This is a world of uncertainty, everything cannot be measured exactly. Thus in this scenario probability plays a very important role. In most cases, probability acts as a measure of the outcome and set the parameters if not used directly.
In every part of our life, we use probability like in medicine, if the test is positive or negative, in a CBI inquiry the probability of the evidence to occur, in judiciary the probability of truth, in a class test the probability of the students to pass in a particular subject.
RELATION BETWEEN ML AND PROB:
In classification problems, the probability of an image to be a cat or a dog, we pick up the one with the highest probability. In most cases, probability acts as a measure of the outcome and set the parameters if not used directly.
NAIVE definition:
The probability of an event to occur is the total number of favorable outcomes to the total number of possible outcomes.
NON-NAIVE definition:
P is a function which takes an event A as input returns
PROPERTIES:
STORY PROOFS:
It is fun to learn the subjects in form of short stories with real-life examples
1.n(n-1 c k-1)=k(n c k)
2.Vendermonde identity
3.Birthday Problem:
The birthday problem is a quite famous problem whoever studies probability
DIFFERENCES:
1.What is the difference between independent and mutually exclusive events?
Events are mutually exclusive if the occurrence of one event excludes the occurrence of the other. For example: when tossing a coin, the result can either be heads or tails but cannot be both.
Events are independent if the occurrence of one event does not influence the occurrence of the other(s). For example: when tossing two coins, the result of one flip does not affect the result of the other.
2. What is the difference between p(A/B)and p(B/A)?
A=I'm a computer science student
B= I'm as intelligent as Satya Nadella
Here, in the above example
p(A/B) may nearly be equal to 1 but
p(B/A) might be low.
HOW SHOULD WE UPDATE OUR PROBABILITY OR BELIEFS BASED ON NEW EVIDENCES?
We can do it in 2 approaches:
1. Pebble work:
Initially get rid of the unwanted pebbles from p(A/B) and then renormalize to their total mass=1.
2. Frequentist world:
Imagine we were given a coin and want to check whether it is fair or not. How do we approach this? Let’s try to conduct some experiments and record 1 if heads come up and 0 if we see tails. Repeat this 1000 tosses and count each 0 and 1. After we had some tedious time experimenting, we got those results: 600 heads (1s) and 400 tails (0s). If we then count how frequent heads or tails came up in the past, we will get 60% and 40% respectively. Those frequencies can be interpreted as probabilities of a coin coming up heads or tails. This is called a frequentist view on the probabilities.
These are a few intuitions I thought would be helpful.
Thank you
In every part of our life, we use probability like in medicine, if the test is positive or negative, in a CBI inquiry the probability of the evidence to occur, in judiciary the probability of truth, in a class test the probability of the students to pass in a particular subject.
RELATION BETWEEN ML AND PROB:
In classification problems, the probability of an image to be a cat or a dog, we pick up the one with the highest probability. In most cases, probability acts as a measure of the outcome and set the parameters if not used directly.
NAIVE definition:
The probability of an event to occur is the total number of favorable outcomes to the total number of possible outcomes.
NON-NAIVE definition:
P is a function which takes an event A as input returns
0 <= P(A) <= 1
such that it accepts the following axiom.
PROPERTIES:
STORY PROOFS:
It is fun to learn the subjects in form of short stories with real-life examples
1.n(n-1 c k-1)=k(n c k)
2.Vendermonde identity
3.Birthday Problem:
The birthday problem is a quite famous problem whoever studies probability
DIFFERENCES:
1.What is the difference between independent and mutually exclusive events?
Events are mutually exclusive if the occurrence of one event excludes the occurrence of the other. For example: when tossing a coin, the result can either be heads or tails but cannot be both.
Events are independent if the occurrence of one event does not influence the occurrence of the other(s). For example: when tossing two coins, the result of one flip does not affect the result of the other.
2. What is the difference between p(A/B)and p(B/A)?
A=I'm a computer science student
B= I'm as intelligent as Satya Nadella
Here, in the above example
p(A/B) may nearly be equal to 1 but
p(B/A) might be low.
HOW SHOULD WE UPDATE OUR PROBABILITY OR BELIEFS BASED ON NEW EVIDENCES?
We can do it in 2 approaches:
1. Pebble work:
Initially get rid of the unwanted pebbles from p(A/B) and then renormalize to their total mass=1.
2. Frequentist world:
Imagine we were given a coin and want to check whether it is fair or not. How do we approach this? Let’s try to conduct some experiments and record 1 if heads come up and 0 if we see tails. Repeat this 1000 tosses and count each 0 and 1. After we had some tedious time experimenting, we got those results: 600 heads (1s) and 400 tails (0s). If we then count how frequent heads or tails came up in the past, we will get 60% and 40% respectively. Those frequencies can be interpreted as probabilities of a coin coming up heads or tails. This is called a frequentist view on the probabilities.
These are a few intuitions I thought would be helpful.
Thank you
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