ܐ ܕܟܬܝܒ̈ܐ ܝܢܐ ܩܐ ܒܨܘ̈ܝܐ: ܥܠ ܡܪܕܝܬܐ (Kapoor & Narayanan, 2023)، ܥܠ ܬܚܘ̈ܡܐ ܕܡܢܒܝܢܘܬܐ (Salganik et al., 2020) ܘܥܠ ܦܘܪܫܢܐ ܒܝܢܝ ܫܘܪܪܐ ܕܡܘܕܝܠ ܡܦܫܩܢܐ ܘܫܘܪܪܐ ܕܡܘܕܝܠ ܡܢܒܝܢܐ (Shmueli, 2010)؛ ܘܩܐ ܦܣܩܐ 6 – ܟܬܒܐ ܫܬܐܣܝܐ ܕܝܘܠܦܢܐ ܐܣܘܪܝܐ (relational learning) (Getoor & Taskar, 2007). ܘܡܒܘܥܐ ܚܡܝܫܝܐ، ܡܢ ܓܢܒܐ ܕܦܪܘܓܪܡ (software): ܟܬܒܐ ܕܝܘܠܦܢܐ ܕ-Truong (2026) ܩܐ SPSS Modeler، ܕܟܬܝܒܐ ܝܠܗ "ܩܐ ܝܠܘ̈ܦܐ ܡܢ ܚܩܠ̈ܐ ܠܐ ܛܟܢܝܩ̈ܝܐ ܘܩܐ ܒܨܘ̈ܝܐ ܡܕܪ̈ܒܐ ܐܟܚܕܐ" – ܘܟܐܡܪ ܐܝܟܢ ܐܢܝ ܚܙ̈ܝܬܐ ܓܢܝܗܝ ܟܡܬܩܪܝܢ ܓܘ ܪܫܝ̈ܡܬܐ ܕ-IBM، ܡܘܕܝ ܟܥܒܕ ܦܪܘܓܪܡ ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ، ܘܐܝܟܢ ܟܟܬܒܚ ܬܘܢܝܐ. ܘܡܘܕܝ ܟܗܘܐ ܐܝܡܢ ܕܠܝܬ ܡܫܬܚܠܦܢܐ ܬܠܝܐ ܒܟܠܗ – ܘܡܛܠ ܗܕܟܐ ܠܝܬ ܡܚܘܝܢܐ – ܓܘ ܝܘܠܦܢܐ ܕܠܐ ܡܕܒܪܢܐ.

1. ܡܚܘܝܢܐ: ܠܦܘܬ ܦܘܠܚܢܐ ܘܠܦܘܬ ܚܘܣܪܢܐ ܕܛܥܝܘܬܐ

ܡܚܘܝܢܐ ܓܒܝܐ ܝܠܗ ܒܫܘܪܝܐ ܕܦܪܘܝܩܛ، ܠܐ ܒܚܪܬܗ – ܡܛܠ ܕܗܘ ܟܦܣܩ ܐܝܢܐ ܡܘܕܝܠ "ܛܒܐ" ܝܠܗ (Géron, 2022, Chapter 2, "Select a Performance Measure"). ܩܐ ܪܝܓܪܫܢ – RMSE، ܫܪܫܐ ܕܡܨܥܝܬܐ ܕܡܪ̈ܒܥܐ ܕܛܥ̈ܝܘܬܐ، ܒܡܫܘ̈ܚܬܐ ܕܢܝܫܐ، ܕܟܝܗܒ ܡܬܩܠܐ ܪܡܐ ܠܛܥ̈ܝܘܬܐ ܪ̈ܒܐ؛ ܝܢ MAE، ܡܨܥܝܬܐ ܕܛܥ̈ܝܘܬܐ ܫܪܝܪ̈ܬܐ (absolute)، ܐܝܡܢ ܕܐܝܬ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܣܓܝ̈ܐܐ. ܩܐ ܦܘܪܫܐ ܠܓܢ̈ܣܐ – ܐܟܐ ܟܫܪܐ ܥܩܬܐ. ܨܚܚܐ 3 ܕ-Géron ܟܡܝܠܦ ܡܘܕܝܠ ܕܦܘܪܫܐ ܕܬܪܝܢ ܛܝ̈ܡܐ ܩܐ ܡܫܬܘܕܥܢܘܬܐ ܕܡܢܝܢܐ 5 ܓܘ ܨܘܪ̈ܬܐ ܕܡܢܝ̈ܢܐ ܒܟܬܒܬ ܐܝܕܐ: ܫܘܪܪܐ ܡܚܠܦܢܐ ܟܡܚܘܐ ܚܬܝܬܘܬܐ ܟܠܢܝܬܐ (accuracy، ܡܢܬܐ ܕܦܘܪ̈ܫܐ ܬܪ̈ܝܨܐ) ܠܥܠ ܡܢ 95% ܓܘ ܟܠ ܡܢܬܐ (fold). ܘܒܬܪܟܐ ܡܘܕܝܠ ܕܦܘܪܫܐ ܣܦܝܩܐ (dummy classifier) ܕܟܐܡܪ ܥܠ ܟܠ ܨܘܪܬܐ "ܠܐ 5" – ܘܟܫܩܠ ܠܥܠ ܡܢ 90%، ܡܛܠ ܕܒܣ ܩܪܝܒ ܚܕ ܡܢ ܥܣܪܐ ܡܢ ܨܘܪ̈ܬܐ ܝܢܐ 5. "ܟܙܟܐ ܠ-Nostradamus." ܫܘܠܡܐ: "ܚܬܝܬܘܬܐ ܠܐ ܝܠܗ̇ ܒܥܕܢܐ ܫܚܝܡܐ ܡܚܘܝܢܐ ܕܥܒܕܐ ܓܒܝܐ ܩܐ ܡܘܕ̈ܝܠܐ ܕܦܘܪܫܐ، ܒܝܚܝܕܝܘܬܐ ܐܝܡܢ ܕܥܣܝ̈ܩܐ ܝܘܬܚ ܒܛܘ̈ܟܣܐ ܕܝܗܝ̈ܒܬܐ ܠܐ ܫܘ̈ܝܐ" (Chapter 3, "Performance Measures") – ܘܛܘ̈ܟܣܐ ܕܒܘܨܝܐ ܕܟܢܫܐ ܩܪܝܒ ܟܠܙܒܢ ܠܐ ܫܘ̈ܝܐ ܝܢܐ: ܫܒܩܬܐ ܕܡܕܪܫܬܐ، ܥܘܠܐ، ܒܛܝܠܘܬܐ، ܩܠܐ ܩܐ ܓܒܐ ܙܥܘܪܐ. Bishop ܟܡܝܬܐ ܐܗܘ ܡܬܠܐ ܓܢܗ ܡܢ ܐܣܝܘܬܐ: ܣܪܛܢܐ ܓܘ 1 ܡܢ ܟܠ 1,000 ܨܘܪ̈ܬܐ ܕܪܢܛܓܢ – "ܡܘܕܝܠ ܕܦܘܪܫܐ ܕܟܡܣܡܟ ܟܠ ܢܘܩܙܐ ܠܓܢܣܐ ܢܘܪܡܠܝܐ ܟܡܛܐ ܡܢ ܩܕܡ ܠ-99.9% ܚܬܝܬܘܬܐ، ܘܥܣܩܐ ܟܗܘܐ ܠܡܬܦܠܛܐ ܡܢ ܐܗܐ ܫܪܝܐ ܦܫܝܛܐ"؛ ܫܪܝܐ ܕܝܠܗ ܝܠܗ ܝܘܠܦܢܐ ܥܠ ܛܘܟܣܐ ܫܘܝܐ ܘܒܬܪܟܐ ܬܘܪܨܐ ܕܡܣܬܒܪܢ̈ܘܝܬܐ ܠܦܘܬ ܡܢܘ̈ܬܐ ܕܓܢ̈ܣܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ (Bishop, 2006, p. 45).

ܡܐܛܪܝܟܣ ܕܫܓܘܫܝܐ (confusion matrix) ܝܠܗ ܡܐܢܐ: ܣܕܪ̈ܐ – ܓܢܣܐ ܫܪܝܪܐ، ܥܡܘ̈ܕܐ – ܓܢܣܐ ܡܢܒܝܐ؛ ܓܘ ܡܬܠܐ ܕ-Géron 53,892 ܕܒܨܪܐ ܫܪܝܪ̈ܐ، 687 ܕܙܘܕܐ ܛܥ̈ܝܐ (ܛܥܝܘܬܐ ܕܙܢܐ I)، 1,891 ܕܒܨܪܐ ܛܥ̈ܝܐ (ܛܥܝܘܬܐ ܕܙܢܐ II) ܘ-3,530 ܕܙܘܕܐ ܫܪܝܪ̈ܐ – ܘܗܝ ܚܫܝܒܬܐ ܝܠܗ̇ ܥܠ ܡܢܒܝܢ̈ܘܝܬܐ "ܕܟ̈ܝܬܐ"، ܠܒܪ ܡܢ ܕܘܡܝܐ، ܕܡܘܕܝܠ ܝܗܒܠܗܘܢ ܠܚܙ̈ܝܬܐ ܕܠܐ ܚܙܐ ܓܘ ܝܘܠܦܢܐ. ܡܢܗ̇ ܟܡܬܦܩܝ precision ("ܚܬܝܬܘܬܐ ܕܙܘܕܐ": ܐܝܡܢ ܕܡܘܕܝܠ ܟܐܡܪ 5 – ܒܐܝܢܐ ܡܢܬܐ ܗܘ ܬܪܝܨܐ ܝܠܗ؛ 83.7%) ܘܪܓܝܫܘܬܐ (recall: ܐܝܢܐ ܡܢܬܐ ܡܢ 5 ܫܪܝܪ̈ܐ ܗܘ ܟܐܚܕ؛ 65.1%)، ܘ-F1 – ܡܨܥܝܬܐ ܗܪܡܘܢܝܬܐ (harmonic mean) ܕܬܪܘܝܗܝ (.73)، ܕܪܡܐ ܝܠܗ ܒܣ ܐܝܡܢ ܕܬܪܘܝܗܝ ܪ̈ܡܐ ܝܢܐ. ܘܐܝܢܐ ܡܢܝܗܝ ܚܫܝܚܐ ܝܠܗ – ܐܗܐ ܫܘܐܠܐ ܝܠܗ ܕܚܘܣܪܢܐ ܕܛܥܝܘܬܐ، ܠܐ ܕܣܛܐܛܝܣܛܝܩܐ: ܡܨܠܠܢܐ ܕܒܝܕܝܘ̈ܐ ܩܐ ܝܠܘ̈ܕܐ ܣܢܝܩܐ ܝܠܗ ܠ-precision ܪܡܐ ܐܦܢ ܒܚܘܣܪܢܐ ܕܪܓܝܫܘܬܐ ܢܚܝܬܬܐ؛ ܡܫܟܚܢܐ ܕܓܢܒ̈ܐ ܓܘ ܚܢܘܬܐ ܡܨܐ ܕܣܦܩ ܒ-30% precision ܐܢ ܪܓܝܫܘܬܐ 99% ܝܠܗ̇. ܬܪܘܝܗܝ ܟܡܚܠܦܝ ܚܕ ܒܚܕ ܒܝܕ ܬܚܘܡܐ ܕܦܘܪܫܐ: ܡܪܡܝܬܐ ܕܬܚܘܡܐ ܟܡܪܡܐ precision ܘܟܡܢܚܬܐ ܪܓܝܫܘܬܐ (Chapter 3, "The Precision/Recall Trade-off"). ܣܪܛܐ ܟܦܝܦܐ ROC ܟܡܚܘܐ ܪܓܝܫܘܬܐ ܩܘܒܠ ܡܢܬܐ ܕܕܙܘܕܐ ܛܥ̈ܝܐ ܥܠ ܟܠ ܬܚܘ̈ܡܐ، ܘܫܛܝܚܘܬܐ ܬܚܘܬܗ (AUC) – 1 ܩܐ ܡܘܕܝܠ ܕܦܘܪܫܐ ܓܡܝܪܐ، 0.5 ܩܐ ܓܕܫܢܝܐ – ܟܦܚܡܐ ܡܘܕ̈ܝܠܐ ܕܦܘܪܫܐ ܕܠܐ ܓܘܒܝܐ ܕܬܚܘܡܐ؛ ܐܠܐ ܓܘ ܓܢܣܐ ܢܕܝܪܐ ROC ܟܡܫܒܚ ܒܙܘܕܐ، ܘ"ܐܝܟ ܢܡܘܣܐ ܕܨܒܥܐ، ܓܪܓ ܕܓܒܚ ܣܪܛܐ ܟܦܝܦܐ PR ܟܠ ܓܗܐ ܕܓܢܣܐ ܕܙܘܕܐ ܢܕܝܪܐ ܝܠܗ ܝܢ ܐܝܡܢ ܕܒܙܘܕܐ ܚܫܝܚܝ ܩܐܠܘܟܘܢ ܕܙܘܕܐ ܛܥ̈ܝܐ ܡܢ ܕܒܨܪܐ ܛܥ̈ܝܐ" (Chapter 3, "The ROC Curve"). ܠܣܪܛܐ ܟܦܝܦܐ ܒܓܢܗ – ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܩܐ ܫܛܝܚܘܬܐ، ܬܚܘܡܐ ܕܦܘܪܫܐ ܠܦܘܬ ܡܚܘܝܢܐ ܕ-Youden، ܪܓܝܫܘܬܐ ܘܝܚܝܕܝܘܬܐ ܓܘ ܟܠ ܬܚܘܡܐ ܘܦܘܚܡܐ ܒܝܢܝ ܡܚܘ̈ܝܢܐ – ܟܚܫܒܚ ܓܘ ܦܐܬܐ ܦܘܫܩܐ ROC. ܡܢ ܕܟܝܕܥ ܠܘܚܐ ܕܦܘܪܫܐ ܠܓܢ̈ܣܐ ܓܘ SPSS ܟܝܕܥ ܠܬܚܘܡܐ 0.5 ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ ܕܚܕ ܠܐ ܟܡܫܚܠܦ ܠܗ؛ ܐܟܐ ܗܘ ܦܘܣܩܢܐ ܝܠܗ ܕܟܡܬܢܚ ܠܗ.

ܓܢܣܐ ܢܕܝܪܐ: ܡܘܕܝ ܟܥܒܕܚ – ܘܡܘܕܝ ܠܐ. Truong ܟܡܛܟܣ ܐܣܘ̈ܬܐ ܠܦܘܬ ܛܟܣܐ ܕܩܕܡܝܘܬܐ: ܩܕܡܝܐ ܡܚܘ̈ܝܢܐ ܣܓܝ̈ܐܐ ܒܕܘܟܬ ܚܬܝܬܘܬܐ ܟܠܢܝܬܐ، ܒܬܪܟܐ ܦܘܠܓܐ ܘܫܘܪܪܐ، ܒܬܪܟܐ ܝܘܠܦܢܐ ܪܓܝܫܐ ܠܚܘܣܪܢܐ (cost-sensitive learning) – ܘܒܣ "ܐܢ ܐܘܪ̈ܚܬܐ ܕܩܕܡ ܠܐ ܟܫܪܝ ܒܚܝܠܐ ܥܩ̈ܬܐ ܕܠܐ ܫܘܝܘܬܐ ܘܐܝܬ ܙܕܥܬܐ ܕܡܘܕ̈ܝܠܐ ܕܝܠܢ ܠܐ ܝܢܐ ܬܪ̈ܝܨܐ، ܓܘܒܝܐ ܕܕܘܡܝܐ ܡܢ ܪܝܫ ܟܗܘܐ ܓܘܒܝܐ ܦܫܝܛܐ" (Truong, 2026, pp. 78-79). ܝܘܠܦܢܐ ܪܓܝܫܐ ܠܚܘܣܪܢܐ ܝܠܗ ܢܘܣܚܐ ܪܫܡܝܐ ܕ"ܚܘܣܪܢܐ ܕܛܥܝܘܬܐ": ܡܐܛܪܝܟܣ ܕܦܘܣܩܢܐ ܕܒܓܘܗ ܩܐ ܟܠ ܛܥܝܘܬܐ ܐܝܬ ܚܘܣܪܢܐ – C(FN) ܩܐ ܦܠܛܬܐ، C(FP) ܩܐ ܙܘܗܪܐ ܕܓܠܬܐ – ܘܡܘܕܝܠ ܓܒܝܐ ܝܠܗ ܐܗܘ ܕܓܘܡܪܐ ܕܚܘܣܪܢܐ ܕܝܠܗ، C(FP) × FP + C(FN) × FN، ܢܚܝܬܐ ܝܠܗ ܡܢ ܟܠ، ܠܐ ܐܗܘ ܕܡܢܬܐ ܕܛܥܝܘܬܐ ܕܝܠܗ ܢܚܝܬܬܐ ܝܠܗ̇ ܡܢ ܟܠ؛ "ܣܓܝܐܐ ܡܢ ܦܪܘܓܪ̈ܡܐ ܐܝܬ ܓܘܝܗܝ ܓܘܒܝܐ ܕܡܥܠܬܐ ܕܡܐܛܪܝܟܣ ܕܦܘܣܩܢܐ" (ܦܐܬܐ 203-204). ܘܐܦ ܓܘܒܝܐ ܝܬܝܪܐ ܕܕܘܡܝܐ (oversampling) ܕܓܢܣܐ ܢܕܝܪܐ (ܢܣܚܐ ܕܚܙ̈ܝܬܐ، ܝܢ SMOTE – ܚܙ̈ܝܬܐ ܡܬܒܢ̈ܝܬܐ ܒܝܢܝ ܫܒܒ̈ܐ ܩܪܝܒ̈ܐ) ܘܓܘܒܝܐ ܒܨܝܪܐ ܕܕܘܡܝܐ (undersampling) ܕܓܢܣܐ ܕܣܓܝ ܡܬܚܙܐ – ܕܥܠ ܩܕܡܝܐ Truong ܒܓܢܗ ܟܡܥܝܪ ܕ"ܢܣܚܐ ܕܝܗܝ̈ܒܬܐ ܟܥܒܕ ܠܡܘܕ̈ܝܠܐ ܡܛܝ̈ܢܐ ܒܙܘܕܐ ܠܦܐܝܘܬܐ ܝܬܝܪܬܐ" (ܦܐܬܐ 79) – ܒܚܝܪ̈ܐ ܝܢܐ ܒܕܡܘܬܐ (simulation) ܥܠ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ: ܬܠܬܝܗܝ "ܝܗܒܠܗܘܢ ܡܘܕ̈ܝܠܐ ܕܟܝܠܐ ܕܝܠܗܘܢ ܒܝܫܐ ܝܠܗ (poorly calibrated): ܡܣܬܒܪܢܘܬܐ ܕܗܘܝܬܐ ܓܘ ܓܢܣܐ ܕܙܥܘܪܘܬܐ ܫܥܝܪܬܐ ܝܠܗ̇ ܒܙܘܕܐ ܣܓܝ"، ܠܐ ܡܪܡܝܠܗܘܢ AUC ܩܘܒܠ ܡܘܕܝܠ ܕܠܐ ܬܘܪܨܐ، ܘܠܫܘܝܘܬܐ ܒܝܢܝ ܪܓܝܫܘܬܐ ܘܝܚܝܕܝܘܬܐ ܕܡܛܝܠܗܘܢ ܠܗ̇ "ܡܨܝܐ ܗܘܐ ܕܡܛܝܚ ܠܗ̇ ܗܕܟܐ ܨܐ ܒܫܘܢܝܐ ܕܬܚܘܡܐ ܕܡܣܬܒܪܢܘܬܐ ܒܕܘܟܬܐ"؛ ܫܘܠܡܐ – "ܠܐ ܫܘܝܘܬܐ ܓܘ ܦܐܪܐ ܠܐ ܝܠܗ̇ ܥܩܬܐ ܒܓܢܗ̇، ܘܬܘܪܨܐ ܕܠܐ ܫܘܝܘܬܐ ܡܨܐ ܕܡܒܝܫ ܐܦ ܥܒܕܐ ܕܡܘܕܝܠ" (van den Goorbergh et al., 2022, ܟܢܘܫܝܐ). ܬܪܬܝܢ ܩܪܝ̈ܢܬܐ ܟܫܠܡܝ: ܓܢܣܐ ܢܕܝܪܐ ܥܩܬܐ ܝܠܗ̇ ܕܡܚܘܝܢܐ ܘܕܬܚܘܡܐ ܕܦܘܪܫܐ، ܠܐ ܕܝܗܝ̈ܒܬܐ. ܒܨܘܝܬܐ ܕܣܢܝܩܬܐ ܝܠܗ̇ ܠܡܣܬܒܪܢ̈ܘܝܬܐ – ܩܐ ܡܢܝܢܐ ܕܣܘܟܢܐ، ܩܐ ܬܘܢܝܐ – ܠܐ ܟܡܫܘܝܐ؛ ܐܝܗܝ ܕܟܡܫܘܝܐ ܐܦܢ ܗܕܟܐ، ܟܥܒܕܐ ܗܕܟܐ ܒܣ ܓܘ ܡܢܬܐ ܕܝܘܠܦܢܐ (ܡܪܕܝܬܐ L1.2، ܦܣܩܐ 5) ܘܟܡܬܢܝܐ ܕܡܣܬܒܪܢ̈ܘܝܬܐ ܕܡܘܕܝܠ ܟܡܦܩ ܠܐ ܝܢܐ ܡܣܬܒܪܢ̈ܘܝܬܐ ܒܬܪ ܐܗܐ. ܟܬܒܐ ܕܝܘܠܦܢܐ ܕ-Modeler ܩܝܡܐ ܝܠܗ ܓܘ ܓܢܒܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ ܡܢ ܪܝܫ – ܟܬܘ̈ܒܐ "ܡܨܛܠܝ ܠܦܘܠܚܢܐ ܕܛܘ̈ܟܣܐ ܕܝܗܝ̈ܒܬܐ ܒܐܘܪ̈ܚܬܐ ܕܫܘܝܘܬܐ ܝܢ ܕܓܘܒܝܐ ܕܕܘܡܝܐ ܡܢ ܪܝܫ" ܐܝܡܢ ܕܓܢܣܐ ܕܙܥܘܪܘܬܐ ܝܠܗ "10% ܝܢ ܒܨܝܪ" (ܦܘܚܡܐ ܕ-10:1 ܝܢ 20:1) – ܐܠܐ ܟܫܠܡܝ ܥܠ ܬܪܝܢ ܡܕܡ̈ܐ ܕܚܫܝ̈ܚܐ ܝܢܐ ܐܟܐ: "ܚܕ ܓܗܐ ܠܐ ܓܪܓ ܕܣܡܟܚ ܒܣ ܥܠ ܚܬܝܬܘܬܐ ܟܠܢܝܬܐ"، ܘ"ܩܐ ܦܪܫܐ ܕܕܘܡܝܐ ܙܥܘܪܐ ܕܒܘܚܪܢܐ ܕܟܡܚܘܐ ܠܟܠܗ، ܓܪܓ ܕܦܠܚܚ ܒܐܘܪܚܐ ܕܦܘܠܓܐ ܩܕܡ ܦܘܠܚܢܐ ܕܐܘܪܚܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ ܡܢ ܪܝܫ" (Wendler & Gröttrup, 2021, pp. 1148, 1150).

ܘܒܝܢܝ "ܐܝܢ" ܘ"ܠܐ" – ܠܐ ܦܣܩܬܐ. ܬܐܘܪܝܐ ܕܦܘܣ̈ܩܢܐ (decision theory) ܕ-Bishop ܟܡܘܣܦ ܓܘܒܝܐ ܕܡܣܠܝܢܘܬܐ (reject option): ܦܠܛܬܐ ܡܢ ܦܘܣܩܢܐ ܓܘ ܗܘ̈ܝܐ ܕܒܓܘܝܗܝ ܡܣܬܒܪܢܘܬܐ ܒܬܪܝܬܐ (posterior) ܪܡܬܐ ܡܢ ܟܠ ܢܚܝܬܬܐ ܝܠܗ̇ ܡܢ ܬܚܘܡܐ، ܘܫܒܩܬܐ ܕܝܗܘܢ "ܩܐ ܡܗܝܪܐ ܒܪܢܫܝܐ" (Bishop, 2006, p. 42). ܩܐ ܒܨܘܝܬܐ ܕܟܪܡܙܐ ܦܘܢ̈ܝܐ ܦܬܝ̈ܚܐ ܒܡܘܕܝܠ (ܦܐܬܐ ܕ-NLP، ܦܣܥܬܐ 6)، ܐܗܐ ܝܠܗ ܐܘܪܚܐ ܬܪܝܨܐ: ܡܘܕܝܠ ܟܦܪܫ ܠܡܐ ܕܓܠܝܐ ܝܠܗ، ܒܪܢܫܐ ܠܡܐ ܕܬܪܝܢ ܣܘܟ̈ܠܐ ܐܝܬ ܠܗ، ܘܫܠܡܘܬܐ ܒܝܢܬܝܗܘܢ ܡܫܝܚܬܐ ܝܠܗ̇ ܒܫܪܝܪܘܬܐ ܒܝܢܝ ܪܡܙ̈ܢܐ.

2. ܥܠ ܐܝܢܐ ܝܗܝ̈ܒܬܐ: ܝܘܠܦܢܐ، ܫܘܪܪܐ، ܒܘܚܪܢܐ

ܦܘܪܫܢܐ ܡܢ ܫܘܪܪܐ ܕܪܝܓܪܫܢ ܡܦܫܩܢܐ. Shmueli ܟܦܪܫܐ: ܓܘ ܡܘܕܝܠܘܬܐ ܡܦܫܩܢܝܬܐ (explanatory modeling)، ܫܘܪܪܐ ܟܒܚܪ ܕܡܘܕܝܠ ܟܡܚܘܐ ܬܐܘܪܝܐ ܘܕܦܐܐ ܝܠܗ ܠܝܗܝ̈ܒܬܐ – ܒܘܚܪ̈ܢܐ ܕܬܚܘܝܬܐ ܕܡܘܕܝܠ (specification tests)، ܫܪܝܪܘܬܐ ܘܬܪܝܨܘܬܐ ܕܦܣܘ̈ܩܐ، ܦܘܫܩܐ ܕܫܪ̈ܟܐ؛ ܓܘ ܡܘܕܝܠܘܬܐ ܡܢܒܝܢܝܬܐ (predictive modeling) ܫܘܪܪܐ "ܟܡܟܢܫ ܥܠ ܟܠܢܝܘܬܐ، ܐܗܐ ܝܠܗ ܥܠ ܡܨܝܢܘܬܐ ܕܡܘܕܝܠ ܠܡܢܒܝܐ ܝܗܝ̈ܒܬܐ ܚܕ̈ܬܬܐ"، ܘ"ܣܘܟܢܐ ܪܒܐ ܡܢ ܟܠ ܩܐ ܟܠܢܝܘܬܐ ܝܠܗ̇ ܦܐܝܘܬܐ ܝܬܝܪܬܐ ܠܝܗܝ̈ܒܬܐ ܕܝܘܠܦܢܐ" (Shmueli, 2010, Section 2.6.1). ܘܡܛܠ ܗܕܟܐ "ܐܘܪܚܐ ܝܚܝܕܝܬܐ ܕܝܕܥܬܐ ܟܡܐ ܡܘܕܝܠ ܒܕ ܥܒܕ ܛܒܐ ܥܠ ܗܘ̈ܝܐ ܚܕ̈ܬܐ ܝܠܗ̇ ܢܣܝܢܐ ܕܝܠܗ ܒܥܒܕܐ ܥܠ ܗܘ̈ܝܐ ܚܕ̈ܬܐ" – ܟܦܪܫܚ ܓܘܕܐ ܕܒܘܚܪܢܐ (test set)، ܫܚܝܡܐܝܬ 20% ܡܢ ܝܗܝ̈ܒܬܐ (Géron, 2022, Chapter 1, "Testing and Validating"). "ܛܥܝܘܬܐ ܕܝܘܠܦܢܐ ܠܐ ܝܠܗ̇ ܫܘܥܪܐ ܛܒܐ ܕܛܥܝܘܬܐ ܕܒܘܚܪܢܐ" – ܐܝܗܝ ܟܢܚܬܐ ܟܠܙܒܢ ܥܡ ܡܪܟܒܘܬܐ ܕܡܘܕܝܠ، ܗܠ ܨܦܪܐ، "ܐܠܐ ܡܘܕܝܠ ܥܡ ܛܥܝܘܬܐ ܕܝܘܠܦܢܐ ܨܦܪܐ ܦܐܐ ܝܠܗ ܒܝܬܝܪܘܬܐ ܠܝܗܝ̈ܒܬܐ ܕܝܘܠܦܢܐ ܘܒܥܕܢܐ ܫܚܝܡܐ ܒܕ ܥܒܕ ܒܝܫ ܥܠ ܝܗܝ̈ܒܬܐ ܚܕ̈ܬܬܐ" (Hastie et al., 2009, pp. 220-221)؛ ܘܒܢܘܣܚܐ ܕܡܫܬܘܕܥܢܘܬܐ ܕܐܣܟܝ̈ܡܐ (pattern recognition)، ܛܥܝܘܬܐ ܕ"ܕܥܪܬܐ" (resubstitution، ܒܘܚܪܢܐ ܕܡܘܕܝܠ ܕܦܘܪܫܐ ܥܠ ܐܢܝ ܚܙ̈ܝܬܐ ܓܢܝܗܝ ܕܝܠܦܠܗ ܡܢܝܗܝ) ܝܠܗ̇ ܬܚܘܡܐ ܬܚܬܝܐ ܕܛܥܝܘܬܐ ܫܪܝܪܬܐ ܘܛܥܝܘܬܐ ܕܒܘܚܪܢܐ ܬܚܘܡܐ ܥܠܝܐ – ܫܪܪܐ ܒܝܢܬܝܗܝ ܝܠܗ (Ishii et al., 2026, pp. 113-114).

ܩܕܡ ܒܨܝܐ، ܠܐ ܒܬܪܗ. "ܡܨܐ ܕܡܬܚܙܐ ܢܘܟܪܝܐ ܕܡܢܚܚ ܒܓܢܒܐ ܡܢܬܐ ܡܢ ܝܗܝ̈ܒܬܐ ܓܘ ܐܗܐ ܕܪܓܐ"، ܟܟܬܒ Géron، ܐܠܐ "ܡܘܚܐ ܕܝܘܟܘܢ ܛܘܟܣܐ ܬܡܝܗܐ ܝܠܗ ܩܐ ܡܫܬܘܕܥܢܘܬܐ ܕܐܣܟܝ̈ܡܐ، ܘܐܗܐ ܨܐ ܟܐܡܪ ܕܗܘ ܡܛܝܐ ܝܠܗ ܣܓܝ ܠܦܐܝܘܬܐ ܝܬܝܪܬܐ": ܡܢ ܕܚܐܪ ܓܘ ܓܘܕܐ ܕܒܘܚܪܢܐ ܒܕ ܓܒܐ ܡܘܕܝܠ ܠܦܘܬ ܡܐ ܕܚܙܐ ܬܡܢ، ܘܫܘܥܪܐ ܕܟܠܢܝܘܬܐ ܕܝܠܗ ܒܕ ܗܘܐ ܣܒܪܢܐ ܒܙܘܕܐ – ܡܣܒ ܒܐܦ̈ܐ ܕܚܝܪܬܐ (data snooping bias; Chapter 2, "Create a Test Set"). ܬܘܣܦܬܐ ܐ ܕܟܬܒܐ ܟܟܬܒܐ ܐܗܐ ܐܝܟ ܦܘܩܕܢܐ: "ܓܒܘܢ ܓܘܕܐ ܕܒܘܚܪܢܐ، ܡܢܚܘܢ ܠܗ̇ ܒܓܢܒܐ، ܘܚܕ ܓܗܐ ܠܐ ܚܐܪܘܢ ܒܗ̇". ܬܪܝܢ ܦܪ̈ܨܘܦܐ ܛܟܢܝܩ̈ܝܐ ܕܚܫܝ̈ܚܐ ܝܢܐ ܩܐ ܥܒܕܐ ܡܢ ܪܝܫ: ܦܘܠܓܐ ܓܪܓ ܕܗܘܐ ܩܝܡܐ ܒܝܢܝ ܪ̈ܗܛܐ (ܙܪܥܐ ܩܝܡܐ، ܝܢ hash ܕܡܢܝܢܐ ܡܦܪܫܢܐ ܕܡܫܬܘܬܦܢܐ – ܗܕܟܐ ܕܡܫܬܘܬܦܢܐ ܕܗܘܐ ܓܘ ܝܘܠܦܢܐ ܠܐ ܥܒܪ ܠܒܘܚܪܢܐ ܐܝܡܢ ܕܝܗܝ̈ܒܬܐ ܟܡܬܘܣܦܝ)؛ ܘܓܪܓ ܕܗܘܐ ܦܠܝܓܐ ܠ-strata (stratified) – Géron ܟܡܦܫܩ ܐܗܐ ܒܝܕ ܒܘܨ̈ܝܐ ܕܫܘ̈ܐܠܐ: ܟܢܫܐ ܟܠܢܝܐ ܕܐܬܪ̈ܘܬܐ ܡܚܝ̈ܕܐ ܝܠܗ 51.1% ܢܫ̈ܐ، ܘܡܛܠ ܗܕܟܐ ܕܘܡܝܐ ܕ-1,000 ܒܕ ܢܛܪ 511 ܢܫ̈ܐ؛ ܓܘ ܓܘܒܝܐ ܓܕܫܢܝܐ ܕܟܝܐ ܐܝܬ ܡܣܬܒܪܢܘܬܐ ܕ-10.7% ܩܐ ܕܘܡܝܐ ܕܠܐ ܫܘܐ (ܒܨܝܪ ܡܢ 48.5% ܝܢ ܒܙܘܕܐ ܡܢ 53.5% ܢܫ̈ܐ). ܒܐܗܝ ܐܘܪܚܐ ܓܢܗ̇ ܟܦܠܓܚ ܓܘܕܐ ܕܒܘܚܪܢܐ ܠ-strata ܠܦܘܬ ܡܫܬܚܠܦܢܐ ܪܝܫܝܐ – ܘܓܘ ܓܢܣܐ ܢܕܝܪܐ، ܠܦܘܬ ܦܐܪܐ ܒܓܢܗ.

ܬܠܬܐ ܓܘ̈ܕܐ، ܠܐ ܬܪܬܝܢ. ܐܢ ܟܬܩܢܚ ܡܘܕܝܠ – ܟܓܒܚ ܒܝܢܝ ܡܘܕ̈ܝܠܐ، ܝܢ ܟܦܣܩܚ ܗܝܦܪ-ܦܪܡܝܛܪ (hyperparameter) ܐܝܟ ܚܝܠܐ ܕ-regularization – ܠܦܘܬ ܓܘܕܐ ܕܒܘܚܪܢܐ، ܡܫܚܠܢ ܠܛܥܝܘܬܐ ܕܟܠܢܝܘܬܐ "ܣܓܝ ܓܗ̈ܐ ܥܠ ܓܘܕܐ ܕܒܘܚܪܢܐ، ܘܬܩܢܠܢ ܠܡܘܕܝܠ ܘܠܗܝܦܪ-ܦܪܡܝ̈ܛܪܐ ܕܡܦܩܚ ܡܘܕܝܠ ܛܒܐ ܡܢ ܟܠ ܩܐ ܐܗܝ ܓܘܕܐ ܝܚܝܕܝܬܐ"؛ ܡܘܕܝܠ ܕܟܡܬܚܙܐ ܥܡ 5% ܛܥܝܘܬܐ ܟܥܒܕ 15% ܓܘ ܥܠܡܐ ܫܪܝܪܐ. ܫܪܝܐ ܝܠܗ ܓܘܕܐ ܕܫܘܪܪܐ (validation set، ܨܐ dev set): ܟܦܪܫܚ ܡܢܬܐ ܡܢ ܓܘܕܐ ܕܝܘܠܦܢܐ، ܟܓܒܚ ܥܠܗ̇ ܒܝܢܝ ܡܘܕ̈ܝܠܐ ܡܬܚܫ̈ܒܢܐ (candidates)، ܟܝܠܦܚ ܠܡܘܕܝܠ ܓܒܝܐ ܥܠ ܟܠ ܝܘܠܦܢܐ، ܘܒܣ ܒܬܪܟܐ – ܚܕ ܓܗܐ – ܟܡܫܚܚ ܥܠ ܒܘܚܪܢܐ (Chapter 1, "Hyperparameter Tuning and Model Selection"). ܘܡܘܕܝ ܟܗܘܐ ܒܬܪ ܡܫܘܚܬܐ: "ܓܪܓ ܕܩܝܡܝܬܘܢ ܩܘܒܠ ܢܣܝܘܢܐ ܕܬܩܢܐ ܕܗܝܦܪ-ܦܪܡܝ̈ܛܪܐ ܕܡܢܝ̈ܢܐ ܡܬܚܙܝ ܛܒ̈ܐ ܥܠ ܓܘܕܐ ܕܒܘܚܪܢܐ؛ ܛܘ̈ܒܐ ܠܐ ܡܨܝ̈ܐ ܕܥܒܕܝ ܥܠ ܝܗܝ̈ܒܬܐ ܚܕ̈ܬܬܐ" (Chapter 2, "Evaluate Your System on the Test Set")؛ ܬܘܣܦܬܐ ܐ: "ܠܐ ܫܚܠܦܘܢ ܠܡܘܕܝܠ ܒܬܪ ܕܡܫܚܠܘܟܘܢ ܛܥܝܘܬܐ ܕܟܠܢܝܘܬܐ: ܒܣ ܒܕ ܫܪܝܬܘܢ ܠܦܐܝܘܬܐ ܝܬܝܪܬܐ ܠܓܘܕܐ ܕܒܘܚܪܢܐ". ܐܦ ܡܢܝܢܐ ܥܠ ܓܘܕܐ ܕܒܘܚܪܢܐ ܟܐܬܐ ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ: ܓܘ ܡܬܠܐ ܕ-Géron RMSE ܕ-41,424 ܘܬܚܘܡܐ ܕ-95% – ܒܦܘܠܓܐ t ܥܠ ܛܥ̈ܝܘܬܐ ܡܪ̈ܒܥܬܐ – ܒܝܢܝ 39,275 ܘ-43,467.

ܫܡܗ̈ܐ ܟܡܫܚܠܦܝ ܒܝܢܝ ܦܪܘܓܪ̈ܡܐ. "ܒܙܒܢܐ ܕܣܓܝܐܐ ܡܢ ܦܪܘܓܪ̈ܡܐ ܟܩܪܝ ܟܠܙܒܢ ܠܕܘܡܝܐ ܩܕܡܝܐ ܕܦܘܠܓܐ 'ܝܘܠܦܢܐ'، ܫܡܗ̈ܐ ܕܕܘܡܝܐ ܬܪܝܢܐ ܘܬܠܝܬܝܐ ܟܡܫܚܠܦܝ، ܘܐܗܐ ܡܨܐ ܕܡܚܠܛ" (Truong, 2026, p. 85): ܓܘ SPSS Modeler ܦܘܠܓܐ ܝܠܗ Train / Test / Validation – "ܒܘܚܪܢܐ" ܡܦܠܚ ܝܠܗ ܩܐ ܦܘܚܡܐ ܕܡܘܕ̈ܝܠܐ ܘܩܐ ܬܘܪܨܐ ܕܝܠܗܘܢ، ܘ"ܫܘܪܪܐ" ܝܠܗ ܡܫܘܚܬܐ ܐܚܪܝܬܐ – ܒܠܫܢܐ ܕܟܬܒܐ ܕܡܕܒܪܢܘܬܐ (documentation): "ܝܘܠܦܢܐ ܕܡܘܕܝܠ ܓܘ ܕܘܡܝܐ ܚܕ، ܒܘܚܪܢܐ ܘܬܘܪܨܐ ܕܡܘܕܝܠ ܓܘ ܕܘܡܝܐ ܬܪܝܢܐ، ܘܫܘܪܪܐ ܕܦܐܪ̈ܐ ܓܘ ܬܠܝܬܝܐ" (IBM Corporation, 2016, p. 157)؛ ܓܘ SAS Enterprise Miner – Train / Validation / Test، ܗܦܝܟܐ (ܠܘܚܐ 3.8 ܬܡܢ)؛ ܘ-Géron ܘ-Hastie ܘܚܒܪ̈ܘܗܝ، ܕܐܗܐ ܦܐܬܐ ܟܐܙܠ ܒܬܪܝܗܝ، ܟܐܙܠܝ ܐܝܟ SAS: ܫܘܪܪܐ ܩܐ ܓܘܒܝܐ، ܒܘܚܪܢܐ ܩܐ ܡܫܘܚܬܐ ܐܚܪܝܬܐ. ܛܟܣܐ ܝܠܗ ܪܝܫܝܐ، ܠܐ ܫܡܐ – ܘܒܨܘܝܬܐ ܕܟܡܬܢܝܐ "ܚܬܝܬܘܬܐ ܥܠ ܓܘܕܐ ܕܒܘܚܪܢܐ" ܡܢ ܡܦܩܢܐ ܕ-Modeler ܟܡܬܢܝܐ، ܒܫܡܗ̈ܐ ܕܐܗܐ ܦܐܬܐ، ܓܘܕܐ ܕܫܘܪܪܐ. ܐܦ ܦܘܚܡ̈ܐ ܦܪ̈ܝܫܐ ܝܢܐ: Truong ܟܡܠܟ 60-20-20 ܩܐ ܕܘܡܝܐ ܕܐܠܦܐ ܗܠ ܡܠܝܘܢ ܚܙ̈ܝܬܐ، ܘ"ܒܨܝܪ ܡܢ 1,000 ܚܙ̈ܝܬܐ – 60-40 ܕܠܐ ܓܘܕܐ ܬܠܝܬܝܬܐ" (ܦܐܬܐ 87)، ܘܡܠܟܐ ܕܝܠܗ ܩܐ ܕܘܡܝܐ ܕܚܦܪܬܐ ܕܝܗܝ̈ܒܬܐ (data mining) ܝܠܗ "ܒܨܘܪܐ 100,000 ܗܘ̈ܝܐ" (ܦܐܬܐ 73). ܐܗܐ ܥܠܡܐ ܐܚܪܢܐ ܝܠܗ ܡܢ ܒܘܨܝܐ ܕܫܘ̈ܐܠܐ ܕ-300 ܡܫܬܘܬܦ̈ܢܐ – ܘܓܘܗ ܓܘܕܐ ܕܫܘܪܪܐ ܩܝܡܬܐ ܕ-60 ܡܫܬܘܬܦ̈ܢܐ ܡܢܝܢܐ ܝܠܗ ܕܬܠܐ ܒܓܕܫܐ، ܘܡܛܠ ܗܕܟܐ ܦܣܩܐ 3. ܘܡܘܕܝ Truong ܟܝܗܒ ܩܐ ܐܝܗܝ ܕܥܒܕܐ ܝܠܗ̇ ܒܪܒܘܬܐ ܙܥܘܪܬܐ: ܦܘܪܫܐ ܕܝܠܗ ܒܝܢܝ ܫܪܝܪܘܬܐ ܕܡܘܕܝܠ – "ܫܠܡܘܬܐ ܓܘܝܝܬܐ"، ܐܢܝ ܦܐܪ̈ܐ ܓܢܝܗܝ ܥܠ ܕܘ̈ܡܝܐ ܦܪ̈ܝܫܐ – ܘܬܪܝܨܘܬܐ – "ܚܬܝܬܘܬܐ"، ܡܢܒܝܢܘܬܐ ܬܪܝܨܬܐ ܕܢܝܫܐ؛ "ܒܫܪܪܐ، ܬܪܝܨܘܬܐ ܕܡܘܕܝܠ ܐܗܝ ܓܢܗ̇ ܝܠܗ̇ ܐܝܟ ܚܝܠܐ ܕܡܢܒܝܢܘܬܐ"، ܘܫܪܝܪܘܬܐ ܕܠܐ ܬܪܝܨܘܬܐ ܝܠܗ̇ ܡܬܩܠܐ ܕܟܠܙܒܢ ܟܡܚܘܐ ܩܪܝܒ 22 ܠܝܒܪ̈ܐ ܥܠ ܫܩܐ ܕ-25 (ܦܐܬܐ 186). ܣܗܕܘܬܐ ܩܐ ܫܪܝܪܘܬܐ، ܠܘܬܗ، ܝܠܗ̇ ܦܘܪܫܢܐ ܙܥܘܪܐ ܒܝܢܝ ܡܚܘܝܢܐ ܥܠ ܝܘܠܦܢܐ ܘܡܚܘܝܢܐ ܥܠ ܒܘܚܪܢܐ – "ܐܢ ܦܘܪܫܢܐ ܒܨܝܪܐ ܝܠܗ ܡܢ 5%، ܡܨܝܚ ܕܚܫܒܚ ܠܡܘܕܝܠ ܫܪܝܪܐ" (ܦܐܬܐ 187) – ܘܐܗܐ ܝܠܗ ܒܚܬܝܬܘܬܐ ܦܘܪܫܢܐ ܕܦܣܩܐ 7 ܟܒܥܐ ܕܡܬܢܚ ܠܗ.

ܐܝܟܢ ܐܗܐ ܟܡܬܚܙܐ ܒܪܒܘܬܐ ܪܒܬܐ. ܓܘ ܐܬܓܪܐ ܕܒ̈ܢܝ ܒܝܬܐ ܬܒܝܪ̈ܐ (Fragile Families Challenge)، ܡܬܩ̈ܢܢܐ ܕܬܚܪܘܬܐ ܦܠܓܠܗܘܢ ܦܠܓܐ ܕܝܗܝ̈ܒܬܐ ܕܠܐ ܦܠܚܠܗ ܩܐ ܝܘܠܦܢܐ ܠܬܪܬܝܢ ܓܘ̈ܕܐ: "ܠܘܚܐ ܕܦܐܪ̈ܐ" (leaderboard)، ܕܥܠܗ 160 ܓܘ̈ܕܐ ܡܨܝܐ ܗܘܘ ܕܒܚܪܝ ܓܢܝܗܝ ܓܘ ܙܒܢܐ ܕܬܚܪܘܬܐ، ܘ"ܡܛܫܝܬܐ" (holdout)، ܕܚܬܝܬܘܬܐ ܕܝܠܗ̇ "ܠܐ ܗܘܐ ܝܕܝܥܐ ܠܡܫܬܘܬܦ̈ܢܐ – ܘܠܡܬܩ̈ܢܢܐ – ܗܠ ܚܪܬܐ ܕܐܬܓܪܐ" (Salganik et al., 2020, Section Methods). ܘܐܦܢ ܗܕܟܐ ܟܬܘ̈ܒܐ ܟܡܣܝܓܝ: ܦܘܠܚܢܐ ܒܐܗܝ ܓܘܕܐ ܓܢܗ̇ ܕܡܛܫܝܬܐ ܨܐ ܩܐ ܓܘܒܝܐ ܕܡܫܕܪܬܐ ܛܒܬܐ ܡܢ ܟܠ ܡܢ ܒܝܢܝ 160 ܘܨܐ ܩܐ ܫܘܥܪܐ ܕܝܠܗ̇ "ܥܒܕܠܗ ܫܘ̈ܥܪܐ ܣܒܪ̈ܢܐ ܩܠܝܠ" – ܡܣܒ ܒܐܦ̈ܐ ܙܥܘܪܐ ܓܘ ܗܘܝܐ ܕܝܠܗܘܢ، ܐܠܐ ܐܝܬܘܗܝ (Section Results). ܩܐ ܐܝܗܝ ܕܒܚܪܐ ܚܕ ܓܗܐ ܥܠ ܕܘܡܝܐ ܕ-300، ܐܗܐ ܡܣܒ ܒܐܦ̈ܐ ܠܐ ܝܠܗ ܙܥܘܪܐ.

3. ܫܘܪܪܐ ܡܚܠܦܢܐ: ܠܐ ܒܣ ܡܢܝܢܐ، ܨܐ ܚܬܝܬܘܬܐ ܕܝܠܗ

ܓܘܕܐ ܕܫܘܪܪܐ ܚܕܐ ܟܝܗܒܐ ܡܢܝܢܐ ܚܕ، ܕܬܠܐ ܒܓܕܫܐ ܒܐܝܢܐ ܦܘܠܓܐ ܦܠܛܠܗ. ܫܘܪܪܐ ܡܚܠܦܢܐ (k-fold cross-validation) ܟܦܠܓ ܠܓܘܕܐ ܕܝܘܠܦܢܐ ܠ-k ܡܢܘ̈ܬܐ (folds)، ܟܝܠܦ k ܓܗ̈ܐ ܥܠ k − 1 ܘܟܒܚܪ ܥܠ ܡܐ ܕܦܝܫܐ، ܘܟܫܩܠ "ܠܐ ܒܣ ܫܘܥܪܐ ܕܥܒܕܐ ܕܡܘܕܝܠ ܐܠܐ ܨܐ ܡܚܘܝܢܐ ܕܚܬܝܬܘܬܐ ܕܫܘܥܪܐ – ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܝܠܗ" (Géron, 2022, Chapter 2, "Better Evaluation Using Cross-Validation"). ܓܘ ܡܬܠܐ ܕܛܝ̈ܡܐ ܕ-Géron: ܐܝܠܢܐ ܕܦܘܣܩܢܐ (decision tree) ܥܡ ܛܥܝܘܬܐ ܕܝܘܠܦܢܐ 0.0 ܟܫܩܠ ܓܘ ܫܘܪܪܐ ܡܚܠܦܢܐ ܕ-10 ܡܢܘ̈ܬܐ RMSE ܕ-66,868 (±2,061) – ܩܪܝܒ ܐܝܟ ܪܝܓܪܫܢ ܣܪܛܢܝܐ (69,858 ±4,182)؛ ܥܒܐ ܓܕܫܢܝܐ (random forest) 47,019 (±1,034)، ܐܠܐ ܥܠ ܓܘܕܐ ܕܝܘܠܦܢܐ ܒܓܢܗ̇ ܩܪܝܒ 17,474 – ܗܠ ܗܫܐ ܦܐܝܘܬܐ ܝܬܝܪܬܐ ܪܒܬܐ. ܬܪܝܢ ܡܢܝ̈ܢܐ ܩܐ ܟܠ ܡܘܕܝܠ، ܘܐܢܝ ܡܢܘ̈ܬܐ ܓܢܝܗܝ ܩܐ ܟܠ ܡܘܕ̈ܝܠܐ.

ܟܡܐ ܡܢܘ̈ܬܐ. "ܒܟܠܗ، ܫܘܪܪܐ ܡܚܠܦܢܐ ܒܚܡܫܐ ܝܢ ܒܥܣܪܐ ܡܢܘ̈ܬܐ ܡܬܡܠܟܐ ܝܠܗ ܐܝܟ ܫܠܡܘܬܐ ܛܒܬܐ": ܡܢܘ̈ܬܐ ܒܨܝܪ̈ܐ ܟܝܠܦܝ ܥܠ ܕܘܡܝܐ ܙܥܘܪܐ ܒܙܘܕܐ ܘܟܡܣܒܝ ܒܐܦ̈ܐ ܫܘܥܪܐ ܕܛܥܝܘܬܐ ܠܥܠ؛ ܫܒܩܬܐ ܕܚܕ (leave-one-out، k = N) ܕܠܐ ܡܣܒ ܒܐܦ̈ܐ ܝܠܗ̇ ܐܠܐ ܡܬܬܙܝܥܢܝܬܐ (Hastie et al., 2009, p. 243). ܘܢܡܘܣܐ ܕܚܕܐ ܛܥܝܘܬܐ ܬܩܝܢܬܐ (one-standard-error rule): ܡܢ ܒܝܢܝ ܡܘܕ̈ܝܠܐ ܕܒܚܝܪ̈ܐ ܝܢܐ، ܟܓܒܚ ܐܗܘ ܕܦܫܝܛܐ ܝܠܗ ܡܢ ܟܠ ܕܛܥܝܘܬܐ ܕܝܠܗ ܠܐ ܥܒܪܐ ܚܕܐ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܠܥܠ ܡܢ ܡܘܕܝܠ ܛܒܐ ܡܢ ܟܠ – ܡܛܠ ܕܣܪܛܐ ܟܦܝܦܐ ܕܫܘܪܪܐ ܡܚܠܦܢܐ ܒܓܢܗ ܡܫܘܥܪܐ ܝܠܗ ܥܡ ܛܥܝܘܬܐ (ܦܐܬܐ 244). ܚܘܣܪܢܐ، ܠܘܬ Bishop: "ܚܕ ܚܘܣܪܢܐ ܪܝܫܝܐ ܕܫܘܪܪܐ ܡܚܠܦܢܐ ܝܠܗ ܕܡܢܝܢܐ ܕܪ̈ܗܛܐ ܕܝܘܠܦܢܐ ܟܪܒܐ S ܓܗ̈ܐ" (Bishop, 2006, p. 33) – ܓܘ ܡܚܫܒ̈ܢܐ ܕܣܐܝܛ ܐܗܐ ܠܐ ܡܕܡ ܝܠܗ، ܓܘ ܡܨܝܕܬܐ ܕܢܝܘܪܘܢ̈ܐ (neural network) ܐܗܐ ܝܘܡ̈ܬܐ ܝܢܐ. ܘܩܐ ܡܘܕܝ ܫܘܪܪܐ ܡܚܠܦܢܐ ܘܠܐ ܓܘܕܐ ܕܫܘܪܪܐ ܚܕܐ: ܓܘ ܐܘܪܚܐ ܕܡܛܫܝܬܐ (hold-out) ܡܐ ܕܝܗܝܒܐ ܝܠܗ ܩܐ ܒܘܚܪܢܐ ܟܡܬܒܨܪ ܡܢ ܝܘܠܦܢܐ، ܘܗܦܟܐ – "ܐܝܡܢ ܕܡܢܝܢܐ ܕܚܙ̈ܝܬܐ ܙܥܘܪܐ ܝܠܗ، ܐܘܪܚܐ ܕ-H ܠܐ ܝܠܗ̇ ܐܘܪܚܐ ܚܬܝܬܬܐ" ܩܐ ܫܘܥܪܐ ܕܛܥܝܘܬܐ، ܘܫܘܪܪܐ ܡܚܠܦܢܐ "ܟܡܫܪܪ ܕܟܠ ܗܕ̈ܡܐ ܒܕ ܦܠܚܝ ܩܐ ܝܘܠܦܢܐ ܘܩܐ ܒܘܚܪܢܐ" (Ishii et al., 2026, p. 89). ܩܐ ܥܒ̈ܐ ܓܕܫܢ̈ܝܐ ܐܝܬ ܫܘܪܪܐ ܡܓܢ: ܟܠ ܐܝܠܢܐ ܝܠܝܦܐ ܝܠܗ ܥܠ ܕܘܡܝܐ ܥܡ ܕܥܪܬܐ ܕܟܫܒܩ ܩܪܝܒ 37% ܡܢ ܚܙ̈ܝܬܐ ܠܒܪ، ܘܫܘܥܪܐ ܕܛܥܝܘܬܐ ܥܠ ܚܙ̈ܝܬܐ "ܠܒܪ ܡܢ ܫܩܐ" (out-of-bag) "ܩܪܝܒ ܐܗܘ ܓܢܗ ܝܠܗ" ܐܝܟ ܫܘܪܪܐ ܡܚܠܦܢܐ ܕ-N ܡܢܘ̈ܬܐ (Hastie et al., 2009, p. 593).

ܐܦ ܬܘܩܢܐ – ܓܘ ܫܘܪܪܐ ܡܚܠܦܢܐ. ܒܨܝܐ ܕܡܨܝܕܬܐ (grid search؛ ܟܠ ܚܘ̈ܠܛܐ ܕܗܝܦܪ-ܦܪܡܝ̈ܛܪܐ) ܝܢ ܒܨܝܐ ܓܕܫܢܝܐ (ܡܢܝܢܐ ܩܝܡܐ ܕܚܘ̈ܠܛܐ؛ ܓܒܝܐ ܝܠܗ ܒܙܘܕܐ ܐܝܡܢ ܕܚܠܐ ܕܚܘ̈ܠܛܐ ܪܒܐ ܝܠܗ – ܬܘܣܦܬܐ ܐ: ܓܒܝܬܐ ܕܓܕܫܢܝܐ ܐܠܐ ܐܢ ܐܝܬ ܛܝ̈ܡܐ ܩܠܝ̈ܠܐ) ܟܥܒܕܝ ܫܘܪܪܐ ܡܚܠܦܢܐ ܩܐ ܟܠ ܚܘܠܛܐ، ܘܟܓܒܚ ܠܦܘܬ ܡܨܥܝܬܐ. ܢܡܘܣܐ: ܟܠ ܦܘܣܩܢܐ ܕܣܡܝܟܐ ܝܠܗ ܥܠ ܥܒܕܐ – ܡܘܕܝܠ، ܗܝܦܪ-ܦܪܡܝܛܪ، ܬܚܘܡܐ ܕܦܘܪܫܐ، ܡܨܠܠܢܘܬܐ ܕܬܚܘܝ̈ܬܐ – ܥܒܝܕܐ ܝܠܗ ܓܘ ܡܢܘ̈ܬܐ، ܠܐ ܥܠܝܗܝ (ܦܣܩܐ 5).

4. ܡܣܒ ܒܐܦ̈ܐ، ܫܘܚܠܦܐ – ܘܬܚܘܡܐ ܕܛܥܝܘܬܐ

ܛܥܝܘܬܐ ܕܟܠܢܝܘܬܐ ܕܡܘܕܝܠ ܓܘܡܪܐ ܝܠܗ̇ ܕܬܠܬܐ: ܡܣܒ ܒܐܦ̈ܐ – ܫܪ̈ܛܐ ܛܥ̈ܝܐ (ܣܪܛܐ ܬܪܝܨܐ ܩܐ ܝܗܝ̈ܒܬܐ ܡܪ̈ܒܥܬܐ) – ܕܟܡܛܝܐ ܠܦܐܝܘܬܐ ܒܨܝܪܬܐ (underfitting)؛ ܫܘܚܠܦܐ – ܪܓܝܫܘܬܐ ܝܬܝܪܬܐ ܠܫܘܚܠܦ̈ܐ ܙܥܘܪ̈ܐ ܓܘ ܝܗܝ̈ܒܬܐ ܕܝܘܠܦܢܐ، ܡܢܬܐ ܕܡܘܕ̈ܝܠܐ ܥܡ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ ܣܓܝ̈ܐܐ – ܕܟܡܛܝܐ ܠܦܐܝܘܬܐ ܝܬܝܪܬܐ؛ ܘܛܥܝܘܬܐ ܕܠܐ ܡܨܝܐ ܕܙܥܪܐ (irreducible error) – ܩܠܐ ܓܘ ܝܗܝ̈ܒܬܐ ܒܓܢܝܗܝ، ܕܒܣ ܡܕܟܝܢܘܬܐ ܕܝܗܝ̈ܒܬܐ ܟܡܙܥܪܐ ܠܗ. ܡܪܒܝܬܐ ܕܡܪܟܒܘܬܐ ܕܡܘܕܝܠ ܟܡܪܡܐ ܫܘܚܠܦܐ ܘܟܡܢܚܬܐ ܡܣܒ ܒܐܦ̈ܐ، ܘܗܦܟܐ – "ܘܡܛܠ ܗܕܟܐ ܟܡܬܩܪܝܐ ܫܠܡܘܬܐ" (Géron, 2022, Chapter 4, "The Bias/Variance Trade-Off"). ܦܘܪܫܐ ܪܫܡܝܐ ܠܡܢܘ̈ܬܐ – ܛܥܝܘܬܐ ܡܣܬܟܝܬܐ ܕܡܢܒܝܢܘܬܐ ܓܘ ܢܘܩܙܐ = ܫܘܚܠܦܐ ܕܩܠܐ + ܡܪܒܥܐ ܕܡܣܒ ܒܐܦ̈ܐ + ܫܘܚܠܦܐ ܕܡܫܘܥܪܢܐ – ܝܠܗ ܫܘܝܘܬܐ 7.9 ܠܘܬ Hastie ܘܚܒܪ̈ܘܗܝ (ܦܐܬܐ 223)، ܘܓܘ ܡܫܬܘܕܥܢܘܬܐ ܕܐܣܟܝ̈ܡܐ "ܥܩܬܐ ܕܡܣܒ ܒܐܦ̈ܐ ܘܫܘܚܠܦܐ": MSE = Bias² + Var، ܘܡܛܠ ܗܕܟܐ ܐܝܡܢ ܕܟܡܪܡܚ ܕܪܓܐ ܕܦܘܢܩܣܝܐ ܕܦܘܪܫܐ (discriminant function) ܘܟܒܚܪܚ ܥܠ ܚܙ̈ܝܬܐ ܚܕ̈ܬܬܐ، ܛܥܝܘܬܐ ܟܢܚܬܐ "ܗܠ ܕܪܓܐ ܡܥܝܢܐ، ܘܒܬܪܟܐ" ܟܣܠܩܐ (Ishii et al., 2026, pp. 111-112). ܒܘܚܪܢܐ: ܛܒܐ ܥܠ ܝܘܠܦܢܐ ܘܒܝܫܐ ܓܘ ܫܘܪܪܐ ܡܚܠܦܢܐ – ܦܐܝܘܬܐ ܝܬܝܪܬܐ؛ ܒܝܫܐ ܓܘ ܬܪܘܝܗܝ – ܦܐܝܘܬܐ ܒܨܝܪܬܐ. ܣܪ̈ܛܐ ܟܦܝ̈ܦܐ ܕܝܘܠܦܢܐ (learning curves) – ܛܥܝܘܬܐ ܕܝܘܠܦܢܐ ܘܛܥܝܘܬܐ ܕܫܘܪܪܐ ܐܝܟ ܦܘܢܩܣܝܐ ܕܪܒܘܬܐ ܕܕܘܡܝܐ – ܟܡܚܘܝ ܐܗܐ ܠܥܝܢܐ، ܘ-Bishop ܟܡܘܣܦ ܡܘܕܝ ܟܡܥܕܪ: "ܩܐ ܡܪܟܒܘܬܐ ܝܗܝܒܬܐ ܕܡܘܕܝܠ، ܥܩܬܐ ܕܦܐܝܘܬܐ ܝܬܝܪܬܐ ܟܗܘܝܐ ܒܨܝܪ ܩܫܝܬܐ ܟܡܐ ܕܛܘܟܣܐ ܕܝܗܝ̈ܒܬܐ ܟܪܒܐ" (Bishop, 2006, p. 9). ܥܠ ܦܘܚܡܐ ܒܝܢܝ ܡܢܝܢܐ ܕܚܙ̈ܝܬܐ ܘܡܢܝܢܐ ܕܦܪܡܝ̈ܛܪܐ ܘܬܚܘܝ̈ܬܐ – ܢܡܘܣܐ ܕܨܒܥܐ ܕ-Bishop ܘܗܘܝܐ ܕ-Hughes – ܚܙܝܡܘܢ ܦܐܬܐ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ، ܦܣܩܐ 2.

ܘܡܘܕܝ ܡܨܐ ܕܗܘܐ ܡܢܝܢܐ ܒܟܠܗ. ܐܝܬ ܬܚܘܡܐ ܕܚܕ ܡܘܕܝܠ ܠܐ ܢܚܬ ܠܬܚܬܗ: ܛܥܝܘܬܐ ܕ-Bayes – "ܬܚܘܡܐ ܕܡܣܬܒܪܢܘܬܐ ܕܛܥܝܘܬܐ ܠܐ ܡܨܝܐ ܕܗܘܝܐ ܒܨܝܪܬܐ ܡܢܗ، ܒܡ̈ܠܐ ܐܚܪ̈ܢܝܬܐ 'ܦܓܥܬܐ ܕܦܘܠ̈ܓܐ'، ܕܝܠܗ̇ 'ܛܥܝܘܬܐ ܕܠܐ ܡܨܝܐ ܕܡܬܦܠܛܐ' ܕܐܗܐ ܛܘܟܣܐ ܕܡܦܩܬܐ ܕܬܚܘܝ̈ܬܐ (feature extraction) ܟܡܥܠܐ" (Ishii et al., 2026, p. 101). ܐܝܡܢ ܕܬܚܘܝ̈ܬܐ ܠܐ ܟܦܪܫܝ ܒܝܢܝ ܓܢ̈ܣܐ، ܠܝܬ ܐܠܓܘܪܝܬܡ ܕܦܪܫ. ܐܗܐ ܝܠܗ̇ ܩܪܝܢܐ ܬܪܝܨܐ ܕܐܬܓܪܐ ܕܒ̈ܢܝ ܒܝܬܐ ܬܒܝܪ̈ܐ: 160 ܓܘ̈ܕܐ، 4,242 ܒ̈ܢܝ ܒܝܬܐ ܘ-12,942 ܡܫܬܚܠܦ̈ܢܐ ܥܠ ܟܠ ܚܕ – ܘ-R² ܥܠ ܝܗܝ̈ܒܬܐ ܕܡܛܫܝܬܐ ܩܪܝܒ 0.2 ܩܐ ܥܩܬܐ ܕܡܐܢ̈ܐ (material hardship) ܘܩܐ ܡܨܥܝܬܐ ܕܡܢܝ̈ܢܐ ܕܡܕܪܫܬܐ ܘܩܪܝܒ 0.05 ܩܐ ܐܪܒܥܐ ܦܐܪ̈ܐ ܐܚܪ̈ܢܐ، "ܒܣ ܩܠܝܠ ܛܒܐ ܒܙܘܕܐ" ܡܢ ܡܘܕܝܠ ܕܦܘܚܡܐ ܕܪܝܓܪܫܢ ܥܠ ܐܪܒܥܐ ܡܫܬܚܠܦ̈ܢܐ ܕܓܒܐ ܡܗܝܪܐ؛ ܛܥܝܘܬܐ ܕܡܢܒܝܢܘܬܐ ܐܣܝܪܬܐ ܗܘܐ ܚܝܠܬܢܐܝܬ ܥܡ ܒܝܬܐ ܕܟܡܢܒܝܚ ܘܒܣ ܟܪܝܗܐܝܬ ܥܡ ܐܘܪܚܐ (Salganik et al., 2020، ܟܢܘܫܝܐ ܘܦܣܩܐ Results). "ܡܛܠ ܕܡܐ̈ܐ ܒܨܘ̈ܝܐ ܢܣܝܠܗܘܢ ܦܘܠܚܢܐ ܘܚܕ ܠܐ ܡܨܐ ܗܘܐ ܕܡܢܒܐ ܒܚܬܝܬܘܬܐ"، ܚܬܝܬܘܬܐ ܢܚܝܬܬܐ "ܠܐ ܡܨܝܐ ܕܡܬܬܣܡܟܐ ܒܦܫܝܩܘܬܐ ܥܠ ܚܘܣܪ̈ܢܐ ܕܒܨܘܝܐ ܝܢ ܕܐܘܪܚܐ ܝܚܝܕܝܐ" (Section Discussion) – ܐܗܐ ܝܠܗ ܬܚܘܡܐ، ܠܐ ܡܦܘܠܬܐ. Kapoor ܘ-Narayanan ܟܡܢܝܝ "ܠܐ ܦܗܡܬܐ ܕܬܚܘ̈ܡܐ ܕܡܢܒܝܢܘܬܐ" ܐܝܟ ܟܘܪܗܢܐ ܩܕܡܝܐ ܕܝܠܗܘܢ ܩܐ ܡܦܘ̈ܠܬܐ ܕܥܒܕܐ ܡܢ ܪܝܫ: ܛܘ̈ܒܐ ܓܘ ܡܫܬܘܕܥܢܘܬܐ ܕܨܘܪ̈ܬܐ "ܟܝܗܒܝ ܪܘܫܡܐ" ܕܡܘܕ̈ܝܠܐ ܟܥܒܪܝ ܒ̈ܢܝ ܐܢܫܐ ܓܘ ܟܠ ܦܘܠܚܢܐ، ܘܟܡܚܠܛܝ ܒܨܘ̈ܝܐ ܥܠ ܡܐ ܕܡܨܝܚ ܕܣܟܚ ܓܘ ܡܢܒܝܢܘܬܐ ܕܦܐܪ̈ܐ ܕܟܢܫܐ؛ ܡܠܟܐ – ܡܫܬܘܕܥܢܘܬܐ ܕܬܚܘ̈ܡܐ ܥܠ̈ܝܐ ܩܐ ܚܬܝܬܘܬܐ، ܘܐܝܡܢ ܕܡܛܝܐ ܠܗܘܢ، ܡܫܒܩܬܐ ܕܢܣܝܘܢܐ ܕܥܒܪܬܐ ܡܢܝܗܝ ܘܡܬܠܬܐ ܕܦܘܠܓ ܪܥܝܢܐ ܥܠ ܦܐܪ̈ܐ ܕܟܐܡܪܝ ܕܥܒܪܠܗܘܢ (Kapoor & Narayanan, 2023, Section Discussion, D1-R1). ܩܐ ܒܨܘܝܬܐ: ܡܘܕܝܠ ܕܟܡܬܢܐ AUC = .95 ܥܠ ܫܒܩܬܐ ܕܡܕܪܫܬܐ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܕܪܩܥܐ ܠܐ ܝܠܗ ܦܬܝܚܘܬܐ ܕܐܘܪܚܐ – ܗܘ ܐܬܐ ܝܠܗ ܩܐ ܦܣܩܐ 5.

5. ܡܪܕܝܬܐ ܕܝܗܝ̈ܒܬܐ: ܡܢܝܢܐ ܬܡܝܗܐ ܕܕܓܠܘܬܐ ܝܠܗ

Kapoor ܘ-Narayanan ܒܨܝܠܗܘܢ ܟܬ̈ܒܐ ܕܝܕܥܬܐ ܕܣܡܝܟܬܐ ܝܠܗ̇ ܥܠ ܝܘܠܦܢܐ ܕܡܟܝܢܐ ܘܡܘܫܟܚܠܗܘܢ ܡܪܕܝܬܐ (leakage) ܓܘ 294 ܡܐܡܪ̈ܐ ܓܘ 17 ܚܩܠ̈ܐ، "ܓܘ ܚܠܐ ܗܘ̈ܝܐ ܥܡ ܫܘ̈ܠܡܐ ܣܒܪ̈ܢܐ ܕܠܐ ܬܚܘܡܐ" (Kapoor & Narayanan, 2023, Section Summary). ܛܘܟܣܐ ܕܙܢ̈ܐ (taxonomy) ܕܝܠܗܘܢ ܝܠܗ ܪܫܝܡܬܐ ܕܒܘܚܪܢܐ ܕܐܗܐ ܦܐܬܐ: [L1] ܠܝܬ ܦܘܪܫܐ ܕܟܝܐ ܒܝܢܝ ܝܘܠܦܢܐ ܘܒܘܚܪܢܐ – ܠܝܬ ܓܘܕܐ ܕܒܘܚܪܢܐ ܒܟܠܗ (L1.1)؛ ܡܛܝܒܘܬܐ ܩܕܡܝܬܐ ܥܠ ܟܠ ܝܗܝ̈ܒܬܐ (preprocessing) – ܡܠܝܐ ܕܛܝ̈ܡܐ ܚܣܝ̈ܪܐ، ܡܬܩܢܘܬܐ ܝܢ ܓܘܒܝܐ ܝܬܝܪܐ ܕܕܘܡܝܐ ܩܕܡ ܦܘܠܓܐ (L1.2؛ ܐܗܐ ܝܠܗ ܙܘܗܪܐ ܕ-Géron: "ܚܕ ܓܗܐ ܠܐ ܡܦܠܚܘܢ ܒ-fit() ܝܢ ܒ-fit_transform() ܩܐ ܚܕ ܡܕܡ ܠܒܪ ܡܢ ܓܘܕܐ ܕܝܘܠܦܢܐ"، ܨܚܚܐ 2، "Feature Scaling and Transformation")؛ ܓܘܒܝܐ ܕܬܚܘܝ̈ܬܐ ܥܠ ܟܠ ܝܗܝ̈ܒܬܐ (L1.3)؛ ܣܕܪ̈ܐ ܬܢܝ̈ܢܐ (duplicates) (L1.4). [L2] ܬܚܘܝ̈ܬܐ ܠܐ ܬܪ̈ܝܨܐ – ܕܒܫܪܪܐ ܐܢܝ ܢܝܫܐ ܝܢܐ: ܡܬܠܐ ܕܝܠܗܘܢ ܝܠܗ ܒܘܨܝܐ ܕܡܢܒܐ ܠܚܝܠܐ ܪܡܐ ܕܕܡܐ (hypertension) ܡܢ ܫܩܠܬܐ ܕܣܡ̈ܡܢܐ ܩܐ ܚܝܠܐ ܪܡܐ ܕܕܡܐ. [L3] ܓܘܕܐ ܕܒܘܚܪܢܐ ܕܠܐ ܝܠܗ̇ ܡܢ ܦܘܠܓܐ ܕܥܠܗ ܐܝܬ ܡܐܡܪܐ – ܡܪܕܝܬܐ ܓܘ ܙܒܢܐ (ܒܘܚܪܢܐ ܥܠ ܝܗܝ̈ܒܬܐ ܩܕܡܝ̈ܬܐ ܡܢ ܝܘܠܦܢܐ، L3.1)، ܘܠܐ ܬܠܝܘܬܐ ܕܬܒܝܪܬܐ ܝܠܗ̇ (L3.2, Section 6). ܡܚܘܝܢܘܬܐ ܕܝܠܗܘܢ ܝܠܗ̇ ܡܢ ܝܕܥܬܐ ܕܡܕܝܢܝܘܬܐ (political science): ܓܘ ܡܢܒܝܢܘܬܐ ܕܩܪ̈ܒܐ ܓܘܝ̈ܐ، ܕܓܘܗ ܡܘܕ̈ܝܠܐ ܡܪܟ̈ܒܐ "ܚܫܝܒ̈ܐ ܗܘܘ ܙܟܝ̈ܐ ܒܦܘܪܫܢܐ ܪܒܐ" ܥܠ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ، "ܐܝܡܢ ܕܛܥ̈ܝܘܬܐ ܬܘܪ̈ܨܐ ܝܢܐ، ܡܘܕ̈ܝܠܐ ܡܪܟ̈ܒܐ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ ܠܐ ܟܥܒܕܝ ܛܒܐ ܒܙܘܕܐ ܒܓܘܢܐ ܪܝܫܝܐ ܡܢ ܡܘܕ̈ܝܠܐ ܕ-LR ܕܐܝܬ ܠܗܘܢ ܥܣܪ̈ܐ ܕܫܢ̈ܐ" (Section Summary). ܡܠܟܐ ܕܝܠܗܘܢ – "ܓܠܝܘܢܐ ܕܡܥܠܘܡܘܬܐ ܩܐ ܡܘܕܝܠ" (model info sheet) ܕܒܓܘܗ ܒܨܘܝܐ ܟܦܢܐ ܥܠ ܟܠ ܙܢܐ ܕܡܪܕܝܬܐ – ܘܩܐ ܩܪ̈ܘܝܐ: "ܚܫܒܬܐ ܕܦܐܪ̈ܐ ܡܢ ܝܕܥܬܐ ܕܣܡܝܟܬܐ ܝܠܗ̇ ܥܠ ܝܘܠܦܢܐ ܕܡܟܝܢܐ ܐܝܟ ܙܒܢܢ̈ܝܐ" (R2).

ܢܣܝܘܢܐ ܕܚܘܝܠܗ ܐܗܐ ܐܪܒܥܣܪ ܫܢ̈ܐ ܩܕܡ. Hastie ܘܚܒܪ̈ܘܗܝ ܟܥܒܕܝ ܕܡܘܬܐ (simulation) ܕ-50 ܡܫܬܘܬܦ̈ܢܐ ܓܘ ܬܪܝܢ ܓܢ̈ܣܐ ܫܘ̈ܝܐ ܘ-5,000 ܡܢܒ̈ܝܢܐ ܓܕܫܢ̈ܝܐ ܕܠܐ ܝܢܐ ܐܣܝܪ̈ܐ ܥܡ ܓܢܣܐ ܒܟܠܗ – ܡܢܬܐ ܫܪܝܪܬܐ ܕܛܥܝܘܬܐ ܕܦܘܪܫܐ ܝܠܗ̇ 50%. "ܐܘܪܚܐ ܠܐ ܬܪܝܨܬܐ": ܡܨܠܠܬܐ ܥܠ ܟܠ ܕܘܡܝܐ ܕ-100 ܡܢܒ̈ܝܢܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕܝܠܗܘܢ ܥܡ ܓܢܣܐ ܪܒܐ ܝܠܗ ܡܢ ܟܠ، ܘܒܬܪܟܐ ܫܘܥܪܐ ܕܛܥܝܘܬܐ ܒܫܘܪܪܐ ܡܚܠܦܢܐ – ܡܨܥܝܬܐ 3% ܓܘ 50 ܕܡܘ̈ܝܬܐ، "ܢܚܝܬܐ ܒܣܓܝ ܡܢ ܡܢܬܐ ܫܪܝܪܬܐ ܕܛܥܝܘܬܐ"، ܡܛܠ ܕܡܢܒ̈ܝܢܐ "ܚܙܝܠܗܘܢ ܡܢ ܩܕܡ" ܠܡܫܬܘܬܦ̈ܢܐ ܕܦܝܫܝܠܗܘܢ ܠܒܪ؛ "ܐܘܪܚܐ ܬܪܝܨܬܐ": ܦܘܠܓܐ ܠܡܢܘ̈ܬܐ ܩܕܡ، ܘܡܨܠܠܬܐ، ܒܢܝܢܐ ܕܡܘܕܝܠ ܕܦܘܪܫܐ ܘܡܢܒܝܢܘܬܐ ܓܘ ܟܠ ܡܢܬܐ (Hastie et al., 2009, pp. 245-246). ܐܗܐ ܝܠܗ L1.3 ܒܚܬܝܬܘܬܐ – ܘܗܘ ܥܠܬܐ ܝܠܗ ܕܡܨܠܠܬܐ ܕܦܣܘ̈ܩܐ ܠܦܘܬ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܥܡ ܦܐܪܐ، ܥܝܕܐ ܡܩܒܠܐ ܓܘ ܒܢܝܢܐ ܕܣܒ̈ܠܬܐ، ܠܐ ܫܠܝܛܐ ܝܠܗ ܩܕܡ ܦܘܠܓܐ. ܫܪܝܐ ܛܟܢܝܩܝܐ ܝܠܗ ܩܢܝܐ (Pipeline ܓܘ scikit-learn): ܟܠ ܕܪ̈ܓܐ ܕܡܛܝܒܘܬܐ ܘܡܘܕܝܠ ܐܝܟ ܚܕ ܚܘܝܕܐ، ܕܬܩܝܢܐ ܝܠܗ ܥܠ ܡܢܬܐ ܕܝܘܠܦܢܐ ܘܡܦܠܚܐ ܝܠܗ ܥܠ ܡܢܬܐ ܕܒܘܚܪܢܐ – ܘܡܛܠ ܗܕܟܐ ܠܐ ܡܨܐ ܕܕܠܦ.

6. ܝܗܝ̈ܒܬܐ ܕܠܐ ܝܢܐ ܠܐ ܬܠܝ̈ܐ: ܒ̈ܢܝ ܒܝܬܐ، ܣܕܪ̈ܐ ܕܡܕܪܫܬܐ، ܡܨܝ̈ܕܬܐ

ܟܠ ܡܐ ܕܠܥܠ ܟܡܢܚ ܕܚܙ̈ܝܬܐ ܠܐ ܬܠܝ̈ܐ ܝܢܐ ܘܦܠܝ̈ܓܐ ܐܝܟ ܚܕ (i.i.d.) – ܘܓܘ ܒܘܨܝܐ ܕܟܢܫܐ ܐܢܝ ܩܪܝܒ ܚܕ ܓܗܐ ܠܐ: ܬܠܡܝ̈ܕܐ ܓܘ ܐܗܘ ܣܕܪܐ ܓܢܗ، ܒ̈ܢܝ ܐܗܘ ܒܝܬܐ ܓܢܗ، ܚܒܪ̈ܐ ܓܘ ܡܨܝܕܬܐ، ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ ܕܐܗܘ ܒܪܢܫܐ ܓܢܗ. ܥܩܬܐ ܡܬܚܘܝܬܐ ܝܠܗ̇ ܐܝܟ ܡܟܫܠܢܐ ܩܐ ܫܘܪܪܐ ܓܘ ܦܣܩܐ L3.2 ܕ-Kapoor ܘ-Narayanan: "ܬܠܝܘܬܐ (non-independence) ܒܝܢܝ ܕܘ̈ܡܝܐ ܕܝܘܠܦܢܐ ܘܕܒܘܚܪܢܐ ܝܠܗ̇ ܡܪܕܝܬܐ، ܐܠܐ ܐܢ ܡܐܡܪܐ ܝܕܥܢܝܐ ܥܠ ܦܘܠܓܐ ܝܠܗ ܕܐܝܬ ܠܗ ܐܗܘ ܒܢܝܢܐ ܓܢܗ ܕܬܠܝܘܬܐ. ܓܘ ܗܘܝܐ ܪܚܝܩܐ (ܐܠܐ ܒܚܘܣܪܢܐ ܣܓܝ ܡܬܚܙܝܐ)، ܕܘ̈ܡܝܐ ܕܝܘܠܦܢܐ ܘܕܒܘܚܪܢܐ ܟܐܬܝ ܡܢ ܐܢܝ ܐܢܫ̈ܐ ܝܢ ܚܘ̈ܝܕܐ ܓܢܝܗܝ" (Kapoor & Narayanan, 2023، L3.2). ܟܬ̈ܒܐ ܕܝܘܠܦܢܐ ܐܣܘܪܝܐ ܟܡܬܚܘܝ ܠܐܗܝ ܡܕܡ ܓܢܗ̇ ܐܝܟ ܟܝܢܐ ܕܝܗܝ̈ܒܬܐ، ܠܐ ܐܝܟ ܛܥܝܘܬܐ ܕܒܨܘܝܐ: "ܣܓܝܐܐ ܪܒܐ ܕܥܒܕܐ ܓܘ ܐܘܪ̈ܚܬܐ ܣܛܐܛܝܣܛܝܩ̈ܝܬܐ ܕܦܘܪܫܐ ܠܓܢ̈ܣܐ ܟܢܝܫܐ ܗܘܐ ܥܠ ܝܗܝ̈ܒܬܐ 'ܦܫܝܛ̈ܬܐ' – ܝܗܝ̈ܒܬܐ ܕܡܪ̈ܟܒܐ ܝܢܐ ܡܢ ܐܝܬܘ̈ܬܐ ܕܐܝܬ ܠܗܘܢ ܒܢܝܢܐ ܐܗܘ ܓܢܗ، ܕܒܥܕܢܐ ܫܚܝܡܐ ܟܡܢܚܝ ܕܐܢܝ i.i.d. ܝܢܐ. ܐܠܐ ܛܘ̈ܟܣܐ ܣܓܝ̈ܐܐ ܕܝܗܝ̈ܒܬܐ ܓܘ ܥܠܡܐ ܫܪܝܪܐ ܐܣܘܪ̈ܝܐ ܝܢܐ ܒܟܝܢܐ ܕܝܠܗܘܢ: ܦܐܬ̈ܐ ܕܐܝܢܛܪܢܝܬ ܐܣܝܪ̈ܬܐ، ܡܘܬܒ̈ܢܘܝܬܐ ܚܕ ܠܚܕ ܓܘ ܦܐܛܢܛ̈ܐ ܘܓܘ ܡܐܡܪ̈ܐ ܝܕܥܢ̈ܝܐ، ܡܨܝ̈ܕܬܐ ܕܟܢܫܐ، ܪ̈ܫܝܡܬܐ ܕܐܣܝܘܬܐ" (Taskar, Abbeel, Wong & Koller, 2007, p. 175)؛ "ܠܐ ܐܝܟ ܓܘ ܗܘ̈ܝܐ ܥܬܝܩ̈ܐ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ، ܕܒܓܘܝܗܝ ܛܘܟܣܐ ܕܝܘܠܦܢܐ ܟܫܩܠ ܐܝܟ ܡܥܠܬܐ (input) ܫܪܫܠܬܐ ܕܚܙ̈ܝܬܐ i.i.d.، ܡܥܠܬܐ ܠܐܠܓܘܪܝܬܡ ܕܝܘܠܦܢܐ ܐܣܘܪܝܐ ܣܓܝ ܓܗ̈ܐ ܝܠܗ̇ ܡܬܠܐ ܝܚܝܕܝܐ، ܐܣܝܪܐ ܒܥܘܬܪܐ" (Getoor & Taskar, 2007, p. 4). ܡܝܟܐܢܝܙܡ ܝܠܗ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܥܡ ܓܢܗ (autocorrelation): "ܬܠܝܘܬܐ ܣܛܐܛܝܣܛܝܩܝܬܐ ܒܝܢܝ ܛܝ̈ܡܐ ܕܐܗܘ ܡܫܬܚܠܦܢܐ ܓܢܗ ܥܠ ܐܝܬܘ̈ܬܐ ܐܣܝܪ̈ܬܐ"، ܕ"ܝܠܗ̇ ܟܝܢܐ ܩܪܝܒ ܟܠܢܝܐ ܕܛܘ̈ܟܣܐ ܐܣܘܪ̈ܝܐ ܕܝܗܝ̈ܒܬܐ" – Neville ܘ-Jensen ܟܡܢܝܝ، ܒܝܢܝ ܐܚܪ̈ܢܐ، ܦܘܪܫܐ ܕܚܩܠܐ ܕܫܪ̈ܟܘܬܐ ܕܡܫܘܬܦܝ ܗܕ̈ܡܐ ܕܡܘܬܒܐ ܕܡܕܒܪ̈ܢܐ، ܐܝܟܢܝܘܬܐ ܕܢܟܠܐ ܕܡܦܠܚ̈ܢܐ ܕܬܠܦܘܢ ܡܬܬܙܝܥܢܐ ܕܟܩܪܝ ܠܡܢܝ̈ܢܐ ܡܫܘܬ̈ܦܐ، ܘܡܥܒܪܢܘܬܐ ܕܫܥܠܐ ܕܪܐܬܐ (tuberculosis) ܒܝܢܝ ܐܢܫ̈ܐ ܒܦܓܥܬܐ ܩܪܝܒܬܐ (Neville & Jensen, 2007, p. 240). ܐܗܐ "ܦܘܪܨܐ ܝܚܝܕܝܐ ܠܛܘܒܐ ܕܥܒܕܐ ܕܡܘܕܝܠ، ܡܛܠ ܕܫܘܠܡܐ ܥܠ ܚܕ ܐܝܬܘܬܐ ܡܨܐ ܕܡܬܪܣܐ ܫܘܠܡܐ ܥܠ ܐܝܬܘ̈ܬܐ ܐܣܝܪ̈ܬܐ" (ܬܡܢ) – ܘܒܚܬܝܬܘܬܐ ܡܢ ܐܗܝ ܥܠܬܐ ܓܢܗ̇، ܡܘܕܝܠ ܫܚܝܡܐ ܕܟܫܩܠ ܬܠܡܝܕܐ ܓܘ ܝܘܠܦܢܐ ܘܚܒܪܐ ܕܝܠܗ ܕܣܕܪܐ ܓܘ ܒܘܚܪܢܐ "ܟܡܚܡܐ" ܡܢ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܥܡ ܓܢܗ، ܠܐ ܡܢ ܬܚܘܝ̈ܬܐ.

ܡܘܕܝ ܟܥܒܕܚ. ܦܘܠܓܐ – ܠܝܘܠܦܢܐ ܘܠܒܘܚܪܢܐ، ܘܠܡܢܘ̈ܬܐ ܕܫܘܪܪܐ ܡܚܠܦܢܐ – ܥܒܝܕܐ ܝܠܗ ܠܦܘܬ ܚܘܝܕܐ ܕܡܐܡܪܐ ܥܠܘܗܝ ܝܠܗ: ܠܦܘܬ ܡܫܬܘܬܦܢܐ ܓܘ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ، ܠܦܘܬ ܣܕܪܐ ܝܢ ܡܕܪܫܬܐ ܓܘ ܝܗܝ̈ܒܬܐ ܡܩܢ̈ܢܬܐ، ܠܦܘܬ ܒܝܬܐ، ܠܦܘܬ ܟܢܘܫܬܐ (ܓܘ ܡܐܢ̈ܐ: GroupKFold ܘܕܡܝ̈ܐ ܠܗ ܓܘ scikit-learn). ܟܡܫܚܚ ܠܦܘܬ ܚܘܝܕܐ: ܛܥܝܘܬܐ ܩܐ ܬܠܡܝܕܐ ܠܐ ܝܠܗ̇ ܛܥܝܘܬܐ ܩܐ ܣܕܪܐ. ܡܢܒܝܢܘܬܐ ܠܩܕܡ ܓܘ ܙܒܢܐ – ܒܘܚܪܢܐ ܒܬܪ ܝܘܠܦܢܐ ܝܠܗ (L3.1)، ܠܐ ܡܚܠܛܐ ܒܓܘܗ. ܘܡܢ ܕܒܥܐ ܕܦܠܚ ܒܬܠܝܘܬܐ – ܕܡܢܒܐ ܬܠܡܝܕܐ ܡܢ ܚܒܪ̈ܘܗܝ – ܟܥܒܪ ܠܡܘܕ̈ܝܠܐ ܐܣܘܪ̈ܝܐ (ܫܘܠܡܐ ܟܢܘܫܝܐ، ܡܘܕ̈ܝܠܐ ܕܕܪ̈ܓܐ (hierarchical)؛ ܨܘܪܬܐ ܕܡܐܢ̈ܐ، ܦܣܩܐ 4)، ܘܟܡܬܢܐ ܕܡܐܡܪܐ ܥܠ ܡܨܝܕܬܐ ܝܠܗ ܕܐܝܬ ܠܗ̇ ܐܗܘ ܒܢܝܢܐ ܓܢܗ، ܠܐ ܥܠ ܡܫܬܘܬܦܢܐ ܝܚܝܕܝܐ. ܒܘܚܪܢܐ ܕܣܐܝܛ: ܫܐܠܬܐ "ܐܢ ܫܩܠܢ ܠܐܗܐ ܡܫܬܘܬܦܢܐ ܡܢ ܓܘܕܐ ܕܒܘܚܪܢܐ، ܡܢ ܡܢ ܓܘܕܐ ܕܝܘܠܦܢܐ ܕܡܐ ܝܠܗ ܠܗ ܒܙܘܕܐ ܡܢ ܕܣܢܝܩ؟" – ܘܐܢ ܐܝܬ ܦܘܢܝܐ، ܦܘܠܓܐ ܛܥܝܐ ܝܠܗ.

7. ܡܘܕܝ ܟܡܬܢܚ

ܦܣܩܐ ܓܡܝܪܬܐ، ܠܦܘܬ ܛܟܣܐ: ܡܚܘܝܢܐ ܘܩܐ ܡܘܕܝ (ܚܘܣܪܢܐ ܕܛܥܝܘܬܐ؛ ܬܚܘܡܐ ܕܦܘܪܫܐ ܓܒܝܐ)؛ ܦܘܠܓܐ – ܡܢܬܐ ܕܒܘܚܪܢܐ، ܦܘܠܓܐ ܠ-strata، ܠܦܘܬ ܐܝܢܐ ܚܘܝܕܐ، ܙܪܥܐ؛ ܫܘܪܪܐ ܡܚܠܦܢܐ – ܟܡܐ ܡܢܘ̈ܬܐ، ܡܨܥܝܬܐ ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ ܩܐ ܟܠ ܡܘܕܝܠ ܕܒܚܝܪܐ ܝܠܗ، ܥܡ ܐܗܘ ܕܦܠܠܗ؛ ܣܪܛܐ ܕ-baseline (baseline) – ܡܘܕܝܠ ܕܦܘܪܫܐ ܣܦܝܩܐ ܘܪܝܓܪܫܢ ܥܠ ܡܫܬܚܠܦ̈ܢܐ ܝܕܝ̈ܥܐ؛ ܡܢܝܢܐ ܚܫܝܚܐ ܝܠܗ ܦܘܪܫܢܐ ܡܢܗ، ܠܐ ܡܚܘܝܢܐ ܒܓܢܗ؛ ܓܘܕܐ ܕܒܘܚܪܢܐ – ܚܕ ܓܗܐ، ܡܚܘܝܢܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ، ܡܐܛܪܝܟܣ ܕܫܓܘܫܝܐ، ܘܦܘܪܫܢܐ ܡܢ ܫܘܪܪܐ ܡܚܠܦܢܐ؛ ܓܘ̈ܕܐ ܙܥܘܪ̈ܐ – Géron ܟܒܥܐ ܕܡܫܪܪܚ ܕܡܘܕܝܠ ܟܥܒܕ ܠܐ ܒܣ ܒܡܨܥܝܬܐ ܐܠܐ "ܥܠ ܟܠ ܓܢ̈ܣܐ ܕܦܢܝ̈ܬܐ، ܩܘܪ̈ܝܐ ܝܢ ܡܕܝܢ̈ܝܐ، ܥܬܝܪ̈ܐ ܝܢ ܡܣܟܢ̈ܐ، ܓܪܒܝ̈ܝܐ ܝܢ ܬܝܡܢ̈ܝܐ، ܙܥܘܪܘܬܐ ܝܢ ܠܐ"، ܘܐܢ ܦܐܠ ܥܠ ܓܢܣܐ ܓܡܝܪܐ، ܠܐ ܡܦܪܣܬܐ ܕܝܠܗ ܩܐ ܐܗܘ ܓܢܣܐ "ܡܛܠ ܕܡܨܐ ܕܡܚܣܪ ܒܙܘܕܐ ܡܢ ܕܡܘܬܪ" (Géron, 2022, Chapter 2, "Analyzing the Best Models and Their Errors")؛ ܡܪܕܝܬܐ – ܦܘܢܝܐ ܓܠܝܐ ܩܐ ܟܠ ܙܢܐ ܓܘ ܛܘܟܣܐ ܕܙܢ̈ܐ، ܒܢܘܣܚܐ ܕ"ܓܠܝܘܢܐ ܕܡܥܠܘܡܘܬܐ ܩܐ ܡܘܕܝܠ"؛ ܘܡܘܕܝ ܠܐ ܟܐܡܪ ܡܘܕܝܠ – ܡܢܒܝܢܘܬܐ ܠܐ ܝܠܗ̇ ܥܠܬܐ. ܟܠ ܡܕܡ ܡܨܝܐ ܕܡܬܥܒܕܐ ܡܢ ܪܝܫ ܡܢ ܟܘܢܫܐ (notebook) ܕܡܣܡܟܐ ܝܠܗ – ܐܗܘ ܢܡܘܣܐ ܓܢܗ ܕܟܠ ܡܚܫܒ̈ܢܐ ܕܣܐܝܛ: ܦܐܪܐ ܚܘܫܒܢܝܐ ܕܠܐ ܟܬܝܒܐ ܝܠܗ ܠܐ ܝܠܗ ܡܫܟܚܢܘܬܐ.

ܘܐܝܟܢ ܐܗܐ ܟܡܬܚܙܐ ܓܘ ܬܘܢܝܐ. ܨܚܚܐ 11 ܕ-Truong ܝܠܗ ܨܚܚܐ ܝܚܝܕܝܐ ܓܘ ܚܡܫܐ ܟܬ̈ܒܐ ܕܥܣܝܩܐ ܝܠܗ ܒܟܬܝܒܘܬܐ. ܒܢܝܢܐ ܕܝܠܗ ܩܐ ܡܐܡܪܐ ܝܕܥܢܝܐ ܝܠܗ ܒܢܝܢܐ ܝܕܝܥܐ – ܪܝܫܐ، ܟܢܘܫܝܐ، ܡܥܠܬܐ (introduction)، ܒܨܝܐ ܕܟܬ̈ܒܐ، ܐܘܪܚܐ، ܦܐܪ̈ܐ، ܡܫܘܚܠܦܬܐ ܘܫܘ̈ܠܡܐ – ܐܠܐ ܓܘ ܐܘܪܚܐ ܐܪܒܥܐ ܦܣ̈ܩܐ ܙܥܘܪ̈ܐ ܕܠܝܬ ܓܘ ܪܝܓܪܫܢ: ܡܒܘܥܐ ܕܝܗܝ̈ܒܬܐ ܘܬܚܘܝܬܐ ܕܡܫܬܚܠܦ̈ܢܐ (ܥܡ ܦܘܠܚܢܐ ܕܟܠ ܡܫܬܚܠܦܢܐ – ܢܝܫܐ ܝܢ ܡܥܠܬܐ – ܘܣܒܠܬܐ ܕܝܠܗ)؛ ܐܘܪܚܐ ܕܚܦܪܬܐ ܕܝܗܝ̈ܒܬܐ؛ "ܐܠܓܘܪܝ̈ܬܡܐ ܘܬܘܩ̈ܢܐ" – ܠܘܚܐ ܕܒܓܘܗ ܩܐ ܟܠ ܡܘܕܝܠ ܐܝܬ ܗܝܦܪ-ܦܪܡܝ̈ܛܪܐ ܕܝܠܗ، ܐܝܟ ܕܥܠܝܠ̈ܐ ܝܢܐ (ܥܘܡܩܐ ܥܠܝܐ ܕܐܝܠܢܐ، ܢܡܘܣܐ ܕܦܘܠܓܐ، ܢܡܘܣܐ ܕܟܠܝܬܐ، ܡܢܬܐ ܕ"ܓܘܕܐ ܕܡܢܥܬܐ ܡܢ ܦܐܝܘܬܐ ܝܬܝܪܬܐ")، "ܐܘܪܚܐ ܦܫܝܩܬܐ ܡܢ ܟܠ ܩܐ ܥܒܕܐ ܕܐܗܐ ܝܠܗ̇ ܟܢܘܫܝܐ ܕܬܘܩ̈ܢܐ ܓܘ ܠܘܚܐ"؛ ܘܡܚܘ̈ܝܢܐ ܕܫܘܥܪܐ – ܐܝܢܝ، ܘܩܐ ܡܘܕܝ (Truong, 2026, pp. 396, 414-415). ܓܘ ܦܐܪ̈ܐ: ܦܘܚܡܐ ܕܟܠ ܡܘܕ̈ܝܠܐ ܥܠ ܐܗܝ ܓܘܕܐ ܓܢܗ̇، ܡܫܬܘܕܥܢܘܬܐ ܕܡܘܕܝܠ ܙܟܝܐ (champion model) – "ܕܗܘ ܒܣ ܙܟܝܐ ܝܠܗ ܡܢ ܒܝܢܝ ܡܘܕ̈ܝܠܐ ܕܝܠܦܠܢ ܘܒܚܪܠܢ ܥܠ ܝܗܝ̈ܒܬܐ ܝܗܝ̈ܒܬܐ"، ܘܡܨܐ ܕܗܘܐ ܛܒܐ ܡܢ ܐܚܪ̈ܢܐ ܘܠܐ ܛܒܐ ܡܢ ܟܠ (ܦܐܬܐ 189) – ܘܒܬܪܟܐ، ܩܐ ܙܟܝܐ ܒܣ، ܡܚܘ̈ܝܢܐ ܥܠ ܟܠ ܓܘ̈ܕܐ ܚܕ ܓܢܒ ܚܕ، ܘܦܘܚܡܐ ܕܐܝܩܪܐ ܕܡܫܬܚܠܦ̈ܢܐ. ܦܘܪܫܢܐ ܚܕ ܡܢ ܐܗܐ ܦܐܬܐ ܛܒܐ ܝܠܗ ܕܡܝܕܥ ܠܗ: Truong ܟܟܬܒ ܕ"ܠܐ ܣܢܝܩܘܬܐ ܐܝܬ ܕܡܬܢܚ ܒܦܪܝܫܘܬܐ ܦܐܪ̈ܐ ܕܕܘܡܝܐ ܕܝܘܠܦܢܐ" (ܦܐܬܐ 188)، ܘܐܟܐ ܦܘܪܫܢܐ ܒܝܢܝ ܝܘܠܦܢܐ ܘܫܘܪܪܐ ܡܚܠܦܢܐ ܡܬܢܝܐ ܝܠܗ – ܡܛܠ ܕܗܘ ܣܗܕܘܬܐ ܝܠܗ ܩܐ ܦܐܝܘܬܐ ܝܬܝܪܬܐ، ܘܡܛܠ ܕ-Truong ܒܓܢܗ ܟܡܫܚ ܒܗ ܫܪܝܪܘܬܐ (ܦܣܩܐ 2). ܘܡܘܕܝ ܠܐ ܓܪܓ ܕܫܩܠܚ ܡܢܗ ܐܝܟ ܕܐܝܬܘܗܝ: ܢܡܘ̈ܣܐ ܕܨܒܥܐ – "ܡܢܬܐ ܕܦܘܪܫܐ ܛܥܝܐ ܕ-5% ܝܢ ܒܨܝܪ ܚܫܝܒܐ ܝܠܗ ܛܒܐ ܣܓܝ، ܘܒܝܢܝ 5% ܘ-10% – ܛܒܐ"، ܘܩܐ ܚܬܝܬܘܬܐ، ܪܓܝܫܘܬܐ، ܝܚܝܕܝܘܬܐ ܘ-F1 "95% ܘܠܥܠ ܛܒܐ ܣܓܝ، 90-95% ܛܒܐ" – ܡܝܬܝ̈ܐ ܝܢܐ ܠܘܬܗ ܓܠܝܐܝܬ ܐܝܟ ܪܥܝܢܐ ܕܝܠܢܝܐ، ܒܬܪ ܡܐܡܪܐ "ܠܝܬ ܛܝ̈ܡܐ ܬܩܝ̈ܢܐ ܕܬܚܘ̈ܡܐ ܩܐ ܐܢܝ ܡܚܘ̈ܝܢܐ؛ ܦܘܣܩܢܐ ܬܠܝܐ ܝܠܗ ܒܚܩܠܐ ܘܒܣܝܒܪܘܬܐ ܠܛܥܝܘܬܐ" (ܦܐܬܐ 199-200). ܓܘ ܡܢܒܝܢܘܬܐ ܕܦܐܪ̈ܐ ܕܒܪܢܫܘܬܐ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܕܪܩܥܐ (ܦܣܩܐ 4) ܐܢܝ ܛܝ̈ܡܐ ܠܝܬ ܠܗܘܢ، ܘܐܝܗܝ ܕܡܛܝܐ ܠܗܘܢ – ܟܕܥܪܐ ܠܦܣܩܐ 5.

8. ܘܐܝܟܢ ܟܥܒܕܚ ܐܗܐ ܒ-R

ܬܪܝܢ ܡܢܘ̈ܬܐ. ܐ. ܡܚܘ̈ܝܢܐ ܕܦܣܩܐ 1 ܥܠ ܡܢܒܝܢ̈ܘܝܬܐ ܠܒܪ ܡܢ ܕܘܡܝܐ: ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܓܘ ܫܘܪܪܐ ܡܚܠܦܢܐ ܕܥܣܪܐ ܡܢܘ̈ܬܐ ܥܠ ܦܐܝܠ ܕܡܬܠܐ ܕܦܐܬܐ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ (320 ܬܠܡܝ̈ܕܐ، ܫܒܩܬܐ ܕܡܕܪܫܬܐ 11.6%)، ܘܒܬܪܟܐ ܡܐܛܪܝܟܣ ܕܫܓܘܫܝܐ ܥܡ ܟܠ ܡܚܘ̈ܝܢܐ (confusionMatrix ܕ-caret، mode = "everything" – ܪܓܝܫܘܬܐ، ܝܚܝܕܝܘܬܐ، precision، F1، ܘ"ܡܢܬܐ ܕܚܘܣܪܢܐ ܕܡܥܠܘܡܘܬܐ" (no information rate)، ܕܝܠܗ̇ ܚܬܝܬܘܬܐ ܕܡܘܕܝܠ ܕܦܘܪܫܐ ܣܦܝܩܐ)، ܣܪܛܐ ܟܦܝܦܐ ROC ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܩܐ AUC، ܬܚܘܡܐ ܕܦܘܪܫܐ "ܛܒܐ ܡܢ ܟܠ" ܠܦܘܬ Youden، ܘܣܪܛܐ ܟܦܝܦܐ precision-recall ܡܢ ܐܢܝ ܡܢܒܝܢ̈ܘܝܬܐ ܓܢܝܗܝ (pROC). ܪܫܝܡܬܐ ܕܡܚܘ̈ܝܢܐ – ܚܬܝܬܘܬܐ، ܪܓܝܫܘܬܐ، ܝܚܝܕܝܘܬܐ، precision، ܡܢܘ̈ܬܐ ܕܕܙܘܕܐ ܛܥ̈ܝܐ ܘܕܒܨܪܐ ܛܥ̈ܝܐ – ܝܠܗ̇ ܐܗܝ ܕ-Gutierrez (2015, Chapter 7, "Measuring Classification Performance")، ܕܨܐ ܟܡܙܗܪ: "ܐܢ ܥܒܕܐ ܕܐܠܓܘܪܝܬܡ ܛܒܐ ܝܠܗ ܒܙܘܕܐ ܡܢ ܕܗܘܐ ܫܪܝܪܐ، ܡܪܕܝܬܐ ܕܝܗܝ̈ܒܬܐ ܡܨܐ ܕܗܘܐ ܥܠܬܐ" (Chapter 7, "Data Leakage"). ܒ. ܥܒܕܐ ܡܢ ܪܝܫ ܕܢܣܝܘܢܐ ܕܦܣܩܐ 5 – "ܐܘܪܚܐ ܠܐ ܬܪܝܨܬܐ ܘܬܪܝܨܬܐ ܩܐ ܫܘܪܪܐ ܡܚܠܦܢܐ" ܕ-Hastie ܘܚܒܪ̈ܘܗܝ (2009، ܦܐܬܐ 245-246) – ܒܡܐܐ ܣܕܪ̈ܐ: 50 ܡܫܬܘܬܦ̈ܢܐ، 5,000 ܡܢܒ̈ܝܢܐ ܓܕܫܢ̈ܝܐ، ܡܨܠܠܬܐ ܕ-100 ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕܝܠܗܘܢ ܪܒܐ ܝܠܗ ܡܢ ܟܠ، ܫܒܒܐ ܩܪܝܒܐ ܚܕ، ܚܡܫܐ ܡܢܘ̈ܬܐ. ܫܒܝܠܐ C:\Rdata\ – ܥܝܕܐ ܕܣܐܝܛ.

# model_evaluation.R - performance measures and validation in R: confusion matrix, ROC, cross-validation - and leakage in numbers
library(readxl); library(caret); library(pROC); library(class)

# --- A. The measures - on out-of-sample predictions, not on the training set ---
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$id <- NULL
ctrl <- trainControl(method = "cv", number = 10, classProbs = TRUE,
                     summaryFunction = twoClassSummary, savePredictions = "final")
set.seed(1)
m <- train(dropout ~ . - school_id, data = d, method = "glm", family = binomial,
           metric = "ROC", trControl = ctrl, preProcess = c("medianImpute", "center", "scale"),
           na.action = na.pass)
cv <- m$pred                                   # one prediction per observation - from the fold where it was held out
confusionMatrix(cv$pred, cv$obs, positive = "yes", mode = "everything")   # at threshold 0.5
r <- roc(cv$obs, cv$yes, levels = c("no", "yes"), direction = "<")
auc(r); ci.auc(r)                              # AUC and confidence interval
coords(r, "best", best.method = "youden", ret = c("threshold", "sensitivity", "specificity", "precision"))
# precision-recall curve - for a rare class - from the same predictions:
pr <- coords(r, x = seq(0.05, 0.6, by = 0.05), ret = c("threshold", "recall", "precision"))
pr

# --- B. The wrong and right way to do cross-validation (Hastie et al., 2009, pp. 245-246) ---
# 50 subjects in two equal classes, 5,000 random predictors - true error 50%.
set.seed(20260920)
N <- 50; P <- 5000; K <- 5; n_keep <- 100
y <- factor(rep(c("A", "B"), each = N / 2))
X <- matrix(rnorm(N * P), N, P)
folds <- createFolds(y, k = K)
screen <- function(X, y, n) {                   # the 100 predictors most correlated with the class
  r <- abs(cor(X, as.numeric(y)))
  order(-r)[1:n]
}
# wrong way: screen on the whole sample, then cross-validate
keep_all <- screen(X, y, n_keep)
err_wrong <- sapply(folds, function(te) {
  tr <- setdiff(seq_len(N), te)
  mean(knn(X[tr, keep_all], X[te, keep_all], y[tr], k = 1) != y[te])
})
# right way: screening inside each fold, on that fold's training data only
err_right <- sapply(folds, function(te) {
  tr <- setdiff(seq_len(N), te)
  keep <- screen(X[tr, ], y[tr], n_keep)
  mean(knn(X[tr, keep], X[te, keep], y[tr], k = 1) != y[te])
})
c(wrong = mean(err_wrong), right = mean(err_right))   # ~0.03 vs ~0.50

ܡܘܕܝ ܦܠܛܠܗ (R 4.3.3، caret 6.0-94، pROC 1.18.5، class 7.3-22؛ ܡܦܩܢܐ ܓܡܝܪܐ – qa/ml/ev_out.txt). ܐ. ܓܘ ܬܚܘܡܐ 0.5: ܚܬܝܬܘܬܐ ܟܠܢܝܬܐ .884 – ܒܚܬܝܬܘܬܐ ܡܢܬܐ ܕܚܘܣܪܢܐ ܕܡܥܠܘܡܘܬܐ (.884)، ܐܗܐ ܟܐܡܪ ܕܡܘܕܝܠ ܠܐ ܝܠܗ ܛܒܐ ܒܙܘܕܐ ܡܢ ܡܘܕܝܠ ܕܦܘܪܫܐ ܣܦܝܩܐ ܓܘ ܐܗܐ ܬܚܘܡܐ؛ ܪܓܝܫܘܬܐ .03، precision .50، F1 .05. ܐܗܘ ܡܘܕܝܠ ܓܢܗ، ܐܢܝ ܡܢܒܝܢ̈ܘܝܬܐ ܓܢܝܗܝ: AUC = .66، ܬܚܘܡܐ ܕܬܘܟܠܢܐ [.57, .76]؛ ܬܚܘܡܐ ܕܦܘܪܫܐ ܠܦܘܬ Youden .13 – ܪܓܝܫܘܬܐ .57، ܝܚܝܕܝܘܬܐ .72، precision .21؛ ܘܒܐܘܪܟܐ ܕܬܚܘ̈ܡܐ، ܡܢ .05 ܗܠ .50، ܪܓܝܫܘܬܐ ܟܢܚܬܐ ܡܢ .89 ܠ-.03 ܘ-precision ܟܣܠܩܐ ܡܢ .14 ܠ-.50 – ܐܗܝ ܝܠܗ̇ ܫܠܡܘܬܐ ܕܦܣܩܐ 1 ܒܡܢܝ̈ܢܐ، ܘܡܐ ܕܡܚܘܝܢܐ ܝܚܝܕܝܐ ܟܛܫܐ. ܒ. ܐܘܪܚܐ ܠܐ ܬܪܝܨܬܐ: ܛܥܝܘܬܐ 2%؛ ܐܘܪܚܐ ܬܪܝܨܬܐ: 60% – ܥܠ ܡܢܒ̈ܝܢܐ ܓܕܫܢ̈ܝܐ ܓܡܝܪܐܝܬ، ܕܛܥܝܘܬܐ ܫܪܝܪܬܐ ܥܠܝܗܝ ܝܠܗ̇ 50% (ܘ-60% ܓܘ 50 ܡܫܬܘܬܦ̈ܢܐ ܝܠܗ 50% ܓܘ ܩܠܐ ܕܚܡܫܐ ܡܢܘ̈ܬܐ). Hastie ܘܚܒܪ̈ܘܗܝ ܬܢܝܠܗܘܢ 3% ܓܘ 50 ܕܡܘ̈ܝܬܐ؛ ܐܟܐ ܕܡܘܬܐ ܚܕܐ، ܙܪܥܐ 20260920. ܡܢ ܕܡܨܠܠ ܦܣܘ̈ܩܐ ܠܦܘܬ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܥܡ ܦܐܪܐ ܩܕܡ ܦܘܠܓܐ ܟܫܩܠ ܠܡܢܝܢܐ ܩܕܡܝܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܬܘܢܝܐ ܕܚܬܝܬܘܬܐ ܟܠܢܝܬܐ ܥܠ ܓܢܣܐ ܢܕܝܪܐ. 94% ܚܬܝܬܘܬܐ ܓܘ ܡܢܒܝܢܘܬܐ ܕܫܒܩܬܐ ܕܡܕܪܫܬܐ ܕ-6% ܡܢ ܬܠܡܝ̈ܕܐ ܝܠܗ̇ ܡܘܕܝܠ ܕܦܘܪܫܐ ܣܦܝܩܐ. ܟܡܬܢܚ ܡܐܛܪܝܟܣ ܕܫܓܘܫܝܐ، precision ܘܪܓܝܫܘܬܐ – ܩܘܒܠ ܡܘܕܝܠ ܕܦܘܪܫܐ ܣܦܝܩܐ (ܦܣܩܐ 1).

ܡܬܩܢܘܬܐ، ܡܠܝܐ ܝܢ ܓܘܒܝܐ ܕܬܚܘܝ̈ܬܐ ܥܠ ܟܠ ܝܗܝ̈ܒܬܐ – ܘܒܬܪܟܐ ܦܘܠܓܐ. ܡܪܕܝܬܐ ܕܣܓܝ ܡܬܚܙܐ ܝܬܝܪ ܡܢ ܟܠ (L1.2-L1.3). ܥܝܕܐ ܡܢ SPSS – "ܩܕܡܝܐ ܟܡܕܟܚ ܠܦܐܝܠ" – ܗܘ ܥܩܬܐ ܝܠܗ. ܩܢܝܐ ܬܩܝܢܐ ܝܠܗ ܥܠ ܝܘܠܦܢܐ ܒܣ (ܦܣܩܐ 5).

ܦܘܠܓܐ ܕܣܕܪ̈ܐ ܐܝܡܢ ܕܚܘܝܕܐ ܡܫܬܘܬܦܢܐ ܝܠܗ، ܣܕܪܐ ܕܡܕܪܫܬܐ ܝܢ ܒܝܬܐ. ܬܠܬܐ ܡܫܘ̈ܚܬܐ ܕܐܗܘ ܒܪܢܫܐ ܓܢܗ ܓܘ ܝܘܠܦܢܐ ܘܓܘ ܒܘܚܪܢܐ – ܘܡܘܕܝܠ "ܟܡܫܬܘܕܥ" ܠܗ ܒܕܘܟܬ ܕܡܢܒܐ (ܦܣܩܐ 6). ܦܘܠܓܐ ܠܦܘܬ ܚܘܝܕܐ ܕܡܐܡܪܐ ܥܠܘܗܝ ܝܠܗ.

ܬܘܩܢܐ ܥܠ ܓܘܕܐ ܕܒܘܚܪܢܐ. ܪܗܛܐ، ܚܙܝܬܐ ܕܦܐܪܐ ܠܐ ܝܠܗ ܛܒܐ، ܫܘܚܠܦܐ، ܪܗܛܐ ܬܘܒ. ܒܬܪ ܓܗܐ ܬܪܝܢܐ ܓܘܕܐ ܕܒܘܚܪܢܐ ܓܘܕܐ ܕܫܘܪܪܐ ܝܠܗ̇، ܘܡܢܝܢܐ ܕܟܡܬܢܚ ܣܒܪܢܐ ܝܠܗ ܒܙܘܕܐ (ܦܣܩܐ 2).

ܡܢܝܢܐ ܚܕ ܕܠܐ ܒܕܪܐ. AUC = .78 ܡܢ ܡܢܬܐ ܚܕܐ ܡܨܐ ܕܗܘܐ .71 ܓܘ ܡܢܬܐ ܐܚܪܬܐ. ܡܨܥܝܬܐ ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ ܥܠ ܡܢܘ̈ܬܐ، ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܥܠ ܒܘܚܪܢܐ (ܦܣܩܐ 3).

ܬܡܗܐ ܡܢ ܡܘܕܝܠ ܕܠܐ ܣܪܛܐ ܕ-baseline. AUC = .78 ܟܡܫܬܡܥ ܛܒܐ ܣܓܝ ܗܠ ܕܚܙܚ ܕܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܥܠ ܐܪܒܥܐ ܡܫܬܚܠܦ̈ܢܐ ܟܝܗܒ .76. ܡܢܝܢܐ ܦܘܪܫܢܐ ܝܠܗ – ܘ-Salganik ܘܚܒܪ̈ܘܗܝ (2020) ܚܘܝܠܗܘܢ ܟܡܐ ܙܥܘܪܐ ܡܨܐ ܕܗܘܐ.

ܚܫܒܬܐ ܕ-R² ܕܒܘܚܪܢܐ ܐܝܟ R² ܕܪܝܓܪܫܢ. ܥܠ ܝܗܝ̈ܒܬܐ ܚܕ̈ܬܬܐ ܡܨܐ ܕܗܘܐ ܨܦܪܐ ܘܐܦ ܬܚܝܬ ܨܦܪܐ؛ 0.2 ܓܘ ܐܬܓܪܐ ܕܒ̈ܢܝ ܒܝܬܐ ܬܒܝܪ̈ܐ ܗܘܐ ܪܘܡܐ ܥܠܝܐ ܕ-160 ܓܘ̈ܕܐ.

ܫܘܝܬܐ ܕܓܢ̈ܣܐ ܒܓܘܒܝܐ ܝܬܝܪܐ ܕܕܘܡܝܐ – ܘܬܘܢܝܐ ܕܡܣܬܒܪܢ̈ܘܝܬܐ. ܒܬܪ SMOTE ܝܢ ܢܣܚܐ، ܡܣܬܒܪܢܘܬܐ ܡܢܒܝܬܐ ܩܐ ܓܢܣܐ ܢܕܝܪܐ ܫܥܝܪܬܐ ܝܠܗ̇ ܒܙܘܕܐ، ܘ-AUC ܠܐ ܟܣܠܩ (van den Goorbergh et al., 2022). ܟܡܙܝܥܚ ܠܬܚܘܡܐ ܕܦܘܪܫܐ، ܝܢ ܟܡܥܠܚ ܡܐܛܪܝܟܣ ܕܦܘܣܩܢܐ (ܦܣܩܐ 1)؛ ܘܐܢ ܟܡܫܘܝܚ – ܒܣ ܓܘ ܡܢܬܐ ܕܝܘܠܦܢܐ.

ܩܪܝܢܐ ܕܡܚܘܝܢܐ ܪܡܐ ܒܙܘܕܐ ܐܝܟ ܛܘܒܐ. ܐܝܡܢ ܕܦܐܪܐ ܟܥܒܪ ܒܣܓܝ ܥܠ ܟܬ̈ܒܐ ܘܥܠ ܣܪܛܐ ܕ-baseline، ܚܘܫܕܐ ܩܕܡܝܐ ܝܠܗ ܡܪܕܝܬܐ (ܦܣܩܐ 5) – ܬܚܘܝܬܐ ܕܝܠܗ ܢܝܫܐ ܒܦܪܨܘܦܐ ܐܚܪܢܐ، ܝܢ ܡܫܬܘܬܦܢܐ ܕܐܝܬܘܗܝ ܓܘ ܬܪܘܝܗܝ ܓܢܒ̈ܐ. "ܚܫܒܬܐ ܕܦܐܪ̈ܐ… ܐܝܟ ܙܒܢܢ̈ܝܐ" (Kapoor & Narayanan, 2023، R2).

ܪܫܝܡܬܐ ܕܒܘܚܪܢܐ (checklist) – ܩܕܡ ܕܬܢܚ ܦܐܪܐ ܕܡܢܒܝܢܘܬܐ

ܡܒܘ̈ܥܐ

Bishop, C. M. (2006). Pattern recognition and machine learning. Springer.

Géron, A. (2022). Hands-on machine learning with Scikit-Learn, Keras, and TensorFlow: Concepts, tools, and techniques to build intelligent systems (3rd ed.). O'Reilly Media.

Getoor, L., & Taskar, B. (2007). Introduction. In L. Getoor & B. Taskar (Eds.), Introduction to statistical relational learning (pp. 1-12). MIT Press. https://doi.org/10.7551/mitpress/7432.003.0003

Gutierrez, D. D. (2015). Machine learning and data science: An introduction to statistical learning methods with R. Technics Publications.

Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning: Data mining, inference, and prediction (2nd ed.). Springer. https://doi.org/10.1007/978-0-387-84858-7

IBM Corporation. (2016). IBM SPSS Modeler 18.0 source, process, and output nodes. IBM. https://public.dhe.ibm.com/software/analytics/spss/documentation/modeler/18.0/en/ModelerSPOnodes.pdf

Ishii, K., Ueda, N., Maeda, E., & Murase, H. (2026). Pattern recognition and machine learning for self-study I: Supervised learning. Springer. https://doi.org/10.1007/978-981-95-1478-6

Kapoor, S., & Narayanan, A. (2023). Leakage and the reproducibility crisis in machine-learning-based science. Patterns, 4(9), Article 100804. https://doi.org/10.1016/j.patter.2023.100804

Kuhn, M. (2008). Building predictive models in R using the caret package. Journal of Statistical Software, 28(5), 1-26. https://doi.org/10.18637/jss.v028.i05

Neville, J., & Jensen, D. (2007). Relational dependency networks. In L. Getoor & B. Taskar (Eds.), Introduction to statistical relational learning (pp. 239-268). MIT Press. https://doi.org/10.7551/mitpress/7432.003.0010

Salganik, M. J., Lundberg, I., Kindel, A. T., Ahearn, C. E., Al-Ghoneim, K., Almaatouq, A., Altschul, D. M., Brand, J. E., Carnegie, N. B., Compton, R. J., Datta, D., Davidson, T., Filippova, A., Gilroy, C., Goode, B. J., Jahani, E., Kashyap, R., Kirchner, A., McKay, S., . . . McLanahan, S. (2020). Measuring the predictability of life outcomes with a scientific mass collaboration. Proceedings of the National Academy of Sciences, 117(15), 8398-8403. https://doi.org/10.1073/pnas.1915006117

Shmueli, G. (2010). To explain or to predict? Statistical Science, 25(3), 289-310. https://doi.org/10.1214/10-STS330

Taskar, B., Abbeel, P., Wong, M.-F., & Koller, D. (2007). Relational Markov networks. In L. Getoor & B. Taskar (Eds.), Introduction to statistical relational learning (pp. 175-200). MIT Press. https://doi.org/10.7551/mitpress/7432.003.0008

Truong, D. (2026). Demystifying AI: Data science and machine learning using IBM SPSS Modeler. Chapman and Hall/CRC. https://doi.org/10.1201/9781003468196

van den Goorbergh, R., van Smeden, M., Timmerman, D., & Van Calster, B. (2022). The harm of class imbalance corrections for risk prediction models: Illustration and simulation using logistic regression. Journal of the American Medical Informatics Association, 29(9), 1525-1534. https://doi.org/10.1093/jamia/ocac093

Wendler, T., & Gröttrup, S. (2021). Data mining with SPSS Modeler: Theory, exercises and solutions (2nd ed.). Springer. https://doi.org/10.1007/978-3-030-54338-9