Explainable AI Whiteboard Technical Series: Mutual Information

0:14 today we're talking about how the

0:15 Juniper missed AI native platform uses

0:18 Mutual information to help you

0:20 understand which network features such

0:21 as mobile device type client Os or

0:24 access point that have the most

0:26 information for predicting failure or

0:27 success in your SLE client metric

0:31 let's start with a definition of mutual

0:33 information Mutual information is

0:35 defined in terms of the entropy between

0:38 random variables mathematically the

0:41 equation for Mutual information is

0:43 defined as the entropy of random

0:45 variable x minus the conditional entropy

0:47 of x given y now what does this mean let

0:51 me give you an example let's say Y is

0:54 one of our random variables that we want

0:56 to predict and represents the SLE metric

0:58 time to connect and can be one of two

1:00 possible values pass or fail next we

1:03 have another random variable X that

1:06 represents a network feature that can

1:07 have a possible value of present or not

1:10 present an example of a network feature

1:12 can be a device type OS type time

1:15 interval or even a user or an AP any

1:19 possible feature of the network can be

1:20 represented by the random variable next

1:23 we'll look at what we mean by

1:25 entropy for most people when they hear

1:28 the term entropy they think of the

1:30 universe and entropy always increasing

1:32 as the universe tends towards less order

1:34 and more Randomness or uncertainty so

1:37 entropy represents the uncertainty of a

1:39 random variable and the classic example

1:42 is a coin toss if I have a fair coin and

1:45 I want to flip that coin the entropy of

1:47 that random variable is going to be

1:49 given by the sum of the probability of x

1:52 i * the log 2 of the probability of X

1:55 and for that Fair coin the probability

1:57 is that 50% will be heads Plus 50% Will

2:00 Be Tails and the entropy is going to be

2:03 equal to one the maximum entropy

2:06 possible when we have maximum

2:08 uncertainty the random variable will

2:10 have maximum entropy if we take an

2:12 example where we don't have a fair coin

2:14 we have some Hustler out there and he's

2:16 using a loaded coin let's say the

2:18 probability of heads is 70% and the

2:20 probability of tails is 30% now in this

2:23 case your maximum entropy is going to be

2:26 0.88 so you can see that as the

2:28 uncertainty goes down your entropy will

2:31 Trend toward zero if you were at zero

2:34 entropy that would mean no uncertainty

2:36 and the coin flip would always be heads

2:38 or tails now let's go back and see how

2:41 Mutual information works with our SLE

2:43 metrics graphically what does this

2:45 equation look like let's say we look at

2:47 how this circle here represents the

2:49 entropy of my sle metric Y and this

2:52 circle is the entropy of my feature

2:54 random variable X so if you look at our

2:57 equation the conditional entropy of

2:59 random variable y given the network

3:01 feature X is this area here if I

3:04 subtract it to what we're looking for is

3:05 this middle segment this represents the

3:08 mutual information of these two random

3:10 variables and it gives you an indication

3:12 of how well your network feature

3:14 provides some information about your SLE

3:16 metric random variable y if the network

3:19 feature tells you everything about the

3:21 SLE metric then the mutual information

3:24 is maximum if it tells you nothing about

3:26 the SLE metric then the mutual

3:28 information between X and Y is zero now

3:31 Mutual information tells you how much

3:34 information and network feature random

3:36 variable y gives you about the SLE

3:38 metric time to connect but it doesn't

3:40 tell you whether the network feature is

3:42 better at predicting failure or success

3:44 of the SLE metric for that we need

3:47 something called the Pearson correlation

3:50 if you look at the picture of the

3:51 correlation it tells us a couple of

3:53 things one is the amount of correlation

3:55 with a range from -1 to 1 the other is

3:59 the sign negative and positive which is

4:01 a predictor of pass or fail so now we

4:03 have these two things first is the

4:06 magnitude indicating how correlated the

4:08 two random variables are second is the

4:11 sign which indicates failure or success

4:13 if the correlation is negative the

4:15 network feature is good at predicting

4:17 failure if it's positive it's good at

4:19 predicting pass if the Pearson

4:21 correlation is zero it means there is no

4:23 linear correlation between the variables

4:26 but there could be mutual information

4:28 between the two but the piercing

4:29 correlation does not tell us the

4:31 importance of the network feature or if

4:33 there's not enough data to make an

4:35 inference between the network feature

4:37 random variable and the SLE metric

4:39 random variable that's given back to our

4:41 graphic of the circles there may be one

4:43 case where I have very high entropy for

4:45 both variables but there may be another

4:47 case where I have much smaller entropy

4:49 on one of those variables both of these

4:51 examples may be highly correlated with a

4:54 high Pearson's value but the entropy of

4:56 mutual information will be much higher

4:58 in the first case which means this

5:00 random variable has much more importance

5:02 in predicting success or failure of a

5:04 feature I hope this gives a little more

5:07 insight into the AI we created at mist

5:10 and if you look at the Mist dashboard

5:12 the result of this process is

5:13 demonstrated by our virtual assistant