Naive Bayesian Classification. Abel Sanchez, John R Williams. Stunningly Simple. The mathematics of Bayes Theorem are stunningly simple. In its most basic ...
1.Naive Bayesian Classification Abel Sanchez, John R Williams
2.Stunningly Simple The mathematics of Bayes Theorem are stunningly simple. In its most basic form, it is just an equation with three known variables and one unknown one. This simple formula can lead to surprising predictive insights.
3.Bayes and Laplace The intimate connection between probability, prediction, and scientific progress was thus well understood by Bayes and Laplace in the eighteenth century— the period when human societies were beginning to take the explosion of information that had become available with the invention of the printing press several centuries earlier, and finally translate it into sustained scientific, technological, and economic progress.
4.Conditional Probability Bayes’s theorem is concerned with conditional probability. That is, it tells us the probability that a hypothesis is true if some event has happened.
5.Bayes Theorem P(A) and P(B) are the probabilities of A and B independent of each other P(A|B) a conditional probability, is the probability of A given that B is true P(B|A) is the probability of B given that A is true
7.Probability that your partner is cheating on you, given an event Event: you come home from a business trip to discover a strange pair of underwear. Condition: you have found the underwear Hypothesis: probability that you are being cheated on
8.p( u/c ) - The probability of underwear u given cheating c Probability of underwear appearing, conditional on his cheating 50%
9.p(u) - The probability of the underwear u appearing if NO cheating Probability of the underwear’s appearing conditional on the hypothesis being false . 5%
10.p(u ) - The probability of cheating c What is the probability you would have assigned to him cheating on you before you found the underwear? 4 %
11.p(u ) - The probability of cheating c What is the probability you would have assigned to him cheating on you before you found the underwear? 4 %
13.Active Learning – Calculate Cheating Probability T he probability of cheating c given underwear u The probability of underwear u given cheating c 50 The probability of the cheating c 4 The probability of the underwear u appearing if NO cheating 5
14.Classification of Drew
15.Example: classification of Drew We have two classes: c 1 =male, and c 2 =female Classifying drew as male or female is equivalent to asking is it more probable that drew is male or female. probability of being called “drew” given that you are a male? Probability of being a male? probability of being named “drew”?
16.Using Data Name Gender Drew Male Claudia Female Drew Female Drew Female Alberto Male Karin Female Nina Female Sergio Male p(male|drew) = 1/3 x 3/8 = 0.125 3/8 3/8 p(female|drew) = 2/5 x 5/8 = 0.250 3/8 3/8 probability of being called “drew” given that you are a male? Probability of being a male? probability of being named “drew”?
17.Bayesian Approach Posterior p robability based on prior probability plus a new event
18.Classification of Documents
19.Questions We Can Answer Is this spam? Who wrote which Federalist papers ? Positive or negative movie review ? What is the subject of this article?
20.Text Classification Assigning subject categories, topics, or genres Authorship identification Age/gender identification Language Identification Sentiment analysis …
21.Bayes Theorem a conditional probability, is the probability of class c given document d is the probability of document d given class c the probability of the class c the probability of the document d For a document d and a class c
22.The probability of a word given a class Count of the word occurring in that class Count of all words in that class Vocabulary – unique instances of words The probability of the class Number of documents with that class Total number of documents
23.Data Doc Words Class Training 1 chinese beijing chinese c Training 2 chinese chinese shanghai c Training 3 chinese macao c Training 4 tokyo japan chinese j Test 5 chinese chinese chinese tokyo japan ? Conditional Probabilities p(chinese| c ) = (5+1)/(8+6) = 6/14 p(tokyo| c ) = (0+1)/(8+6) = 1/14 p(japan| c ) = (0+1)/(8+6) = 1/14 p(chinese| j ) = (1+1)/(3+6) = 2/9 p(tokyo| j ) = (1+1)/(3+6) = 2/9 p(japan| j ) = (1+1)/(3+6) = 2/9 Priors p( c ) = 3/4 p( j ) = 1/4 Choosing a class (category) p(c| d5 ) = (3/4)*(3/7)*(3/7)*(3/7)*(1/14)*(1/14) ≈ 0.0003 p(j| d5 ) = (1/4)*(2/9)*(2/9)*(2/9)*(2/9)*(2/9) ≈ 0.0001
24.For homework we will use*: probability of language given word Probability that word is in language Probability that word is not in language * http://en.wikipedia.org/wiki/Naive_Bayes_spam_filtering
25.Calculating Probabilities // probability that word shows up in a language // probability that word is not in language
18年12月12日，哈佛大学，麻省理工学院，斯坦福大学以及OpenAI等联合发布了第二届人工智能指数（AI Index）年度报告。 人工智能领域这一行业的发展速度，不仅仅是通过实际产品的产生以及研究成果来衡量，还要考虑经济学家和政策制定者的预测和担忧。这个报告的目标是使用硬数据衡量人工智能领域的发展。 报告中多次提及了中国人工智能的发展以及清华大学： 美国仅占到全球论文发布内容的17%，欧洲是论文最高产的国家，18年发表的论文在全球范围内占比28%，中国紧随其后，占比25%。； 大学人工智能和机器学习相关课程注册率在全球范围都有大幅提升，其中最瞩目的是清华大学，相关课程2017年的注册率比2010年高出16倍，比2016年高出了将近3倍； 各国对人工智能应用方向重视不同。中国非常重视农业科学，工程和技术方面的应用，相比于2000年，2017年，中国加大了对农业方面的重视。 吴恩达也在今天的推特中重磅推荐了这份报告，称“数据太多了”，并划重点了两个报告亮点：人工智能在业界和学界都发展迅速；人工智能的发展仍需要更加多样包容。