Naive Bayes klassifikatori: ehtimollar nazariyasi asosida C# tilida modellashtirish

Аннотация

This article explores one of the practical applications of probability theory — the Naive Bayes classifier. This widely used classification algorithm is based on Bayes’ theorem and assumes independence among features, which allows for efficient categorization of data. The paper outlines the theoretical foundation of the Naive Bayes approach and presents a program model implemented in the C# programming language to classify text data (e.g., emails) as either “spam” or “legitimate.” The modeling process illustrates the algorithm’s logic and enables evaluation of its classification accuracy. The research highlights the importance of 716 “JOURNAL OF SCIENCE-INNOVATIVE RESEARCH IN UZBEKISTAN” JURNALI VOLUME 03, ISSUE 06, 2025. JUNE ResearchBib Impact Factor: 9.654/2024 ISSN 2992-8869 algorithmic thinking and the application of probabilistic methods in modern data analysis tasks. Keywords: Naive Bayes classifier, probability theory, Bayes’ theorem, C# programming language, classification, data analysis, spam filtering, statistical modeling, artificial intelligence, probabilistic algorithms. Zamonaviy davrda axborot oqimining keskin ortib borishi sababli, katta hajmdagi ma’lumotlarni avtomatik tarzda tahlil qilish va ular asosida tez va aniq qarorlar qabul qilish zarurati kundan-kunga oshib bormoqda. Ayniqsa, matnli ma’lumotlarni toifalash — masalan, elektron pochta xabarlarini “spam” yoki “normal” deb ajratish — informatsion xavfsizlik, marketing va sun’iy intellekt sohalarida muhim o‘rin tutadi. Ehtimollar nazariyasining amaliy natijalaridan biri bo‘lgan Naive Bayes klassifikatori — shunday masalalarni yechishda eng samarali va sodda algoritmlardan biri hisoblanadi. Ushbu usul Bayes teoremasi asosida tuziladi va har bir xususiyatning tasnif natijasiga ta’sirini mustaqil deb hisoblashga asoslangan. Garchi bu “soddalashtirilgan” taxmin bo‘lsa-da, u ko‘plab real vaziyatlarda yuqori aniqlikdagi natijalarni beradi. Naive Bayes klassifikatori — bu Bayes teoremasiga asoslangan va xususiyatlarning (features) o‘zaro mustaqilligiga tayanuvchi ehtimollik asosidagi klassifikatsiya algoritmidir. U “Naive” deb ataladi, chunki barcha kiruvchi belgilarning (atributlarning) mustaqil ekanligi taxmin qilinadi, bu esa real hayotda kamdan-kam hollarda to‘liq haqiqat bo‘ladi. Shunga qaramasdan, bu algoritm ko‘plab klassifikatsion muammolarda juda samarali ishlaydi. Bayes teoremasi quyidagicha yoziladi: 𝑃(𝐵|𝐴)·𝑃(𝐴) P(A|B) = 𝑃(𝐵) Bu yerda: P(A|B) — B hodisasi sodir bo‘lgandan keyin A hodisasining ehtimoli P(B|A) — A hodisasi sodir bo‘lganda B hodisasining ehtimoli 717 “JOURNAL OF SCIENCE-INNOVATIVE RESEARCH IN UZBEKISTAN” JURNALI VOLUME 03, ISSUE 06, 2025. JUNE ResearchBib Impact Factor: 9.654/2024 ISSN 2992-8869 P(A) — A hodisasining boshlang‘ich ehtimoli P(B) — B hodisasining umumiy ehtimoli Agar bizda quyidagicha tasniflanadigan xususiyatlar bo‘lsa: x = (x , x , …, x ) 1 2 n va biz bu x to‘plam qaysi sinfga tegishli — C — ekanini aniqlamoqchi bo‘lsak, k Naive Bayes formulasi: 𝑃(𝐶 ∏𝑛 𝑃(𝑥 |𝐶 P(C | x , x , …, x ) = 𝑘)· 𝑖=1 𝑖 𝑘) k 1 2 n 𝑃(𝑥) Ammo P(x) barcha sinflar uchun bir xil bo‘lgani uchun, biz faqat yuqori qiymatni topamiz: Classify(x)=arg max[𝑃(𝐶 ∏𝑛 𝑃(𝑥 |𝐶 ] 𝑘)· 𝑖=1 𝑖 𝑘) Bu yerda: • P(C ) — har bir sinfning prior ehtimoli k • P(x | C ) — har bir atributning sinfga bog‘liq ehtimoli i k Naive Bayes klassifikatori ko‘pincha matnni toifalash (text classification) kabi masalalarda qo‘llaniladi. Quyida biz C# dasturlash tilida matnli ma’lumotlar asosida xabarni “Spam” yoki “Normal” turiga ajratuvchi soddalashtirilgan model yaratamiz.Biz quyidagi bosqichlarni bajarishimiz kerak: 1. O‘quv ma’lumotlari — “spam” va “normal” xabarlardan iborat matnlar to‘plami 2. Har bir sinf (spam/normal) uchun so‘zlar soni va ehtimollarini hisoblash 3. Kiruvchi yangi xabar uchun har bir sinfga Naive Bayes formulasi asosida ehtimol hisoblash 4. Ehtimollari eng katta sinfni natija sifatida chiqarish using System; using System.Collections.Generic; using System.Linq; class NaiveBayesClassifier { private Dictionary spamWords = new Dictionary (); private Dictionary normalWords = new Dictionary (); private int spamCount = 0, normalCount = 0; 718 “JOURNAL OF SCIENCE-INNOVATIVE RESEARCH IN UZBEKISTAN” JURNALI VOLUME 03, ISSUE 06, 2025. JUNE ResearchBib Impact Factor: 9.654/2024 ISSN 2992-8869 private int totalSpamWords = 0, totalNormalWords = 0; public void Train(string text, string label) { var words = text.ToLower().Split(' '); if (label == "spam") { spamCount++; foreach (var word in words) { if (!spamWords.ContainsKey(word)) spamWords[word] = 0; spamWords[word]++; totalSpamWords++; } } else { normalCount++; foreach (var word in words) { if (!normalWords.ContainsKey(word)) normalWords[word] = 0; normalWords[word]++; totalNormalWords++; } } } public string Predict(string text) { var words = text.ToLower().Split(' '); double pSpam = Math.Log((double)spamCount / (spamCount + normalCount)); 719 “JOURNAL OF SCIENCE-IN