{"id":92,"date":"2018-08-24T10:04:31","date_gmt":"2018-08-24T10:04:31","guid":{"rendered":"http:\/\/csp15.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=92"},"modified":"2019-01-02T06:01:41","modified_gmt":"2019-01-02T06:01:41","slug":"probability","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/csp15\/chapter\/probability\/","title":{"rendered":"Probability"},"content":{"raw":"
\"epgp<\/a>\r\n<\/span><\/div>\r\n
\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\nWelcome to the e-PG Pathshala Lecture Series on Machine Learning.\r\n\r\n \r\n\r\nLearning Objectives:<\/strong>\r\n\r\n \r\n\r\nThe learning objectives of this module are as follows:\r\n\r\n \r\n

\u2022\u00a0 To understand the definitions of Basics of Probability for Machine Learning<\/p>\r\n

\u2022\u00a0 To understand the mathematics for Machine Learning<\/p>\r\n

\u2022\u00a0 To know the concept of Bayes Theorem and supervised Machine learning<\/p>\r\n

\u2022 To design the Machine Learning problem using Bayes Theorem<\/p>\r\n \r\n\r\n6.1 \u201c7 Giants\u201d of Data<\/strong>\r\n\r\n \r\n\r\nData and analysis of data play a very important role in machine learning. These are the seven so called giants of data\r\n\r\n \r\n

1. Basic Statistics \u2013 This includes basic statistical measures such as counts, contingency table, mean, median, variance, range queries (SQL queries) etc..<\/p>\r\n

2. Generalized N-body Problems which include kernel summations, clustering, spatial correlations, etc.<\/p>\r\n

3. Graph Theoretic Problems which include betweeness, centrality, commute distance, graphical model inference<\/p>\r\n

4. Optimization- general methods of Optimization<\/p>\r\n

5. Linear Algebraic Problems which include Linear algebra, Principal component analysis, Gaussian Process Regression, Mainfold Learning<\/p>\r\n

6. Integration using Bayesian Inference<\/p>\r\n

7. Alignment problem which include BLAST in genomics, string matching, phylogenies, SLAM, cross-match and some other operations specific to bioinformatics<\/p>\r\n\r\n<\/div>\r\n

However in this module we will be discussing only the basic aspects of probability and how these concepts are connected to machine learning.<\/p>\r\n \r\n\r\n6.2 Two views of Probability<\/strong>\r\n\r\n \r\n

When we talk about probability there are basically two aspects that we consider. One is the classical interpretation where we describe the frequency of outcomes in random experiments. The other is Bayesian viewpoint or subjective interpretation of probability where we describe the degree of belief about a particular event.<\/p>\r\n \r\n

Before we go further let us first define probability. Probability<\/strong> is defined as the chance that an uncertain event will occur (always between 0 and 1). In this context Sample Space<\/strong> is defined as the collection of all possible events. Example of a sample space for all the 6 faces of a die is shown in Figure 6.1<\/p>\r\n \r\n\r\n\"\"\r\n\r\n6.3 Types of Probability<\/strong>\r\n\r\n \r\n

There are three approaches to assessing the probability of an uncertain event.<\/p>\r\n

They are defined below.<\/p>\r\n

6.3.1 Apriori classical probability: <\/strong>the probability of an event is based on prior knowledge of the process involved<\/strong>.<\/p>\r\n \r\n\r\n\"\"\r\n\r\nPriori classical probability \u2013 Example 1<\/strong>\r\n\r\n \r\n\r\nFind the probability of selecting a face card (Jack, Queen, or King) from a standard deck of 52 cards.<\/strong>\r\n\r\n \r\n\r\n\"\"\r\n

6.3.2 Empirical classical probability<\/strong>isthe probability of an event is based on observed data<\/strong>.<\/p>\r\n \r\n\r\nempirical classical probability\r\n\r\n \r\n\r\n\"\"\r\n\r\nEmpirical classical probability \u2013 Example 2<\/strong>\r\n\r\n \r\n

Find the probability of selecting a male taking statistics from the population described in the following table (Figure 6.2):<\/p>\r\n\"\"\r\n

\r\n\r\n \r\n\r\n6.3.3\u00a0\u00a0 Subjective probability: <\/strong>the probability of an event is determined by an individual<\/strong>\r\n\r\n \r\n\r\n6.4 Events \u2013 Sample Space<\/strong>\r\n\r\n \r\n

Associated with probability is the concept of an event. Event is defined as each possible type of occurrence or outcome. There are basically different concepts associated with an event.<\/p>\r\n \r\n

\u2022\u00a0\u00a0Simple event <\/strong>is an outcome from a sample space with one characteristic. ex. A red card from a deck of cards<\/p>\r\n

\u2022\u00a0 Complement of an event A <\/strong>(denoted A\/) is defined as all outcomes that are not part of event A<\/p>\r\nex. All cards that are not diamonds\r\n\r\n<\/div>\r\n