Протодьяконов Алгоритмы Data Science и их практическая реализация на Python 2022
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ɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɢ Ɂɚɝɪɭɡɢɦɭɦɟɧɶɲɟɧɧɵɟɢɡɨɛɪɚɠɟɧɢɹ ɭɦɟɧɶɲɢɦɢɯɟɳɟɜ ɪɚɡɚɢɩɪɢ
ɦɟɧɢɦ ɤ ɧɢɦ ɞɨɩɨɥɧɟɧɢɟ DXJPHQWDWLRQ ɫɦɟɳɟɧɢɟ ɤɨɧɬɪɚɫɬɧɨɫɬɶ ɩɨɜɨɪɨɬ ɪɚɡɦɵɬɢɟ
Ɂɚɝɪɭɡɢɦ ɞɚɧɧɵɟ ɢ ɪɚɡɞɟɥɢɦ ɢɯ ɧɚ ɨɛɭɱɚɸɳɢɟ ɢ ɩɪɨɜɟɪɨɱɧɵɟ ɜ ɫɨɨɬɧɨ ɲɟɧɢɢ
ɂɫɩɨɥɶɡɭɟɦ .HUDV ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɧɟɣɪɨɫɟɬɢ ɫ ɥɢɧɟɣɧɵɦ ɫɜɟɪɬɨɱɧɵɦɢ ɫɥɨɹɦɢ ɢ ɫɥɨɹɦɢ ɩɨɞɜɵɛɨɪɤɢ
Ɉɛɭɱɢɦ ɦɨɞɟɥɶ ɢɫɩɨɥɶɡɭɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɭɸ ɡɚɝɪɭɡɤɭ ɞɚɧɧɵɯ ɉɪɨɜɟ ɞɟɦ ɨɰɟɧɤɭ ɤɚɱɟɫɬɜɚ ɩɪɟɞɫɤɚɡɚɧɢɹ ɩɨ ɤɨɷɮɮɢɰɢɟɧɬɭ ɫɯɨɞɫɬɜɚ
Ⱦɚɧɧɵɟ
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ȅȎȟȠȪ ǮǾȃǶȀdzǸȀȁǾȉ ǿǰdzǾȀǼȅǻȉȃ ǻdzǷǾǼǿdzȀdzǷ
LENET
ɉɪɨɞɨɥɠɚɹɢɫɫɥɟɞɨɜɚɧɢɟɫɜɟɪɬɨɱɧɵɯɧɟɣɪɨɫɟɬɟɣ ɪɚɫɫɦɨɬɪɢɦɤɚɤɢɦɨɛ ɪɚɡɨɦ ɨɧɢ ɷɜɨɥɸɰɢɨɧɢɪɨɜɚɥɢ ɨɬ ɪɚɫɩɨɡɧɚɜɚɧɢɹ ɩɪɨɫɬɵɯ ɰɢɮɪ ɞɨ ɜɵɞɟɥɟɧɢɹ ɫɥɨɠɧɵɯ ɦɧɨɝɨɰɜɟɬɧɵɯ ɨɛɴɟɤɬɨɜ ɧɚ ɛɨɥɶɲɢɯ ɢɡɨɛɪɚɠɟɧɢɹɯ ɢ ɥɨɤɚɥɢɡɚɰɢɢ ɦɟɫɬɨɩɨɥɨɠɟɧɢɹ ɷɬɢɯ ɨɛɴɟɤɬɨɜ ɧɚ ɢɡɨɛɪɚɠɟɧɢɹɯ
ɇɚɱɚɥɨɫɶ ɜɫɺ ɫ ɭɫɩɟɲɧɨɣ ɩɟɪɜɨɣ ɫɜɟɪɬɨɱɧɨɣ ɧɟɣɪɨɫɟɬɢ ɪɚɡɪɚɛɨɬɚɧɧɨɣ ɜ ɫɟɪɟɞɢɧɟ ɞɟɜɹɧɨɫɬɵɯ ɝɨɞɨɜ ɜɟɤɚ əɧɨɦ Ʌɟɤɭɧɨɦ Ɉɧɚɧɚɡɵɜɚɥɚɫɶ /H1HW ɩɨ ɫɨɤɪɚɳɟɧɢɸ ɮɚɦɢɥɢɢ ɚɜɬɨɪɚ ɗɬɚ ɫɟɬɶ ɩɨɡɜɨɥɢɥɚ ɧɚ ɨɝɪɚɧɢɱɟɧɧɵɯ ɬɨɝɞɚ ɚɩ ɩɚɪɚɬɧɵɯ ɪɟɫɭɪɫɚɯ ɩɨɫɬɪɨɢɬɶ ɢ ɭɫɩɟɲɧɨ ɨɛɭɱɢɬɶ ɧɟɣɪɨɫɟɬɶ ɤɨɬɨɪɚɹ ɨɬɥɢɱɧɨ ɤɥɚɫɫɢɮɢɰɢɪɨɜɚɥɚ ɱɺɪɧɨ ɛɟɥɵɟ ɧɚɱɟɪɬɚɧɢɹ ɰɢɮɪ ɩɪɚɤɬɢɱɟɫɤɢ ɬɚɤ ɠɟ ɬɨɱɧɨ ɤɚɤ ɱɟɥɨɜɟɤ
ȼ ɬɨ ɜɪɟɦɹ ɷɬɨ ɛɵɥ ɩɪɨɪɵɜ ɜ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɧɟɣɪɨɫɟɬɟɣ ɢ ɩɨɫɥɭɠɢɥɨ ɨɬɩɪɚɜɧɨɣɬɨɱɤɨɣɞɥɹɭɫɩɟɲɧɨɝɨɜɧɟɞɪɟɧɢɹɞɚɥɶɧɟɣɲɢɯɫɜɟɪɬɨɱɧɵɯɧɟɣɪɨɫɟ ɬɟɣ Ɋɚɡɛɟɪɟɦ ɩɪɢɧɰɢɩ ɪɚɛɨɬɵ ɷɬɨɣ ɧɟɣɪɨɫɟɬɢ ɇɚ ɜɯɨɞ ɫɟɬɢ ɩɨɞɚɜɚɥɢɫɶ ɢɡɨɛ ɪɚɠɟɧɢɹ ɰɢɮɪ ɜɫɟɝɨ ɞɟɫɹɬɶ ɤɥɚɫɫɨɜ ɢ ɨɞɢɧɧɚɞɰɚɬɵɣ ɤɥɚɫɫ ɨɛɨɡɧɚɱɚɥ ɨɬɫɭɬ ɫɬɜɢɟ ɰɢɮɪɵ ɪɚɡɦɟɪ ɢɡɨɛɪɚɠɟɧɢɹ ɛɵɥ × ɩɢɤɫɟɥɹ ɉɢɤɫɟɥɢ ɱɟɪɧɨ ɛɟɥɵɟ ɬɨ ɟɫɬɶ ɥɢɛɨ ɰɜɟɬ ɩɪɢɫɭɬɫɬɜɭɟɬ ɥɢɛɨ ɰɜɟɬɚ ɧɟɬ ɉɨ ɷɬɢɦ ɢɡɨɛɪɚɠɟɧɢɹ ɞɜɢɝɚ ɟɬɫɹ ɮɢɥɶɬɪ × ɧɚɩɪɢɦɟɪ
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ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɮɢɥɶɬɪ ɜɵɞɟɥɹɟɬ ɧɟɤɨɬɨɪɭɸ ɜɟɪɬɢɤɚɥɶɧɭɸ ɱɟɪɬɭ ɉɨ ɧɹɬɧɨ ɱɬɨ ɨɧ ɦɨɠɟɬ ɜɵɞɟɥɹɬɶ ɝɨɪɢɡɨɧɬɚɥɶɧɭɸ ɱɟɪɬɭ ɤɪɟɫɬɢɤ ɭɝɨɥɤɢ ɤɜɚɞ ɪɚɬ Ʌɟɤɭɧ ɩɪɟɞɥɨɠɢɥ ɢɫɩɨɥɶɡɨɜɚɬɶ ɷɬɢ ɲɟɫɬɶ ɮɢɥɶɬɪɨɜ × ɱɬɨɛɵ ɢɡ ɢɫɯɨɞ ɧɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ × ɩɨɥɭɱɢɬɶ ɩɪɨɟɤɰɢɣ ×
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Ʉɚɠɞɚɹ ɨɛɥɚɫɬɶ × ɧɚɤɥɚɞɵɜɚɟɬɫɹ ɧɚ ɢɫɯɨɞɧɵɟ ɩɢɤɫɟɥɢ Ɍɨ ɟɫɬɶ ɷɬɨɬ ɮɢɥɶɬɪɤɚɤɛɵɩɪɨɹɜɥɹɟɬɷɬɭɜɟɪɬɢɤɚɥɶɧɭɸɩɨɥɨɫɤɭɧɚɢɡɨɛɪɚɠɟɧɢɢ ɟɫɥɢɱɟɪ ɧɵɟ ɩɢɤɫɟɥɢ ɧɚɥɨɠɢɥɢɫɶ ɧɚ ɜɟɪɬɢɤɚɥɶɧɭɸ ɩɨɥɨɫɤɭ ɬɨ ɜɵɯɨɞɢɬ ɦɚɤɫɢɦɚɥɶɧɚɹ ɫɭɦɦɚ ɢ ɨɧ ɩɟɪɟɯɨɞɢɬ ɜ ɥɟɜɵɣ ɜɟɪɯɧɢɣ ɩɢɤɫɟɥɶ ɋɞɜɢɝɚɹ ɮɢɥɶɬɪ ɧɚ ɟɞɢɧɢɰɭ ɩɨɥɭɱɚɟɦ ɫɥɟɞɭɸɳɢɟ ɡɧɚɱɟɧɢɹ
ɉɨɥɭɱɚɟɬɫɹ ɱɬɨ ɦɚɬɪɢɰɚ ɫɜɟɪɬɤɢ — ɷɬɨ ɧɟɤɢɣ ɮɢɥɶɬɪ ɩɪɟɞɫɬɚɜɥɹɸɳɢɣ ɫɨɛɨɣ ɧɚɛɨɪ ɱɢɫɟɥ ɤɨɬɨɪɵɣ ɧɚɤɥɚɞɵɜɚɟɦ ɧɚ ɨɛɥɚɫɬɢ ɢɫɯɨɞɧɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɩɟɪɟɦɧɨɠɚɟɦ ɫ ɡɧɚɱɟɧɢɹɦɢ ɧɚɩɪɢɦɟɪ ɰɜɟɬɚ ɢɫɯɨɞɧɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɢ ɡɚɬɟɦ ɋɜɟɬɚ ɧɚɩɪɢɦɟɪ ɨɛɥɚɫɬɢ ɢɫɯɨɞɧɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɡɚɬɟɦ ɫɤɥɚɞɵɜɚɟɦ ɩɟɪɟɦɧɨ ɠɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɜ ɨɞɧɨ ɱɢɫɥɨ ɗɬɨ ɢ ɟɫɬɶ ɫɜɟɪɬɤɚ ɩɢɤɫɟɥɟɣ ɫɜɨɪɚɱɢɜɚɟɦ ɜ ɨɞɧɨ ɡɧɚɱɟɧɢɟ ɋɥɟɞɭɸɳɢɟ ɜ ɞɪɭɝɨɟ ɡɧɚɱɟɧɢɟ ɢ ɜ ɤɨɧɰɟ ɩɨɥɭɱɚɟɦ × ɧɨ ɭɠɟ ɲɟɫɬɶ ɩɪɨɟɤɰɢɣ ɉɨɫɤɨɥɶɤɭ ɦɵ ɩɪɢɦɟɧɹɟɦ ɲɟɫɬɶ ɪɚɡɧɵɯ ɜɚɪɢɚɧɬɨɜ ɮɢɥɶɬɪɨɜ ɉɨɥɭɱɚɟɬɫɹ ɱɬɨ ɢɡ ɧɚɱɚɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɜɟɫɨɜ ɦɵ ɭɠɟ ɩɨɥɭɱɢɥɢɡɧɚɱɟɧɢɣ
ɉɨɧɹɬɧɨ ɱɬɨ ɫɨɫɟɞɧɢɟ ɩɢɤɫɟɥɢ ɫɨɞɟɪɠɚɬ ɦɚɥɨ ɪɚɡɥɢɱɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɨɛ ɢɫɯɨɞɧɨɦ ɢɡɨɛɪɚɠɟɧɢɢ ɉɨɷɬɨɦɭ ɩɨɫɥɟ ɫɥɨɹ ɫɜɟɪɬɤɢ ɢɫɩɨɥɶɡɭɸɬ ɫɥɨɣ ɩɨɞ ɜɵɛɨɪɤɢ ɋɥɨɣ ɩɨɞɜɵɛɨɪɤɢ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ ɱɬɨ ɦɵ ɫɜɨɪɚɱɢɜɚɟɦ ɤɚɠɞɵɟ ɱɟɬɵɪɟ ɩɢɤɫɟɥɹ ɬɨ ɟɫɬɶ ɜɵɛɢɪɚɟɦ ɨɞɢɧ ɢɡ ɧɢɯ
ɍ ɧɚɫ ɨɫɬɚɟɬɫɹ ɲɟɫɬɶ ɩɪɨɟɤɰɢɣ ɧɨ ɪɚɡɦɟɪ ɢɡɨɛɪɚɠɟɧɢɹ ɫɨɤɪɚɬɢɥɫɹ ɞɨ× ɋɥɟɞɭɸɳɢɣ ɲɚɝ ɫɜɨɞɢɬɫɹ ɤ ɩɪɢɦɟɧɟɧɢɸ ɧɨɜɨɝɨ ɧɚɛɨɪɚ ɮɢɥɶɬɪɨɜ ɫɨ ɫɬɨɹɳɟɝɨ ɭɠɟ ɢɡ ɲɟɫɬɧɚɞɰɚɬɢ ɜɚɪɢɚɧɬɨɜ ɗɬɢ ɮɢɥɶɬɪɵ ɫɤɥɚɞɵɜɚɸɬɫɹ ɢɡ ɛɚɡɨ ɜɵɯɮɢɥɶɬɪɨɜ ɧɚɩɪɢɦɟɪɝɨɪɢɡɨɧɬɚɥɶɧɚɹɥɢɧɢɹɫɤɪɟɫɬɢɤɨɦ ɥɢɛɨɜɟɪɬɢɤɚɥɶɧɚɹ ɥɢɧɢɹ ɫ ɭɝɨɥɤɨɦ ɉɨɥɭɱɚɟɬɫɹ ɲɟɫɬɧɚɞɰɚɬɶ ɪɚɡɥɢɱɧɵɯ ɧɚɛɨɪɨɜ ɷɬɢɯ ɮɢɥɶɬɪɨɜ
Ɋɚɡɦɟɪ ɦɚɬɪɢɰɵ ɫɜɟɪɬɤɢ ɨɫɬɚɟɬɫɹ ɬɚɤɢɦ ɠɟ × ɉɨɫɥɟ ɧɚɥɨɠɟɧɢɹ ɷɬɨɣ ɦɚɬɪɢɰɵ ɧɚ ɢɡɨɛɪɚɠɟɧɢɟ × ɩɨɥɭɱɚɟɦ ɢɡɨɛɪɚɠɟɧɢɟ × ȼɚɠɧɨ ɩɨɦ ɧɢɬɶ ɤɨɝɞɚ ɩɪɢɦɟɧɹɟɦ ɮɢɥɶɬɪ ɬɨ ɨɧ ɩɪɢɦɟɧɹɟɬɫɹ ɤɨ ɜɫɟɦ ɲɟɫɬɢ ɩɪɨɟɤɰɢɹɦ
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ȼɫɟɦɢɷɬɢɦɢɩɪɨɰɟɫɫɚɦɢɦɵɫɬɪɟɦɢɦɫɹɩɨɥɭɱɢɬɶɦɚɤɫɢɦɚɥɶɧɨɪɚɡɧɨɨɛ ɪɚɡɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɢɫɯɨɞɧɨɣ ɤɨɦɛɢɧɚɰɢɢ Ⱦɚɥɟɟ ɫɧɨɜɚ ɢɞɟɬ ɫɥɨɣ ɩɨɞɜɵ ɛɨɪɤɢ
Ɇɵ ɫɜɟɪɧɭɥɢ ɱɟɬɵɪɟ ɩɢɤɫɟɥɹɜ ɨɞɢɧɢɩɨɥɭɱɢɥɢɲɟɫɬɧɚɞɰɚɬɶ ɢɡɨɛɪɚɠɟ ɧɢɣ × ɒɟɫɬɧɚɞɰɚɬɶ ɢɡɨɛɪɚɠɟɧɢɣ × ɩɢɤɫɟɥɟɣ ɞɚɸɬ ɧɚɦ ɡɧɚ ɱɟɧɢɣ ɤɨɬɨɪɵɟ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɤɨɦɛɢɧɚɰɢɸ ɩɪɨɫɬɵɯ ɮɨɪɦ ɮɢɥɶɬɪɨɜ ɢ ɩɨɞɜɵɛɨɪɤɭ ɢɡ ɧɚɢɛɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɷɬɢɯ ɩɪɨɫɬɵɯ ɮɨɪɦ
ȼ ɤɨɧɰɟ ɩɪɢɫɨɟɞɢɧɹɟɦ ɩɢɤɫɟɥɟɣ ɤ ɧɟɣɪɨɧɚɦ ɡɚɬɟɦ ɤ ɧɟɣɪɨ ɧɚɦɢɜɫɟɷɬɨɩɟɪɟɯɨɞɢɬɜ ɤɥɚɫɫɨɜ ɉɨɥɭɱɚɟɬɫɹɜɚɪɯɢɬɟɤɬɭɪɟ/H1HWɢɦɟɟɬɫɹ ɞɜɚ ɩɨɥɧɨɫɜɹɡɧɵɯ ɫɥɨɹ ɜ ɤɨɧɰɟ Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɜɵɯɨɞɹɬ ɞɜɚ ɤɚɫɤɚɞɚ ɫɜɟɪɬɤɢ ɩɨɞɜɵɛɨɪɤɢ ɬɨ ɟɫɬɶ ɜɨɬ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜɵɞɟɥɹɟɦ ɩɪɨɫɬɵɟ ɮɨɪɦɵ ɩɨɬɨɦ ɤɨɦɛɢɧɚɰɢɢ ɷɬɢɯ ɩɪɨɫɬɵɯ ɮɨɪɦ ɢ ɡɚɬɟɦ ɭɠɟ ɱɟɪɟɡ ɞɜɚ ɩɨɥɧɨɫɜɹɡɧɵɯ ɫɥɨɹ ɩɵ ɬɚɟɦɫɹ ɞɨ ɩɟɪɟɦɧɨɠɢɬɶ ɧɚɣɞɟɧɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɢ ɭɫɩɟɲɧɨ ɜɵɞɟɥɹɟɦ ɜ ɧɢɯɤɥɚɫɫɨɜ
Ʉɚɤ ɩɨɤɚɡɚɥɚ ɩɪɚɤɬɢɤɚ ɫɟɬɶ ɞɨɫɬɚɬɨɱɧɨ ɭɫɩɟɲɧɨ ɫɦɨɝɥɚ ɫɠɚɬɶ ɢɡɨɛɪɚ ɠɟɧɢɟ × ɞɨ ɤɥɚɫɫɨɜ /H1HW ɩɟɪɜɚɹ ɭɫɩɟɲɧɚɹ ɫɜɟɪɬɨɱɧɚɹ ɧɟɣɪɨɫɟɬɶ ɤɨ ɬɨɪɚɹɩɨɡɜɨɥɢɥɚɭɫɩɟɲɧɨɪɟɲɢɬɶɡɚɞɚɱɭɪɚɫɩɨɡɧɚɜɚɧɢɹɪɭɤɨɩɢɫɧɵɯɰɢɮɪ ɗɬɨ ɩɨɥɨɠɢɥɨ ɧɚɱɚɥɨ ɩɪɢɦɟɧɟɧɢɸ ɫɜɟɪɬɨɱɧɵɯ ɚɪɯɢɬɟɤɬɭɪ ɇɚ ɫɟɝɨɞɧɹɲɧɢɣ ɞɟɧɶ ɫɜɟɪɬɨɱɧɵɟ ɧɟɣɪɨɫɟɬɢ ɢɫɩɨɥɶɡɭɸɬɫɹ ɩɨɜɫɟɦɟɫɬɧɨ ɦɨɛɢɥɶɧɵɦɢ ɬɟɥɟɮɨɧɚɦɢ ɭɦɧɵɦɢ ɱɚɫɚɦɢ ɤɚɦɟɪɚɦɢ ɫ ɪɚɫɩɨɡɧɚɜɚɧɢɟɦ ɥɢɰ ɢ ɬɚɤ ɞɚɥɟɟ
ALEXNET
ɋɥɟɞɭɸɳɢɦ ɛɨɥɶɲɢɦ ɲɚɝɨɦ ɜ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɫɜɟɪɬɨɱɧɵɯ ɧɟɣɪɨɫɟɬɟɣ ɫɬɚɥɚ ɧɟɣɪɨɫɟɬɶ $OH[1HW ɫɨɡɞɚɧɧɚɹ ɜ ɝɨɞɭ Ɉɧɚ ɩɨɡɜɨɥɢɥɚ ɪɚɛɨɬɚɬɶ ɫ ɞɨ ɫɬɚɬɨɱɧɨ ɛɨɥɶɲɢɦɢ ɩɨɥɧɨɰɜɟɬɧɵɦɢ ɢɡɨɛɪɚɠɟɧɢɹɦɢ ɢ ɤɥɚɫɫɢɮɢɰɢɪɨɜɚɬɶ ɢɯ ɩɨ ɪɚɡɧɵɯ ɤɥɚɫɫɨɜ ɗɬɨ ɛɵɥɢ ɧɟɤɨɬɨɪɵɟ ɨɛɴɟɤɬɵ ɪɟɚɥɶɧɨɝɨ ɦɢɪɚ ɦɚ ɲɢɧɵ ɫɚɦɨɥɺɬɵ ɠɢɜɨɬɧɵɟ ɢɬɚɤɞɚɥɟɟɜɫɟɝɨ ɤɥɚɫɫɨɜ ɇɟɫɤɨɥɶɤɨ ɦɢɥɥɢ ɨɧɨɜ ɢɥɢ ɞɚɠɟ ɞɟɫɹɬɤɨɜ ɦɢɥɥɢɨɧɨɜ ɢɡɨɛɪɚɠɟɧɢɣ ɧɚ ɤɨɬɨɪɵɯ ɧɟɣɪɨɫɟɬɶ ɨɛɭ ɱɚɥɚɫɶ
ɗɬɨ ɛɵɥ ɛɨɥɶɲɨɣ ɮɭɧɞɚɦɟɧɬɚɥɶɧɵɣ ɩɪɨɪɵɜ ɩɨɫɤɨɥɶɤɭ ɷɬɚ ɚɪɯɢɬɟɤɬɭɪɚ ɫɜɟɪɬɨɱɧɨɣ ɧɟɣɪɨɫɟɬɢ ɩɨɡɜɨɥɢɥɚ ɪɟɲɢɬɶ ɛɨɥɶɲɢɧɫɬɜɨ ɩɪɨɦɵɲɥɟɧɧɵɯ ɡɚɞɚɱ
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ɇɚɩɪɢɦɟɪ ɩɨɞɚɜɚɹ ɧɚ ɜɯɨɞ ɷɬɨɣ ɚɪɯɢɬɟɤɬɭɪɵ ɛɚɡɭ ɥɢɰ ɪɚɛɨɱɢɯ ɩɪɟɞɩɪɢɹɬɢɹ ɧɚ ɜɵɯɨɞɟ ɩɨɥɭɱɚɟɦ ɜɨɡɦɨɠɧɨɫɬɶ ɜɧɟɞɪɟɧɢɹ ɧɚ ɩɪɟɞɩɪɢɹɬɢɢ ɪɚɫɩɨɡɧɚɜɚɧɢɹ ɥɢɰ ɩɨ ɮɨɬɨɝɪɚɮɢɹɦ
Ɋɚɫɫɦɨɬɪɢɦ ɤɚɤ ɨɪɝɚɧɢɡɨɜɚɧɚ ɧɟɣɪɨɫɟɬɶ $OH[1HW ɇɚ ɜɯɨɞ ɩɨɞɚɟɬɫɹ ɢɡɨɛɪɚɠɟɧɢɟ × Ɍɚɤɨɣ ɪɚɡɦɟɪ ɨɛɭɫɥɨɜɥɟɧ ɚɪɯɢɬɟɤɬɭɪɨɣ ɇɭɠɧɨ ɩɨɥɭ ɱɢɬɶ ɰɟɥɨɟ ɱɢɫɥɨ ɩɢɤɫɟɥɟɣ ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɗɬɨ ɧɟ ɡɧɚɱɢɬ ɱɬɨ ɨɧɚ ɧɟ ɦɨɝɥɚ ɛɵ ɢɫɩɨɥɶɡɨɜɚɬɶ ɢɡɨɛɪɚɠɟɧɢɹ ɞɪɭɝɢɯ ɪɚɡɦɟɪɨɜ ɧɨ ɷɬɨ ɬɪɟɛɭɟɬ ɤɨɪɪɟɤɬɢɪɨɜɤɢ ɚɪɯɢɬɟɤɬɭɪɵ Ⱦɥɹ ɬɟɤɭɳɢɯ ɚɪɯɢɬɟɤɬɭɪ ɫɜɟɪɬɨɱɧɵɯ ɧɟɣɪɨɫɟɬɟɣ ɬɚɤɨɣ ɩɪɨ ɛɥɟɦɵ ɧɟɬ
Ɍɚɤɠɟɷɬɨɧɟɩɪɨɫɬɨɱɟɪɧɨ ɛɟɥɨɟɢɡɨɛɪɚɠɟɧɢɟ ɨɧɚɪɚɛɨɬɚɟɬɫɬɪɟɦɹɰɜɟ ɬɨɜɵɦɢ ɤɚɧɚɥɚɦɢ ɞɥɹ ɩɪɢɦɟɪɚ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɢɯ 5*% ɇɚɤɥɚɞɵɜɚɟɦ ɫɜɟɪ ɬɨɱɧɵɣ ɮɢɥɶɬɪ ×
ɋɜɟɪɬɤɚ ɪɚɛɨɬɚɟɬ ɞɥɹ ɜɫɟɯ ɬɪɺɯ ɢɡɨɛɪɚɠɟɧɢɣ ɬɨ ɟɫɬɶ ɫɭɦɦɢɪɭɟɬɫɹ ɧɟɡɧɚɱɟɧɢɣ ɚ ɡɧɚɱɟɧɢɣ ɜ ɨɞɢɧ ɧɨɜɵɣ ɩɢɤɫɟɥɶ ɉɨɫɥɟ ɧɚɥɨɠɟɧɢɹ ɜɫɟɯ ɮɢɥɶɬɪɨɜ ɩɨɥɭɱɢɬɫɹ ɢɡɨɛɪɚɠɟɧɢɣ × ɢɡɨɛɪɚɠɟɧɢɣ ɩɨɥɭɱɚɸɬɫɹ ɢɡ ɡɚ ɫɞɜɢɝɚ ɮɢɥɶɬɪɚ ȼ ɨɬɥɢɱɢɢ ɨɬ /H1HW ɨɧ ɪɚɜɟɧ
Ⱦɚɥɟɟ ɢɞɟɬ ɫɥɨɣ ɩɨɞɜɵɛɨɪɤɢ
Ɂɚɫɱɺɬɫɥɨɹɩɨɞɜɵɛɨɪɤɢ × ɫɜɨɪɚɱɢɜɚɟɦɤɨɞɧɨɦɭɩɢɤɫɟɥɸ ɋɞɜɢɝɫɥɨɹ ɪɚɜɟɧ ɞɜɭɦ ɩɢɤɫɟɥɹɦ Ⱦɚɥɶɲɟ ɩɪɢɦɟɧɹɟɦ ɫɜɟɪɬɨɱɧɵɣ ɮɢɥɶɬɪ × ɨɧ ɬɚɤɠɟ ɩɪɢɦɟɧɹɟɬɫɹ ɨɞɧɨɜɪɟɦɟɧɧɨ ɧɚ ɜɫɟ ɢɡɨɛɪɚɠɟɧɢɣ Ɍɚɤɠɟ ɜɚɠɧɚɹ ɱɚɫɬɶ ɚɪɯɢ ɬɟɤɬɭɪɵ $OH[1HW ɩɪɢɦɟɧɹɟɦ ɮɢɥɶɬɪ ɧɟ ɫ ɥɟɜɨɝɨ ɜɟɪɯɧɟɝɨ ɭɝɥɚ ɚ ɞɟɥɚɟɦ ©ɪɚɦɤɭª ɢɡ ɧɭɥɟɣ ɜ ɞɜɚ ɩɢɤɫɟɥɹ ɜɨɤɪɭɝ ɢɡɨɛɪɚɠɟɧɢɹ
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ɗɬɢɦ ɦɵ ɩɵɬɚɟɦɫɹ ɭɱɟɫɬɶ ɜɫɟ ɩɢɤɫɟɥɢ ɧɟ ɭɦɟɧɶɲɚɹ ɪɚɡɦɟɪ ɢɡɨɛɪɚɠɟ ɧɢɹ ɉɨɥɭɱɚɟɬɫɹ ɮɢɥɶɬɪ × ɞɚɫɬ ɧɚɦ ɬɚɤɠɟ ɢɡɨɛɪɚɠɟɧɢɟ × ɬɨɥɶɤɨ ɱɢɫɥɨ ɢɡɨɛɪɚɠɟɧɢɣ ɫɬɚɧɟɬ ɂ ɡɚ ɫɱɟɬ ɫɞɜɢɝɚ ɧɚ ɩɢɤɫɟɥɹ ɜɨ ɜɫɟ ɫɬɨɪɨɧɵ ɩɪɢɦɟ ɧɹɹ ɮɢɥɶɬɪ × ɧɟ ɭɦɟɧɶɲɢɥɢ ɱɢɫɥɨ ɢɫɯɨɞɧɵɯ ɩɢɤɫɟɥɟɣ
Ⱦɚɥɶɲɟ ɫɧɨɜɚ ɢɞɟɬ ɫɥɨɣ ɩɨɞɜɵɛɨɪɤɢ × ɫ ɫɞɜɢɝɨɦ ɜ ɞɜɚ ɩɢɤɫɟɥɹ
ɂɡ ɢɡɨɛɪɚɠɟɧɢɣ × ɩɨɥɭɱɚɟɦ × ɩɨɬɨɦ ɦɵ ɩɪɢɦɟɧɹɟɦ ɟɳɺ ɩɨ ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɬɪɢ ɫɥɨɹ ɩɨɞɜɵɛɨɪɤɢ ɫ ɮɢɥɶɬɪɚɦɢ
ɮɢɥɶɬɪɚ ɫ ɨɬɫɬɭɩɨɦɮɢɥɶɬɪɚ ɫ ɨɬɫɬɭɩɨɦɮɢɥɶɬɪɨɜ ɫ ɨɬɫɬɭɩɨɦ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɦɵ ɫɨɯɪɚɧɹɟɦ ɪɚɡɦɟɪ ɢɡɨɛɪɚɠɟɧɢɹ ɧɨ ɩɵɬɚɟɦɫɹ ɩɟɪɟ ɦɧɨɠɢɬɶ ɜɫɟ ɜɚɪɢɚɧɬɵ ɧɚɣɞɟɧɧɵɯ ɮɨɪɦ
ɉɨɫɥɟ ɷɬɨɝɨ ɦɵ ɩɨɥɭɱɚɟɦ ɦɧɨɝɨɨɛɪɚɡɢɟ ɫɜɟɪɬɨɤ Ⱦɚɥɟɟ ɫɥɟɞɭɟɬ ɩɨɥ ɧɨɫɜɹɡɧɵɯ ɫɥɨɹ ɩɨ ɧɟɣɪɨɧɨɜ Ɂɚɬɟɦ ɫɥɟɞɭɟɬ ɤɥɚɫɫɨɜ ɨɛɪɚɡɭɹ ɬɟɦ ɫɚɦɵɦ ɜɵɯɨɞɧɨɣ ɫɥɨɣ 6RIWPD[ ɜ ɤɥɚɫɫɨɜ
ȼɚɠɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ $OH[1HW ɹɜɥɹɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɩɪɢ ɨɛɭɱɟɧɢɢ ɩɨɥɭɥɢɧɟɣɧɨɣ ɮɭɧɤɰɢɢ ɚɤɬɢɜɚɰɢɢ ReLU ɜɦɟɫɬɨ ɚɪɤɬɚɧɝɟɧɫɚ ɢɥɢ ɫɢɝɦɨɢɞɵɤɚɤ ɜ ɫɥɭɱɚɟ ɫ LeNHW ɉɪɢɦɟɧɟɧɢɟ ɩɨɥɭɥɢɧɟɣɧɨɣ ɮɭɧɤɰɢɢ ɩɨɡɜɨɥɢɥɨ ɫɭɳɟ ɫɬɜɟɧɧɨ ɭɫɤɨɪɢɬɶ ɩɪɨɰɟɫɫ ɢ ɧɟ ɩɨɬɟɪɹɬɶ ɩɪɢ ɷɬɨɦ ɬɨɱɧɨɫɬɶ ȿɞɢɧɫɬɜɟɧɧɨɟ ɨɬ ɦɟɬɢɦ ɱɬɨ ɫɢɝɦɨɢɞɚ ɜɫɺ ɬɚɤɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɧɨ ɬɨɥɶɤɨ ɜ 6RIW0D[
Ɍɚɤɚɹ ɤɨɧɮɢɝɭɪɚɰɢɹ ɩɨɡɜɨɥɢɥɚ ɜ ɝɨɞɭ ɷɮɮɟɤɬɢɜɧɨ ɪɟɲɢɬɶ ɡɚɞɚɱɭ ɤɥɚɫɫɢɮɢɤɚɰɢɸ ɜ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɦ ɪɚɡɪɟɲɟɧɢɢ – ɩɢɤɫɟɥɟɣ ɩɪɢ ɷɬɨɦ ɭɪɨɜɟɧɶ ɨɲɢɛɤɢ ɜ ɪɚɫɩɨɡɧɚɜɚɧɢɢ ɧɟɫɤɨɥɶɤɨ ɨɛɴɟɤɬɨɜ ɫɨɫɬɚɜɥɹɥ ɬɨɱ ɧɨɫɬɶ ɫɪɚɜɧɢɦɭɸ ɫ ɬɨɱɧɨɫɬɶɸ ɱɟɥɨɜɟɤɚ
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