Markov Chains and Text Generation
Summary
TLDRThis video delves into Markov chains, illustrating their concept through a car's functional and broken states. It explains how to model states and transition probabilities, representing them as a table or matrix. The video progresses to demonstrate generating text using Markov chains, showing how to create states for each word and calculate transition probabilities. It uses 'the quick brown fox jumps over the lazy dog' as a simple example and then scales up with a chain trained on 5,000 Wikipedia articles. The video also touches on advanced text generation using n-grams and concludes with a unique application of Markov chains in generating novel, human-like pen strokes.
Takeaways
- π Markov chains are used to model transitions between states, with each state representing a condition or an event.
- π The script uses the example of a car's condition (working or broken) to explain how Markov chains can model real-life situations.
- π Transition probabilities in a Markov chain can be represented as a table or matrix, showing the likelihood of moving from one state to another.
- π Data collection and analysis are crucial for determining the probabilities within a Markov chain, such as observing the frequency of car breakdowns over time.
- π Markov chains can be applied to text generation by treating each word as a state and modeling the likelihood of subsequent words.
- π The script demonstrates how to create a Markov chain from a simple sentence, showing the transition probabilities between words.
- π Training a Markov chain on a large dataset, like Wikipedia articles, can generate more complex and realistic text predictions.
- π‘ Text generation using Markov chains involves selecting the next word based on the current word's state, using probabilities to bias the choice.
- π Markov chains can be extended to consider n-grams (multiple words) instead of single words, improving the coherence of generated text.
- π¨ Beyond text, Markov chains can model and generate other types of sequences, such as drawing strokes, creating unique and human-like patterns.
Q & A
What is a Markov chain?
-A Markov chain is a mathematical system that models a sequence of possible events where the probability of each event depends only on the state attained in the previous event.
How are states and transitions represented in a Markov chain?
-In a Markov chain, states are represented by nodes or circles, and transitions between states are represented by arrows pointing from one state to another, indicating the likelihood of moving from one state to the next.
What is the significance of the car example used in the script?
-The car example illustrates a simple Markov chain with two states: the car working or the car broken. It demonstrates how probabilities are used to model the likelihood of transitioning between these states.
How can the data from a Markov chain be represented?
-Data from a Markov chain can be represented as a table or a matrix, where rows represent the current state and columns represent the next state, with the values indicating the probability of transitioning from one state to another.
What is the process for converting raw data into probabilities in a Markov chain?
-To convert raw data into probabilities, the total occurrences for each state are calculated and then each occurrence count is divided by the total for that state, resulting in a probability for each transition.
How does the Markov chain model handle text generation?
-In text generation, each word is treated as a state, and the transitions are the probabilities of one word following another. This is used to predict and generate the next word in a sequence based on the previous word or words.
What is the significance of the 'the' word in the Markov chain text generation example?
-The word 'the' is significant because it appears multiple times in the example sentence, allowing for different transition probabilities to be observed and modeled, unlike other words that appear only once.
How can the randomness in text generated by a Markov chain be controlled?
-The randomness in text generated by a Markov chain is controlled by biasing the selection of the next word based on the probabilities defined by the chain, ensuring that some words are more likely to follow others.
What is the limitation of a Markov chain when generating text based on single-word states?
-The limitation of a Markov chain when generating text based on single-word states is that the generated text can diverge in meaning very quickly, as each word only depends on the immediately preceding word.
How can the coherence of generated text be improved in a Markov chain model?
-The coherence of generated text can be improved by making each word depend on the last two or three words instead of just the last word, creating a more complex state that considers word pairs or triplets.
What other applications of Markov chains are mentioned in the script?
-Apart from text generation, the script mentions using Markov chains to model and generate pen strokes for drawing, which can emulate human-like scribbles and create new, never-before-seen images.
Outlines
π Introduction to Markov Chains
The paragraph introduces the concept of Markov chains using a car's functional state as an example. It explains how Markov chains can model the probability of transitioning between different states, such as a car being either functional or broken. The speaker outlines the probabilities of moving from one state to another, like the car remaining functional or breaking down, and the likelihood of fixing a broken car. The concept is visualized through a simple diagram and a transition probability table, which is essentially a matrix representing the probabilities of state transitions. The paragraph also touches on how to gather data to create such a table and how to convert raw data counts into probabilities by dividing the number of occurrences by the total number of observations for each starting state.
π Markov Chains in Text Generation
This paragraph delves into applying Markov chains to text generation. It uses the sentence 'The quick brown fox jumps over the lazy dog' to illustrate how each word can be considered a state with transitions to subsequent words based on their appearance in the sentence. The speaker discusses creating a Markov chain model by determining the probabilities of moving from one word state to another, such as the word 'the' leading to 'quick' or 'lazy' with a 50% chance each. The concept is expanded by training a Markov chain on a larger dataset of 5,000 Wikipedia articles to better understand the probabilities of word sequences in English. The paragraph concludes with an explanation of how to generate random text using a Markov chain by selecting the next word based on the current word's state, using probabilities to bias the selection.
π¨ Advanced Text Generation and Creative Applications
The final paragraph discusses advanced techniques for text generation using Markov chains, such as considering the last two or three words to generate the next word, which helps maintain context and coherence in the generated text. The speaker also shares a creative application of Markov chains in generating artwork based on recorded pen strokes. By training a Markov chain on segments of mouse movement data, the program can generate new drawings that resemble human scribbles. This demonstrates the versatility of Markov chains beyond text generation, showcasing their potential in mimicking complex patterns and behaviors.
Mindmap
Keywords
π‘Markov Chain
π‘State
π‘Transition
π‘Probability
π‘Text Generation
π‘Matrix Representation
π‘Data Gathering
π‘Training
π‘Random Block of Text
π‘Biased Randomness
π‘Pen Strokes
Highlights
Introduction to Markov chains and their applications in text generation.
Explanation of a Markov chain using a simple car maintenance example.
Visual representation of a Markov chain with states and transitions.
Conversion of a Markov chain diagram into a table format for easier understanding.
Gathering data to determine transition probabilities in a Markov chain.
Calculating probabilities from raw data counts to understand state transitions.
Application of Markov chains to text generation using a simple sentence.
Creating states for each word in a sentence to model text with a Markov chain.
Defining transition probabilities between words in a Markov chain model.
Building a larger Markov chain using 5,000 Wikipedia articles for text generation.
Demonstration of predicting the next word in text using a Markov chain.
Explaining the process of generating random text using a Markov chain.
Advantage of using Markov chains for predicting user input in mobile keyboards.
Technique for generating text where each word depends on the last two or three words for better context.
Generating random blocks of text with a Markov chain by picking words in a biased random manner.
Using Markov chains to generate pen strokes that emulate human-like drawings.
Conclusion and summary of the video's exploration of Markov chains.
Transcripts
pictures can also refer to translation
to machine code for correctly rounded
when converted to Islam in material okay
so that probably didn't make a whole lot
of sense but that's because a human
didn't write that sentence a machine did
using something called a Markoff chain
today I'm going to be talking about
markof chains and some of their
applications including things like text
generation like you just saw so I want
to start off by talking about a really
simple example in real life where a
Markoff chain might arise imagine the
only thing I care about is whether or
not my car works so there's just two
states the world can be in either my car
is functional you know I can use it to
drive to work whatever or my car is
broken you know it's useless sitting in
my driveway or whatever and I just
cannot cannot get anywhere with my car
so now I want to start thinking about
the probability you know the likelihood
that I will go between these two
situations so let's say most of the time
if I wake up and my car works in the
morning it's probably going to be
working at night still when I go to bed
you know there's a small chance I'll
have a breakdown in the middle of the
day let's call that let's say a 1%
chance so there's a 1% chance I'll go
from the car Works state to the car
broken State now let's suppose that once
my car is broken I really want it fixed
so if I wake up on a given day and my
car is broken in the morning there's a
90% chance I'll have it fixed by the end
of the day so we can represent that this
way and now there's a final piece of
this picture which I don't already have
drawn here which is you know 99% of the
time my car works it will stay working
and 10% of the time my car is broken
it'll stay broken so I can represent
these just with arrows pointing into the
the same state that they come out of so
this is just an example of a Markov
chain basically what we have is we have
a bunch of States you know in this case
just two different states either my car
is functional or it's broken and we have
transitions between those States you
know the likelihood that you'll go from
one state to another given State and
finally one last thing we can do is we
can represent this Markoff chain instead
of by using like these arrows and these
circles we can also represent it as a
table and in this case I've chosen to
make the the rows the state you're
coming from and the columns the state
you're going to so if uh currently my
car is broken and I want to know the
odds that uh it will stay broken I would
look at the bottom right uh corner of
this table in this case so this is just
another way I can write down a Markoff
chain I can just write it down as a
table or as a matrix so you might be
wondering how could I actually gather
this data you know how would I find out
that 99% of the time my car Works it'll
keep working and 90% of the time my car
is broken I'll get it fixed you know how
do I figure out these probabilities you
know in a real life situation and one
way to do that is to just gather a lot
of data so suppose I spent you know a
little over 2 years just every day I
just in the morning note whether my car
works and at night I note whether my car
works and so I could fill in this table
and so the idea is let's say I started
the day and my car was broken I ended
the day and my car was working I would
just add one to that cell in the table
um and I might get something that looks
a little bit like this so this this is
just the kind of thing I would get if I
just gathered a bunch of data so now
we're left with the task of turning this
table of data into a table of
probabilities you know before we had a
table with you know 90% 99% 1% and now
we just have a table with a bunch of
numbers so how do we get from this to
that so really let's think about what a
probability actually is if I start the
day with a working car and I want to
know the probability that at the end of
the day my car will be broken I want to
know you know maybe nine times out of 10
it'll be broken or you know 50 times out
of 100 it'll be broken or you know
whatever whatever the measure I'm doing
it out of something so if my car is
broken 8 times uh when it was working in
the morning you know eight times out of
what is basically what I'm wondering you
know if I took if I took 800 samples
where I started the day with my car
working and there were only eight where
I was broken at the end of the day it
there's an eight out of 800 chance that
my car will break down on a given day so
to turn this into an actual formal
procedure I'm just going to add another
column to this table which is the total
number uh the total sum of that entire
row so for the first row uh days
starting with my car working you can see
that there's a total of 800 days where I
started my day and my car was working
and there were a total of 10 days when I
started my day and my car wasn't working
and what this allows me to do is in the
first row I can just divide all those
things by 800 and in the second row I
can divide those things by 10 and so now
in the first row I can see that if I
wake up with my car working 792 out of
800 times I will go to bed with my car
working as well so really this just
turns uh turns our you know our raw
counts our raw you know number of days
this happened it turns them into
probabilities and if we express them as
percentages uh we get something like
this which is actually what we had
before um if you remember what did you
know the original example I presented
you before so how do we apply this idea
of states and transition probabilities
to something like the example I showed
at the beginning of the video where I
used a Markov chain to generate a bunch
of text what we're really looking for is
a way to represent a piece of text as a
bunch of states and transitions between
states and so I'm going to show how to
do this and I'm just going to use a toy
sentence the quick brown fox jumps over
the lazy dog because it's pretty simple
to work with this you know this small
amount of text the first thing I'm going
to do is create a state for each word
that appears in this sentence so I have
a state for quick a state for brown a
state forthe and the way I'm going to
Define a state is as you read the
sentence whatever word you're currently
reading is the state that you're in so
if I go through and read this I start
out in theth state I go to quick I go to
Brown I go to Fox I go to jumps I go to
over back to the th State then finally I
go to lazy and then dog the next step to
building this Markov chain is thinking
about the probabilities of going between
each state so let's start with theth
state becausethe is the only word that
appears in this sentence twice the first
time we saw the' we went to quick and
the second time we saw the we went to
Lazy right afterwards so there's
actually a 50% probability in the state
' that we go to Quick next and a 50%
probability that we go from the state
the to the state lazy next now if we
look at any other word let's say we do
fox fox only appears one time in the
sentence and jumps happens right after
it so there's a 100% probability that
the next thing after the fox state will
be the jump State there's just nothing
else that we can go to from the fox
State and this is true for every word
except for the wordthe becausethe is the
only word that even happens multiple
times in this sentence so if we wanted
to turn this into a Markov chain we
would get something like this where the
wordthe branches off into quick and lazy
with a 50% chance in each Direction and
every other word just goes into the next
word with 100% probability because
there's nothing else that ever comes
after that word so the point of this
example is to just show you how we could
build the markof chain using text you
know we represent each word as a a state
we represent the transitions as you know
the likelihood that a given word will
come after the word before it and this
sentence you know because it's just you
know a few words doesn't give us that
good an idea of how the Eng how the
English language is structured you know
it doesn't tell us much about which
words come after other words although it
does show us that the word the is pretty
common um so what I've done to get a
better example of a bigger Markoff chain
is I've taken about 5,000 Wikipedia
articles and I've trained a markof chain
on that you generated a big markof chain
for all the words that appear in there
you know hundreds of thousands of words
and I'm just going to show you the state
for the word the' so here we have uh you
know I've simplified it I have this
thing other stuff in the corner
basically for things I didn't want to
fit in so this is just the most common
transitions out of the wordthe we see
first is the most likely word to come
after the wordthe right after it is
United probably from the United States
then same most Etc and what this shows
is you know if I if I'm just reading
text and all I know all I'm told is the
last word I saw was the word the' I can
predict you know first same most City
are all pretty likely words to happen
and you know I know what's likely to
come next so the Markov chain is a model
basically of the probabilities of you
know certain words following other words
when we use it in terms of text so we've
already done a great deal and this is
actually already a pretty useful model
to have say if you're making a keyboard
for iOS or another mobile operating
system and you want it to be able to
predict what the next word the user is
going to type is uh this is actually a
Fairly reliable system to do that now
it's not necessarily the best system
because it just depends on the last word
that they typed but it does take some
context into account and it could
actually do a pretty decent job uh of
suggesting which word to type so now I
still have to explain how we can use
this to actually generate a random block
of text and basically uh I'm just going
to explain how we generate the next word
in a block of text because if you can
generate the next word then you can keep
generating words and you get a large
string of text in the end so let's say
we've just generated the word the in our
random block of text well we're going to
pick the next word we generate randomly
because it's random but we're going to
do it in a biased way and you know we're
going to bias the next word in a way
where first is more likely than end and
you know United is more likely than
other and actually we're going to bias
it exactly so even if we're picking the
next word randomly we're going to be
picking it randomly in such a way that
first has a 1.33% chance of happening
same has a 0 90% chance of happening
Etc so we're picking randomly but we're
doing it in a biased fashion and we're
biasing it the same way our Markov chain
says we should bias it you know if it
says first happens more than city after
the wordthe then we're going to pick
randomly in that biased way we're going
to do it the way the markof chain says
to do it uh you can think of maybe uh
this is kind of like flipping a biased
coin where instead of being 50% heads
50% taals it's 75% heads 25% taals it's
still random what happens but one CH one
thing is still more likely than the
other thing this is kind of like that
one last thing I'll mention is that this
technique of generating random blocks of
text uh the way it works is each word
only depends on the word that comes
before it and so the thing diverges in
meaning extremely fast you know a couple
words down the line there's just no
connection to what was said before and
one way to fix this problem is to make
each word you generate depend not on the
last word but on the last two words or
the last three words and you can
actually set that up in a way that's
similar to this but instead of you know
all the words coming off ofth you might
have all of the words that come after
the phrase like the the same or the most
you know something like that so you'd
have pairs of words in a state instead
of just a word in a state and that's
actually what I did to generate the
block of text you saw at the beginning
of the video but that's not really
essential to the idea of a Markov chain
uh it's just the same thing but with
more words in a given state so now I
want to conclude the video by just
showing one other cool thing you can do
with Markov chains that has nothing to
do with text generation I made a program
where I could draw tons of stuff and it
would record the pen Strokes that I made
so it would record how I uh move my
finger you know over a brief interval or
my mouse and uh you know the direction
in which I moved it basically and then I
trained a Markoff chain basically based
on uh these pen stroke so I trained to
markof chain on small segments of um of
of where I moved my mouse basically and
so each state is basically you know what
direction is the is the mouse you know
sliding at that time and how fast is it
sliding stuff like that and I used that
to generate new images that had never
been drawn before and what's remarkable
about these images is even though
they're not letters or numbers or
anything uh truly meaningful they
actually do look like something a human
could draw there's curls and squiggles
it's not just a purely random drawing it
actually emulates the pen Strokes that a
human might make while scribbling on uh
on their mouse or on a touch screen so I
thought that was pretty interesting and
just a cool little other uh thing you
could do with a Markoff chain that
doesn't really have to do with text
Generation Um so I hope you enjoyed this
video and I hope you learned something
from it thanks for watching and goodbye
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