在機器學習中,樸素貝葉斯分類器是一係列以假設特征之間強(樸素)獨立下運用貝葉斯定理為基礎的簡單概率分類器。 樸素貝葉斯自20世紀50年代已廣泛研究。在20世紀60年代初就以另外一個名稱引入到文本信息檢索界中,並仍然是文本分類的一種熱門(基準)方法,文本分類是以詞頻為特征判斷文件所屬類別或其他(如垃圾郵件、合法性、體育或政治等等)的問題。通過適當的預處理,它可以與這個領域更先進的方法(包括支持向量機)相競爭。它在自動醫療診斷中也有應用

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題目:Supervised learning

簡介:

監督學習是指利用一組已知類別的樣本調整分類器的參數,使其達到所要求性能的過程,也稱為監督訓練或有教師學習,其同樣是基於示例輸入-輸出數據對,在輸入和輸出數據之間建立數學函數的機器學習任務,而該數學函數來源於對有標簽訓練數據集的學習過程。函數的輸出可以是一個連續的值(稱為回歸分析),或是預測一個分類標簽(稱作分類)。一個監督式學習者的任務在觀察完一些事先標記過的訓練範例(輸入和預期輸出)後,去預測這個函數對任何可能出現的輸入的輸出。要達到此目的,學習者必須以"合理"(見歸納偏向)的方式從現有的資料中一般化到非觀察到的情況。在人類和動物感知中,則通常被稱為概念學習(concept learning)。

主要內容:

  • 監督學習
  • 統計分類
  • 回歸分析
  • 感知器
  • 線性回歸
  • 邏輯回歸
  • 支持向量機
  • 樸素貝葉斯分類器
  • 決策樹學習
  • 人工神經網絡
  • 集成學習
  • k近鄰算法
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Probabilistic graphical models such as Bayesian networks are widely used to model stochastic systems to perform various types of analysis such as probabilistic prediction, risk analysis, and system health monitoring, which can become computationally expensive in large-scale systems. While demonstrations of true quantum supremacy remain rare, quantum computing applications managing to exploit the advantages of amplitude amplification have shown significant computational benefits when compared against their classical counterparts. We develop a systematic method for designing a quantum circuit to represent a generic discrete Bayesian network with nodes that may have two or more states, where nodes with more than two states are mapped to multiple qubits. The marginal probabilities associated with root nodes (nodes without any parent nodes) are represented using rotation gates, and the conditional probability tables associated with non-root nodes are represented using controlled rotation gates. The controlled rotation gates with more than one control qubit are represented using ancilla qubits. The proposed approach is demonstrated for three examples: a 4-node oil company stock prediction, a 10-node network for liquidity risk assessment, and a 9-node naive Bayes classifier for bankruptcy prediction. The circuits were designed and simulated using Qiskit, a quantum computing platform that enable simulations and also has the capability to run on real quantum hardware. The results were validated against those obtained from classical Bayesian network implementations.

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Probabilistic graphical models such as Bayesian networks are widely used to model stochastic systems to perform various types of analysis such as probabilistic prediction, risk analysis, and system health monitoring, which can become computationally expensive in large-scale systems. While demonstrations of true quantum supremacy remain rare, quantum computing applications managing to exploit the advantages of amplitude amplification have shown significant computational benefits when compared against their classical counterparts. We develop a systematic method for designing a quantum circuit to represent a generic discrete Bayesian network with nodes that may have two or more states, where nodes with more than two states are mapped to multiple qubits. The marginal probabilities associated with root nodes (nodes without any parent nodes) are represented using rotation gates, and the conditional probability tables associated with non-root nodes are represented using controlled rotation gates. The controlled rotation gates with more than one control qubit are represented using ancilla qubits. The proposed approach is demonstrated for three examples: a 4-node oil company stock prediction, a 10-node network for liquidity risk assessment, and a 9-node naive Bayes classifier for bankruptcy prediction. The circuits were designed and simulated using Qiskit, a quantum computing platform that enable simulations and also has the capability to run on real quantum hardware. The results were validated against those obtained from classical Bayesian network implementations.

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