PyTorch Lecture 06: Logistic Regression Video Lecture | Pytorch: A Complete Guide - AI & ML

in this lecture we are going to talk
about the logistic regression in our
previous lectures we talked about the
linear model which get inputted in X and
there we do some linear operations and
produce Y in our case examples we both
use the real numbers as an X also
predict real value and real numbers
however in our life the binary
prediction which is 0-1 can be very
useful for example let's say you spend
an hour for study are you gonna pass or
fail which is binary also suppose that
you want to apply our university HKUST
ph.d program you have a certain number
of GPA and GRE scores are you gonna get
a limit or not or we have a soccer game
against the Japan are you gonna win or
lose and then C C or he looks pretty
good so do you want to propose or not in
it in these cases we just need binary
prediction either you want to tweet or
not doing 0 or 1 and then how we're
gonna turn our model to predict the 0 &
1 instead of real numbers one simple
solution is that just we plug into
sigmoid from the output of the linear
and what is the sigmoid the sigmoid
looks like this
and then the graph of the sigmoid looks
like that and you can probably see the
basic idea of the sigmoid is that
Squatch numbers between 0 to 1 so which
means that let's say we get the value
upward from linear as an F F is input of
the sigmoid then this failure here is
2nd IVF and then for given F we produce
Y hat here this is y hat so if F value
is getting really big then the Y hat is
getting too close to 1 if F
getting really smaller then why head
value is close to zero so that means
that always this y hat value will be
between 0 to 1 so we squash the numbers
big numbers small numbers to fit in 0 to
1 the Newton sycamore how can I predict
the output is true or false 1 or 0 a
simple idea is that we're using a
threshold value like 0.5 so our
prediction is greater than 0.5 we assume
that output is 1 otherwise we predict 0
for that very simple in summary we can
show that the model now using a sigmoid
this is our sigmoid and then we just
basically read our linear model this is
our linear model rap with this sigmoid
function and that's it how about the
loss function in our previous model
which just is a simple musical error for
our loss but however in our new model
because we introduced sigmoid the
previous loss does not work very well so
we need to introduce new laws called
cross-entropy
loss it looks a little bit complicated
but there is a very interesting theory
behind of it but however in our lecture
we just are gonna use four cases to see
how this loss function works for our
model basic idea of the losses that if
our prediction is correct loss value
will be small when our prediction is
wrong our loss value is gonna be really
big so that we can't analyze our model
so these four cases we just have like
these numbers in our loss function here
and then see what kind of value we're
gonna get so consider this first case Y
is 1 real value is 1
but our prediction why head is 0.2 so in
this case is our prediction of Syrah so
we expect something lost bill you will
be something high so we just look can
plug in these numbers near and then see
what lost value looks like y value here
is 1 so in this case if you consider
only one case we don't have to compute
this mean so you can just ignore this
for now this is gonna be 1 and this is
gonna be 0.2 a whole pretty huge 30.2
and then Y when y is 1 1 minus 1 is 0 so
we can just err we can just oh we don't
have to consider this term for now and
then what will be the lost value so we
can simply compute minus here minus 1
times log 0.2 but this is our low graph
so if you look at the 0.2 it's gonna be
somewhere here so it's it's gonna be
minus 0.7 so minus minus is plus so it's
gonna be zero point seven so as we
expected we get some bigger number here
and let's look at the other case when y
value true value is 1 without prediction
0.8 so what's good prediction so we
expected value our loss value will be
something similar so we can compute in
the same way minus 1 times log 0.28
ecole so zero point eight is around here
so if you see it's about minus zero
point one I guess
so it's minus minus this plus is gonna
be zero point two one approximately then
as we expect this value is smaller than
the first case let's look at other case
when y real value is zero and then our
prediction is zero point one which is
good so we expect the loss it's gonna be
small so we can just plug in this number
so in that case our Y is zero so this
time we don't have to consider but
system 1 minus 0 becomes 1 so we only
consider this stuff so here as minus 1
times log this is a 1 minus y hat so 1
minus 0.01 equal what is that look zero
point 9 so if you look at zero point
nine so it's really small number here so
it's around minus zero zero five so it's
something like like this such a small
number the same manner we can compute
this one so it's basically minus 1 log 1
minus 0.9 which is log zero point 1 so
here if you see here it's gonna be this
so it's it's minus minus is plus is
gonna be 1 so which is big number so we
show that in our four cases our loss
function works very well with our model
then how can i implement this our
implementation is extremely simple as we
just introduced sigmoid in our equation
we just need to use this sigmoid which
is implemented in the functional that
same way so first we import this
functional as an F and there it has to
call this F the sigmoid so in our class
we just create this linear model and
then we just wrap our linear output from
X with the sigmoid in the witness
written this value and that's it and the
photo laws previously we just used MSE
laws but here we just change these laws
with a PC which is binary cross-entropy
laws the we can just define our
criterion using this API called PC laws
and that's it so let's look at our
entire implementation so in our dataset
it's almost same as previous but only
different thing is that in the wide era
we just used 0 or 1 because it's a
logistic regression which is binary in
our model to directly say I'm adjusting
the creped linear which get one input
and
one input also we produce only one
output in this case so it's a one-to-one
and then when you complete this forward
we just wrap this linear output with
this sigmoid and then for the loss we
just used to BC loss and then optimizer
we also use the same of the magic sgt
and this is our training off and then
for the prediction real use what we did
is that we just get paid new one and
then we pass this value to our model
they rejected output is 2.5 then it's
going to be true or false based on our
prediction so this exactly follows our
redone
so first without just to design our
model using this class in this case is
linear with a sigmoid and then we define
our loss an optimizer like that and then
we rerun the training cycle and that's
it and then let you look at the result
and do we expect as the epic calls on
our loss function or failure is gonna be
getting smaller and smaller and then
finally what we did is the we predict if
we study one hour what is going to be
are we gonna success or non-success is
gonna be fail false and it will start
seven hours of course you will be
successful
in this lecture we just use a sigmoid
often we call this kind of function as
activation functions and there are other
types of activation functions like lelou
or 10h and so on so that you can try
other activation functions for your
exercise in our last lecture we're going
to talk about how we can make this logic
irrigation or neural net with a white in
the deep