Naïve Bayes

Siddharth Jaiswal

21122316

Christ University, Lavasa.

Outline:-

 

1. Conditional Probability for Naïve Bayes
2.  Bayes Rule
3. The Naïve Bayes
4. Assumptions of Naïve Bayes
5. Gaussian Naïve Bayes

 

We start with an interesting Machine learning Algorithm called the Naïve Bayes' Classifier Algorithm, It is essential to formulate Questions which is required to have an understanding about What this classifier algorithm is?, why do we use it?, how do we use it? and What is the objective and conclusion drawn?.

A group of classification algorithms built on the Bayes' Theorem are known as Naïve Bayes classifiers. It is a family of algorithms rather than a single method, and they all operate under the same guiding principle—that is, that each pair of features being classified stand alone. 

 

 Conditional Probability for Naïve Bayes

The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability. Let's use examples to help you comprehend this definition. If I were to ask you to choose a card from the deck, what are the chances of receiving a king if the card was a club? Pay close attention to how I specified that the card must be a club here. Due to the fact that there are 13 total cards in clubs, my denominator for calculating probability will be 13 rather than 52. We only have one king in clubs, so Given that the card is a club, the likelihood of getting a KING is 1/13 = 0.077. Let's look at one more illustration. Imagine conducting a coin toss experiment with two coins. Here, the sample space is: S = HH, HT, TH, TT

If someone were asked to calculate the likelihood of having a tail, their response would be 3/4 = 0.75.

Imagine that someone else conducts the exact same experiment under the same conditions, with the only difference being that both coins must be heads. This suggests that the elementary outcomes HT, TH, and TT could not have occurred if event A, "Both the coins should have heads," had occurred. Consequently, in this scenario, the likelihood of receiving heads on both coins will be 1/4 = 0.25.the aforementioned examples show us that if we are given extra knowledge, the probability may alter. In order to develop any machine learning model, we must first determine the output given a set of features.

 

  

 

 Bayes Rule:-

We are now prepared to state Bayes' Rule, one of the most important conclusions in conditional probability. Thomas Bayes, a British mathematician, proposed the Bayes' theorem in 1763, which offers a way to determine the likelihood of an event given sufficient information.

Bayes' theorem can be expressed mathematically as:

 

In essence, we are attempting to determine the likelihood of event A, assuming that event B is real.

When P(B) is used, it refers to the probability of an event occurring before the evidence, while P(B|A) is used to refer to the chance of an event occurring after the evidence has been observed. 

The formula for the probability of Y given a feature X is given to us by Bayes' rule. We hardly ever encounter a situation in real-world problems where there is just one feature.

When the features are independent, we can expand Bayes' rule to a method known as Naïve Bayes, which is based on the premise that the features are independent, i.e., changing the value of one feature does not affect the values of other variables.

Naïve Bayes can be applied to a wide range of tasks, including sentiment analysis, facial recognition, weather forecasting, medical diagnosis, and many others.

We make things simpler when there are numerous X variables by assuming that they are independent, so

 

 Assumptions of Naïve Bayes:-

They are all independent factors. That is, just because an animal is a dog, doesn't mean that it will be a medium size. Each predictor has a similar impact on the result. That is, whether or not we can pet the animal does not depend more on the fact that it is a dog. Each feature is equally important. We should attempt to use the Naïve Bayes method on the aforementioned dataset, but first we need to perform some precomputations on it.

 Gaussian Naïve Bayes:-

In our previous discussions, we have covered how to forecast probabilities when the predictors take on discrete values. But what if they go on forever? To achieve this, we must add a few more presumptions about the distribution of each feature. The assumptions that different Naïve Bayes classifiers make about the distribution of P(xi | y) are what differentiate them from one another. We'll talk about Gaussian Naïve Bayes here.

When we assume that every continuous variable connected to each feature is evenly dispersed, we utilize a method called Gaussian Naïve Bayes. Normal distribution is yet another name for the Gaussian distribution.

Here, the conditional probability is altered because the current values are different. A normal distribution's (PDF) probability density function is also represented by: 

 

The majority of applications for Naïve Bayes algorithms include sentiment analysis, facial recognition, weather forecasting, medical diagnosis, and news classification. We discovered the mathematical reasoning for this algorithm in this paper.

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Should Euthanasia be legalized ?

Should Euthanasia be legalized ?

Euthanasia is the practice of killing one self to end the pain  and the suffering thus giving up hope resulting in depressed emotional outburst wherein the decision making is due to imbalanced depressed emotions, Its giving up on the human instinct to survive and it is absolutely not human. With such an understanding I absolutely disagree on Euthanasia being legalized

We should not legalize Euthanasia for reasons that it is demotivating and it sets bad example for the Society , It persuades and  develop suicidal tendencies in many people, and last but not the least It’s not basic human instinct for survival.

Euthanasia  is immoral and its practice should be condemned , it is a very demotivating example for the rest of the humans ,and obviously cannot make a society boom with good thinking and to adapt more relevant ways of healthy life to make human survival instinct as a dominent, instead will end up Demotivating and leaving people in dynamics of frustration and social biased perceptions.

Secondly It Persuades people and develops suicidal tendencies with an option to die when people can’t compete and struggle. Thus whoever is Depressed may end up taking advantage of Euthanasia and commit suicide. However this cannot stop people from committing suicide but it will give more people a reason to commit suicide, thus will validate and support that "SUICIDE" is the ultimate solution for every problem. This will make many humans incompetent of many things which includes solving the problem in every kind of situation.

Last but not the least euthanasia is against human nature, which is to survive in every possible condition . There are many examples of survivors of many diseases from worst condition, there have been survivors and they lived longer than many normal people, They could survive because they did not give up hope and followed their instinct of survival.

Therefore concluding Euthanasia is something which once comes to your mind you start thinking about it and later it takes grip of your thoughts and then you think you are suffering. The simple solution to this is not to be asked such a question.. Because once a Question is asked you start finding answers for it with your own favorable condition and try to validate it according to your status of suffering and condition . Thus you forget the real objective of life which is Live Life to its fullest age and live, all the rest aspect comes in between your living life. Thus I think Euthanasia doesn't stand a Chance to be legalized.

What are the Causes and Effects of conflict

Conflict is the disagreement of thoughts or ideas among 2 or more individual or group, The causes of conflict and its aftermath could be negative or positive depending to individual or group ways of taking the situation. 
                                 The causes of conflict and its effect could vary  due to a common cause between two parties governed by misunderstanding, assertion of power, ignorance to needs and feelings of other person, disagreement over facts and opinion, fighting over perceived value, not matching expectation of other individual or group, and most commonly trying to help or give advise .
           Misunderstanding is commonly caused due to rumors and pre-imaging which leads to parties guessing about each other leading to confusion and feeling of mistrust and biased prejudices. Its after effects could be a disaster leading to violent actions sometimes leading to death of one party.The other side could be building a better bond among 2 parties.
                     Assesrtion of power has always been a reason of greatest conflicts between 2 individuals, groups or countries, religion, tribes. This is one kind of conflict which evolved from the day man evolved . Its in Human Nature to lead and be a leader, Assertion of power cannot be compromised easily untill both parties want to fallback or runaway from conflict. The effect of this conflict has always been the same " To rule one should be ruler and other should be follower". One party is always crushed by the other.
                                                                   Ignorance to needs and feelings of other individual concerns friends, family and people around you, these people have a certain set of expectation which is somehow broken by another party. The breaking of expectation could be fatal leading to complete boycott of another party, or it could make the friendship more good.
                                                         Conflict of Disagreement over facts and opinion could be positive and negative .This is the most common type of conflict, the better opinion is always appreciated and wins the course, However the other party is not in agreement and tries to prove his points though many possible ways could be dangerous aswell. Sometimes people really go too far to prove their point and end up loosing everything, even loosing life for an opinion.
                                                      Conflict of fighting over perceived value, set of rules among two parties is very unanimous and unpredictable, it depends upon the individual source of thinking, cultural values, religion, country, even person personality. The consciquences  is devastation, getting physical, abusive, violent is common . This conflict doesn't have a positive aspect at all, it leads to enemity for ages, permanent rivalry, which is not so easily forgotten. 
                                                     Last but not the least Trying to help and advise is one of the major causes of disagreement between 2 different parties which is maximun time between 2 different age groups. This set of conflict is commonly seen among parents and kids, student and teacher. Some times the situation becomes really bad leading one advised party to act very noobishly and do silly acts of Homicide or trying to hurt the parents or teacher by doing something bad, but the idea is to defend himself or herself. It has positive consciquences aswell, which leads to making the advised party to be better. 
                             Thus concluding all aspects of conflicts and their effects entirely depend upon the two parties that how far they are really willing to go with their conflict, Conflict is bad but it sometimes is also good. We humans get into conflict and evolve our ways of thinking and approach towards human understandings. It is through the old conflicts that we learn to live life more properly without conflicts, learning how not to make a conflict and understand the results. Therefore Humans Stay humans by getting involved into conflicts and by solving their conflicts so as they live life peacefully and with harmony.

What are The Causes and Effects of conflict

†šuÇÇ£šš†™ How can success be defined

Success is the virtue by which a person gains a certain kind of respect by accomplishing the work considered by him of Social Diginity , and it is done by excelling in the work or executing the task in hand in the best possible way, thus setting an example for others, so as they can follow it , appreciate it. Success can be categorized into 6 different types depending upon the person set of goals and expectations to what he or she considers as SUCCESS. it can be Puritan, Materialistic, Power, Spiritual, Contributor, Escapist.
                                       Puritan way is the way of proving yourself, Here we depend upon our actions and set up standards, and every time you prove to some task you add that as your achievement giving it sense of worthiness, and its never the end, once you accomplished a task, there will be more of it.
                                        
                                     Materialistic on the other hand is gaining luxury and status, It is something which governs our current society, people who have more money are considered to be most successful. 
                                    However Power category is to gain as much control as possible Its like politicians gaining control of society managers managing a company.
                                      
                                   On the contrary Spiritual is completely different from Power and Materialistic  it is to remove your temptations and transcend in present. It resists desires for material gratification, and instead chooses to be attached to spiritual realm,
                                    
                                  Contributor is some one who has made our society and are making it more better, they rejoice contributing and consider it as their success if people live life more properly, In short they tend to create a better world for other people and future generations. In some way for some people being able to Give back is the most rewarding way of life.
        
                                An escapist is someone who believes in having as much fun as possible and with peak experiences. these people believe in life as one big opportunity to enjoy.These people are most happening people and they are always in search of fun, humor and its endless.    

                           Thus concluding everyone want to be a successful man depending upon their defination of success and every one wants to be successfull throught life and not in parts. Thus SUCCESS is defined when we define ourselves.      

 

†šuÇÇ£šš† Success