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# PSA 7 – Generating Text with Markov Language Model

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PSA 7 – Generating Text with Markov Language Model
To view the table of content, use [View > Show document outline]
Please read the entire document before getting started on coding, so that you can better pace yourself.
Be aware of course policies as explained on the website and linked via past PSA documents.
1. Introduction
Computers are becoming excellent at talking to us, people. Personal assistants such as Siri, Alexa, and
Google Assistant can now listen to people asking questions and responding verbally. We shall implement
a program that does something similar with combinations of words, processing the language through our
algorithms, and producing paragraphs that seem almost human. At the core of the algorithm is the
HashMap, a convenient data structure “mapping” keys to values.
Markov Model
In the early 20th century, Russian mathematician Andrey Markov first proposed the concept of the Markov
Decision Process. It is best characterized by “memorylessness”: any decision made is not dependent on
the previous decision, but only dependent on the current state.
A simple Markov Model with 2 states
The above diagram demonstrates state transitions in a Markov Model. Each state has some numbers on
arrows (a transition function) describing how likely it is going to take a particular path. For example, if I am
currently at state A, here is a 0.6 chance I will stay at A, and a 0.4 chance I will move to state E. Once in
State E regardless of where I was before, I have a 0.3 chance of staying at E and a 0.7 chance of moving
to A.
This decision process seems simple but has many applications, and its variations are widely used in AI
decision making, deep learning, game theory, and more. If you would like to read up more on the Model
or its applications, its Wikipedia page is a good place to start.
Andrey Markov
Markov Language Model
In this assignment, we will explore the usage of a Markov language model, to generate text that looks
very much like the corpus (a collection of written text) used to train the model. In our model, we define the
“current state” as the most recent word(s), and define “decision” as the immediately next word.
Consider the following sentence:
“I do not like Green Eggs and Ham.”
Take an arbitrary position in the sentence, for example, in this case, take the position between the words
“and” and “Ham.” Then the most recent words up to the position taken are “Green Eggs and”, and the
word immediately following is “Ham.”
Suppose this sentence is part of the corpus used to train the language model, then there must exist a
transition:
“Green Eggs and” → “Ham.”
Furthermore, the “degree” of a Markov model is defined as how many most recent words to consider
when generating a next word. In this example, we use degree-3 word model, because we consider the
previous 3 words.
“Formal” Definition
The count distribution function of a Markov Word model, F, is written as follows:
F(w | w , …, ) n+1 n wn−1 wn−i
Where each w is a word that appeared in the training data (also, w represents the word immediately n−1
before wn , and so on. i is the degree of the model.
Equations are hard to understand at the first glance. Let’s again assume a degree-3 model, we know the
sequence “Green Eggs and Ham” appeared a total of 9 times in the text (yes, really), then we know given
the prefix “Green Eggs and”, the prediction “Ham” has a frequency of 9:
F(Ham | Green Eggs and) = 9
Now suppose (hypothetically) that the sequence “Green Eggs and Bacon” also appeared once in the text,
i.e. F(Bacon | Green Eggs and) = 1 . Then we know that when given the prefix “Green Eggs and”, “Ham” is
9 times as likely to be predicted as “Bacon”.
We will use this distribution function F to generate the next word. We will be storing these words into
something called a HashMap.
HashMap
A HashMap is used for storing Key & Value pairs, it is denoted as HashMap<Key, Value> or simply
HashMap<K, V>. Key and Value can be any non-primitive type.
When using a HashMap, use Key to obtain or manipulate the Value that is associated with the Key.
Here are some straightforward examples of using a HashMap in Java:
https://www.javatpoint.com/java-hashmap
You may also want to learn about what methods you can use with a HashMap by reading the Java
documentation:
https://docs.oracle.com/javase/8/docs/api/java/util/HashMap.html
This assignment
The program you implement will:
1. Process a file containing the training corpus to identify possible transitions, store these transitions
(and their frequencies) in HashMaps.
2. Use the trained HashMaps to generate text.
2. Starter Code
All files are in ~/../public/psa7/, copy them to your home directory using command
> cp -r ~/../public/psa7 ~
In addition to skeleton code, and the main program in Generator.java, a few training text files are also
provided:
Turing.txt
Alan Turing’s famous paper “Computing Machinery and Intelligence”, in which he proposes the “Imitation
Game” to determine whether a machine is thinking.
https://www.csee.umbc.edu/courses/471/papers/turing.pdf
Odyssey.txt
An ancient Greek epic poem attributed to Homer.
http://classics.mit.edu/Homer/odyssey.mb.txt
Walden.txt
Walden, and on the Duty of Civil Disobedience by Henry David Thoreau
https://www.gutenberg.org/files/205/205-h/205-h.htm
Lyrics.txt
Lyrics from all Billboard top 100 songs since 2000. Excerpted from
https://www.kaggle.com/rakannimer/billboard-lyrics
GreenEggsAndHam.txt
Children’s poem by Dr. Seuss, written using only 50 unique words
http://www.site.uottawa.ca/~lucia/courses/2131-02/A2/trythemsource.txt
3. How to Run
To compile the main program:
> javac Generator.java
To run the text generator:
> java Generator filename w|c [-d degree] [-n count]
Where the flags are:
filename -> Required. Specify the training data file
w|c -> Either w (word) or c (character) required. Specify which model
[-d degree] -> Specify the degree of the Markov Model. Default at 2, must < count
[-n count] -> Specify how many sentence to generate. Default at 10
For example:
> java Generator Walden.txt w
> java Generator Obama.txt c -d 5 -n 2500
4. Testing
A simple tester is provided, using a contrived test case to verify the correctness of incrementPrediction()
and getFlattenedList() in WordModel.
To run the tester:
> javac TestWordModel.java
> java TestWordModel
In addition to the tester, you should also create your own training data to verify the functionality of your
program. We have also provided you some larger text files that can be used to train the Markov Model.
Make sure you test your program step-by-step as you code along. We have provided a starter code that
will compile in the beginning. Because this is a syntactically-heavy assignment, you should make sure
one of your method have no error before moving on to the next method.
5. Implementation
public class WordModel [total 65pt]
You will now implement a Markov Language Model that is capable of training by reading and
“remembering” all prefix+prediction combinations, where prefix is a list of [degree] words (e.g. 2 words for
a degree-2 model), and prediction is one word. Store these combinations into a HashMap, such that it can
generate text word-by-word once training is finished. This model should work for any degree.
Note: Once you finish implementing WordModel, we will reuse the WordModel’s methods to implement a
CharacterModel, which works similarly except it generates text character-by-character. But you don’t
need to worry about it right now.
The following methods should be implemented in WordModel.java. This is a syntactically heavy
assignment, be sure to compile (and run) as you code along to fix errors early. Also, you might want to
check Generator.java for how these methods are called in the main program.
There is a “debug” option in Generator.java that might help you debug, set it to true if you want to print out
the values of the maps before generating sentences. You can also use HashMap.toString() in various
places to help debug.
public WordModel (int degree); [5pt]
degree: the degree of the Word Model.
This constructor creates a WordModel object of degree degree. For example, a degree-2 model would
use the previous 2 words as a “prefix” when predicting the next word.
Initialize all instance variables in this constructor.
public void incrementPrediction(ArrayList<String> prefix, String prediction); [15pt]
prefix: a list of [degree] words that comes immediately before the prediction word in a sentence.
([degree] is the degree of the current WordModel, for example, in a degree-2 model, the
parameter prefix would be a list of 2 words. Same goes for the rest of the document)
prediction: a word that comes immediately after the prefix words in a sentence.
First let’s take a look at the instance variable:
protected HashMap<ArrayList<String>, HashMap<String, Integer>> predictionMap;
Notice that the keys in this HashMap are of type ArrayList<String>, and the value is another HashMap
whose keys are Strings and values are Integers. To illustrate, the data structure is described by the
following diagram:
For example (a degree-2 model):
This method increases the frequency of a prefix+prediction pair by 1.
Because neither the Keys nor the Values exist in the HashMap in the beginning, we need to check for
existence before doing any incrementation. The logic of checking existence roughly follows:
If prefix (Key of the top level map) exists
If prediction (Key of the bottom level map) exists
Increment frequency (value of the bottom level map) by 1
Else
Put prediction as a Key in the bottom level map, set its Value to 1
Else
Create a new map, put prediction as a key in the new map, set its value to 1
Put prefix as a key in the top level map, set its value to the new map.
DO NOT modify any key (the ArrayList of words) once you insert it into the HashMap.
Think back to PSA2 when you incremented the count of a WordPair object. This should be somewhat
similar.
public int trainFromText(String content); [15pt]
content: a string containing the entire training text
Return: how many words are read from the file
This method trains the model by reading the text word-by-word (and character-by-character later on, but
prefix+prediction pairs in the HashMaps.
First, decide where to start processing each word. Because we need [degree] words as the prefix, it
would probably be a good idea to start after [degree] words.
Starting from this position, call incrementPrediction() using the previous [degree] words as the prefix and
the next word after that as the prediction. Repeat until there are no more words to be read. All words
should be converted to lowercase. Don’t worry about punctuation.
Hint: it might be a good idea to first convert the (very long) content string to a list of words. To do this, you
might need to use a Scanner object.
public ArrayList<String> getFlattenedList(ArrayList<String> prefix); [10pt]
prefix: a list of [degree] words that comes immediately before the prediction word.
Return: a list of words that are predicted by the prefix, where each word is repeated the same amount of
times as its frequency.
First check whether prefix already exists in cache (the instance variable), if it does, directly return the
value. If it does not exist, construct a “flattened list”, add it to the cache (for future use), and return the list.
Here’s an example of how to make such a flattened list. The following diagram demonstrates a HashMap
with some data in it, when calling getFlattenedList() with the prefix “the annoying”:
public String generateNext(ArrayList<String> prefix); [10pt]
prefix: a list of [degree] words that comes immediately before the prediction word.
Return: a word that the model predicts based on the prefix.
In this method, get a “flattened list” of words associated with the specified prefix. Then randomly return a
word from the list.
* You may assume prefix always exist in the HashMap. See Generator.java:87-100 to figure out why
*** Reasoning behind Markov decision making: intuitively, the list returned by getFlattenedList() has more
copies of common words than rare words, so randomly picking an index from this list is more likely to
select a common word than a rare word. Because the flattened list’s word repetition is consistent with the
frequency distribution, it preserves the each individual word’s probability of being selected.
public String generate(int count); [10pt]
Return: a String of [count] words generated
First, randomly select a prefix from all the available prefixes. Recall that all the keys in predictionMap are
available prefixes. The following code will effectively get all the keys in predictionMap into an Arraylist:
ArrayList<ArrayList<String>> keys =
new ArrayList<ArrayList<String>>(predictionMap.keySet());
Now we have [degree] words already selected so far which work as a prefix.
Use the most recent [degree] words as prefix, to generate the next word. Repeat until there are exactly
[count] words generated. Then, return all of them as a single string.
Hint 1: it might be a good idea to keep an ArrayList of words when generating, then, before returning, turn
these words into a single string.
Hint 2: don’t forget to add space between words.
Pause here.
Now that you have finished implementing all methods in WordModel. Test your code thoroughly, by
running the tester or running the main program. Again, you should design your own test cases! Then,
move on to the remaining part when you’ve made sure that your WordModel works correctly.
public class CharacterModel extends WordModel [total 15pt]
Suppose now treating each word as an individual token is not good enough, and we want the model to be
able to generate text character-by-character. Well good news! Because we know that a char can
comfortably fit in a String (e.g. single char String “a”), we can simply tweak the program slightly, to make a
Markov Language Model that can process at the character level.
To do this, we only need to make some changes to the way the WordModel processes training text, and
therefore we can inherit most of the functionality from WordModel.
The following methods should be completed in CharacterModel.java:
public int trainFromText(String content); [10pt]
First, copy over your code from WordModel.trainFromText(). Currently, your code uses the previous
[degree] words as the prefix and the next word as the prediction.
Now, modify your code so that it uses the previous [degree] characters and the next one character,
respectively, instead. However, to satisfy the type String in the HashMaps, put these characters
separately in their own one-char-long String.
For example, again:
“I do not like Green Eggs and Ham.”
Take the position immediately before ‘d’, in a degree-4 CharacterModel, we will have the following
transition:
[“s”, “ ”, “a”, “n”] -> “d”
Also, make a change so that it returns the number of characters (instead of words) read.
public String generate(int count); [5pt]
Copy over your code from WordModel.generate(). Because the space character is now being considered
as a valid prediction, we no longer want to put a space character between every two predictions in the
generated text. Delete the line where you put such a space character.
Pat yourself on the back. You just finished PSA 7. You made Markov very proud! Be sure to test a few
6. Extra Credit: Linear Interpolation of Two Models
Introduction
There are many scenarios where we can improve a Markov Language Model by combining it with another
one. For example, when there are two (relatively large) models, we could combine them to generate text
with a more diverse vocabulary. Or when there are models trained by texts from different authors, we
could combine them to eliminate word-choice biases from an individual author.
One easy way to achieve “combining two Markov Language Models” is by using linear interpolation.
Linear interpolation combines the distribution of “prediction words” from 2 models by linearly proportioning
(i.e. multiplied by some constant) them into one new distribution. The new distribution function, denoted
by F is defined as such:
F(w | w , …, ) aF (w | w , …, ) b F (w | w , …, ) n+1 n wn−1 wn−i = 1 n+1 n wn−1 wn−i + 2 n+1 n wn−1 wn−i
Where a, b are some non-negative constant weights. And F1 and F2 are original distribution functions of
the old models. And i is the degree of the model.
Let’s consider the word sequence “I like apple juice” in two degree-3 models, we have:
F(juice| I, like, apple) = aF (juice| I, ike, pple) b F (juice| I, ike, pple) 1 l a + 2 l a
Suppose in model 1 “I like apple juice” occurred once and in model 2 “I like apple juice” occurred twice, or
simply:
F (juice| I, ike, pple) 1 l a = 1
F (juice| I, ike, pple) 2 l a = 2
Assume a = 2, b = 1 , then in the combined model:
F(juice| I, like, apple) = 2F (juice| I, ike, pple) 1 F (juice| I, ike, pple) 1 l a + 2 l a
F(juice| I, like, apple) = 2 * 1 + 1 * 2 = 4
In other words, in the combined model, the word “juice” effectively occurred 4 times after “I like apple”.
Here is another example, suppose there are these two (small) trained models, with all prefixes and all the
occurrences of the prediction words, followed by their count:
Model 1 Model 2
Prefix Prediction Frequency Prefix Prediction Frequency
“the” “dog” 1 “the” “dog” 2
“cat” 1 “cat” 1
“memer” 2 “sloth” 1
“a” “bunny” 2 “memer” 8
Suppose we use a = 2 and b = 1 (i.e. Model 1 weighs twice as much as Model 2) when combining
these 2 models. Once combined, the new model should have the following distribution.
New Model (constructed with Model 1 weighing twice as much as Model 2)
Prefix Prediction Frequency
“the” “dog” 1*a+ 2*b = 1*2 + 2*1 = 4
“cat” 1*2 + 1*1 = 3
“sloth” 0*2 + 1*1 = 1
“memer” 2*2 + 8*1 = 12
“a” “bunny” 2*2 + 0*1 = 4
Because the total frequency behind the prefix “the” is now 20, if we use the new model to predict the word
after “the” for many times, we can expect 4/20 of all predictions to be “dog”, and 12/20 of all predictions to
be “memer”, and so on.
In a file named CombinedModel.java, implement a class called CombinedModel. This class should
combine two WordModel using the method described above. This class only need to generate the
prediction, it does not need to train from text (because 2 trained model are passed in upon construction),
and does not need to generate a whole document.
You’re free to put any instance variables and methods in this class, but they need to have the following
constructor:
public CombinedModel (WordModel model1, WordModel model2, int a, int b);
model1, model2: 2 trained WordModels to be combined
a: weight of model1, non-negative
b: weight of model2, non-negative
And there must be the following method:
public String generateNext(ArrayList<String> prefix);
prefix: a list of [degree] words that comes immediately before the prediction word.
Return: a word that the model predicts based on the prefix.
Hint 1: you can use all the methods in class WordModel, and you can get a reference predictionMap
using the getter method.
Hint 2: make sure the check whether the prefix exists in either model. For example, in the example, the
prefix “a” only exists in model 1 but not model 2
Testing
A good way to test this might be training 2 models with a small training data, create a CombinedModel
and call generateNext() with the same prefix for many times. See whether the output is consistent with
expectation.
Complete this part in a file named README.md after you finish implementing the program.
7.a. High-level program description [3pt]
Describe in high level what the program does. Mention how to run the program and explain why this
program is useful. Make it simple so that a person with no prior CS knowledge could understand it. Make
it short enough so that graders do not get bored reading it.
7.b. Testing [3pt]
In addition to the provided tester, describe how you tested your code (i.e. what testing method, what test
cases, etc.)
7.c. Questions [14pt]
1. What is a HashMap?
2. How is a HashMap different from an ArrayList?
3. Do you recommend implementing this program with only ArrayLists instead of HashMaps? Why
or why not?
4. Name one one limitation of the Markov Model.
5. Text generated by a Markov Model sometimes does not make sense semantically (i.e. does not
have meaningful content). Why is that?
6. Suppose your data is trained with many real news articles, and you need to generate some fake
news (fake news are text that are different in content compared to real news). Would you choose
a very high degree (say 20) for your WordModel? Why or why not?
7. Based on Generator.java:87-100, why do you think we can assume prefix always exists in the
HashMap, in method generateNext()?
Refer to the website with a more complete guideline and set of examples of what your style should look
like. There are ten possible points that can be deducted.
9. Submission
Your code must be able to compile using the Java compiler on ieng6 to receive any credit.
Submit the following files:
If you’re also attempting the extra credit, also submit:
CombinedModel.java
A1. Sample Output
Because of the random nature, text generated probably will not be exactly the same
> java Generator Walden.txt c -d 0
Constructing a Markov character model of degree: 0
Training from data: Walden.txt
Generating text…
eyysat, “iyeoriy owcr eroeonra slarocsmsedaaiagsh pilitnyb cefnaroiaeeoer,tttsh m
a,nhmae mthaweina
> java Generator Turing.txt w -d 3
Constructing a Markov word model of degree: 3
Training from data: Turing.txt
Generating text…
the machine, “do your homework now,” being included amongst the well-established
facts, and this, by the construction of the machine, will mean that the homework
actually gets started, but the effect is very satisfactory. the processes of
inference used by the machine need not be troubled by this objection. it might be
urged that when playing the “imitation game” the best strategy for her is probably to
give truthful answers. she can add such things as “i am the woman, don’t listen to
him!” to her answers, but it will avail nothing as the man can make similar remarks.
we
> java Generator GreenEggsAndHam.txt c -d 7 -n 200
Constructing a Markov character model of degree: 7
Training from data: GreenEggsAndHam.txt
Generating text…
em here and there.
i do not like then with a goat!
would you in the rain?
i do not like them with a mouse.
and i will not eat them with a mouse.
i do not like them, sam-i-am.
a train.
not
PSA 7 – Markov Language Model
“I put so much wax in my beard you can light it like a candle.” – Andrey Markov
Real or generated?
“Kings and queens who wear a suit but once,
though made by some tailor or dressmaker to their
majesties, cannot know the comfort of wearing a suit
that fits. They are no better than wooden horses to
hang the clean clothes on.”
Real or generated?
“The question, perhaps from the leisure
fruitful. ‘But,’ says pertinently that sound asleep.
Yet his gentle rain while to choose. If he was
nearly level, and wisely; as he sprang upon the
entrance of goldenrod (Solidago stricta) grows a
half-hour’s nap after practising various animals.”
Real or generated?
will eat them here or there. i do not like them,
sam-i-am. say! in the dark. not on a boat. i will eat them
in a tree! not in a box? would you eat them in a tree! not
in the dark. would you like then with a mouse. i do not
like green eggs and ham! i do not like them in a house. i
do not like them,sam-i-am. i do not like them,sam-i-am. i
do not like them,sam-i-am. i do not like them with a fox.
not in a box. not with a mouse. not with a goat!
Real or generated?
Henry is the best
When I am at state A:
– How likely will I go to state E?
– How likely will I remain in state A?
Markov Decision Making:
Making a decision according to only the
current state.
Markov Decision Making (Language Model):
Making a decision according to only the “current state”.
The “current state” is the previous n words.
The “degree” of the model is how many previous words to look at (3 in this example)
“I do not like Green Eggs and Ham.”
“Green Eggs and” → “Ham.”
prefix (current state) prediction (decision)
Try to predict the next word at this position
Markov Decision Making (Language Model):
Making a decision according to only the “current state”.
The “current state” is the previous n words.
The “degree” of the model is how many previous words to look at (3 in this example)
[Green,
Eggs,
and]
Ham
Some non-zero chance
?
“Formal” Definition
A distribution function:
F ( prediction | prefix ) = however many times prediction word appeared after
prefix
I do not like Green Eggs and Ham.
I do not like Green Eggs and Ham.
I do not like Green Eggs and Ham.
I do not like Green Eggs and Bacon.
F ( Ham | [Green, Eggs, and] ) = 3
F ( Bacon | [Green, Eggs, and] ) = 1
Because we have:
F ( Ham | [Green, Eggs, and] ) = 3
F ( Bacon | [Green, Eggs, and] ) = 1
After training, when predicting the word after [Green, Eggs, and]
“Ham” is 3 times as likely to be predicted as “Bacon”
That’s all great.
But how do I implement this function in
Java?
HashMap
new WordModel(3)
The life of a WordModel
trainFromText()
generate()
incrementPrediction()
getFlattenedList()
generateNext()
calls
calls
calls
Coming back to the distribution function
F ( Ham | [Green, Eggs, and] ) = 3
F ( Bacon | [Green, Eggs, and] ) = 1
[“Green”, “Eggs”, “and”] “Ham” 3
“Bacon” 1
public void incrementPrediction(ArrayList<String> prefix, String prediction)
This method increases the frequency of a prefix+prediction pair by 1.
Method number 1
Before incrementPrediction([“Green”, “Eggs”, “and”], “Ham”) the first time
After incrementPrediction([“Green”, “Eggs”, “and”], “Ham”) the first time
[“Green”, “Eggs”, “and”] “Ham” 1
[“Green”, “Eggs”, “and”] “Ham”
1
predictionMap
After incrementPrediction([“Green”, “Eggs”, “and”], “Ham”) the second time
[“Green”, “Eggs”, “and”] “Ham” 2
After incrementPrediction([“Green”, “Eggs”, “and”], “Ham”) the third time
[“Green”, “Eggs”, “and”] “Ham” 3
After incrementPrediction([“Green”, “Eggs”, “and”], “Bacon”)
[“Green”, “Eggs”, “and”] “Ham” 3
“Bacon” 1
public int trainFromText(String content);
This method trains the model by reading the text word-by-word , while
incrementing frequencies of occurring prefix+prediction pairs in the HashMaps.
* prefix is a list of [degree] words
Everything lowercase.
Method number 2
public int trainFromText(String content);
“I do not like Green Eggs and Ham.”
public int trainFromText(String content);
incrementPrediction([“i”, “do”, “not”], “like”);
“I do not like Green Eggs and Ham.”
public int trainFromText(String content);
incrementPrediction([“i”, “do”, “not”], “like”);
incrementPrediction([“do”, “not”, “like”], “green”);
“I do not like Green Eggs and Ham.”
public int trainFromText(String content);
incrementPrediction([“i”, “do”, “not”], “like”);
incrementPrediction([“do”, “not”, “like”], “green”);
incrementPrediction([“not”, “like”, “green”], “eggs”);
incrementPrediction([“like”, “green”, “eggs”], “and”);
incrementPrediction([“green”, “eggs”, “and”], “ham.”);
“I do not like Green Eggs and Ham.”
Question: What is the degree here?
public ArrayList<String> getFlattenedList(ArrayList<String> prefix);
[“Green”, “Eggs”, “and”] “Ham” 3
“Bacon” 1
Return a list of word associated with a specific prefix, where each unique
word is repeated the same number of times as its frequency.
“Ham” “Ham” “Ham” “Bacon”
public ArrayList<String> getFlattenedList(ArrayList<String> prefix);
Cache:
A hardware or software component that stores data so future requests for
that data can be served faster. Imagine the program reading the entire
Harry Potter series and then writing books 8-10. Speed would be crucial.
How do we implement a cache in this assignment?
HashMap (surprise)
getFlattenedList([“Green”, “Eggs”, “and”]); for the first time
[“Green”, “Eggs”, “and”] “Ham” 3
“Bacon” 1
Look in cache, is the key [“Green”, “Eggs”, “and”] in the cache? No
cache
getFlattenedList([“Green”, “Eggs”, “and”]); for the first time
[“Green”, “Eggs”, “and”] “Ham” 3
“Bacon” 1
[“Green”, “Eggs”, “and”] “Ham” “Ham” “Ham” “Bacon”
Look in cache, is the key [“Green”, “Eggs”, “and”] in the cache? No
cache
Create the list, Put it in the cache, Return the list
getFlattenedList([“Green”, “Eggs”, “and”]); for the second time
[“Green”, “Eggs”, “and”] “Ham” 3
“Bacon” 1
[“Green”, “Eggs”, “and”] “Ham” “Ham” “Ham” “Bacon”
Look in cache, is the key [“Green”, “Eggs”, “and”] in the cache?
Yes, directly return the list
cache
getFlattenedList([“Green”, “Eggs”, “and”]); for the millionth time
[“Green”, “Eggs”, “and”] “Ham” 3
“Bacon” 1
[“Green”, “Eggs”, “and”] “Ham” “Ham” “Ham” “Bacon”
Look in cache, is the key [“Green”, “Eggs”, “and”] in the cache?
Yes, directly return the list
We only needed to create the list once! The other 999,999 times we just had to access it!
cache
public String generateNext(ArrayList<String> prefix);
Call getFlattenedList();
“Ham” “Ham” “Ham” “Bacon”
Randomly return a word from this ^ list
public String generate(int count)
Generate a random key -> [“will”, “eat”, “them”]
Use it to generate a word (What method does this) -> “here”
Save this generated word as you will return all of the generated words at the end. You
could use an ArrayList.
ArrayList -> [“will”, “eat”, “them”, “here”]
public String generate(int count)
Generate a random key -> [“will”, “eat”, “them”]
Use it to generate a word (What method does this) -> “here”
Save this generated word as you will return all of the generated words at the end. You
could use an ArrayList.
ArrayList -> [“will”, “eat”, “them”, “here”]
Now once again use the new prefix to generate another word.
The new prefix should be [“eat”, “them”, “here”].
Use it to generate a word -> “or”
ArrayList -> [“will”, “eat”, “them”, “here”, “or”]
public String generate(int count)
Generate a random key -> [“will”, “eat”, “them”]
Use it to generate a word (What method does this) -> “here”
Save this generated word as you will return all of the generated words at the end. You
could use an ArrayList.
ArrayList -> [“will”, “eat”, “them”, “here”]
Now once again use the new prefix to generate another word.
The new prefix should be [“eat”, “them”, “here”].
Use it to generate a word -> “or”
ArrayList -> [“will”, “eat”, “them”, “here”, “or”]
Do this until you have [count] words total.
Then return a string of all of the words.
“Will eat them here or ………………..”
public String generate(int count)
The end result:
“will eat them here or there. i do not like them, sam-i-am. say! in the dark. not on
a boat. i will eat them in a tree! not in a box? would you eat them in a tree! not in the
dark. would you like then with a mouse. i do not like green eggs and ham! i do not like
them in a house. i do not like them,sam-i-am. i do not like them,sam-i-am. i do not like
them,sam-i-am. i do not like them with a fox. not in a box. not with a mouse. not with a
goat!”
CharacterModel
is almost exactly the same as WordModel, except each string
in the ArrayLists and HashMaps are exactly one character long.
The logic should be similar.
Go make Dr. Seuss proud!

Extra Credit: linear interpolation
WordModel 1 WordModel 2
CombinedModel
A way to combine 2 distribution functions into 1
Extra Credit: linear interpolation
The combined frequency of a certain phrase is
that phrase’s frequency in model 1 * weight 1
+
that phrase’s frequency in model 2 * weight 2
Extra Credit: linear interpolation
?
Extra Credit: linear interpolation
Model 1 Model 2
Prefix Prediction Frequency Prefix Prediction Frequency
“the” “dog” 1 “the” “dog” 2
“cat” 1 “cat” 1
“memer” 2 “sloth” 1
“a” “bunny” 2 “memer” 8
New Model (constructed with Model 1 weight = 2, Model 2 weight = 1)
Prefix Prediction Frequency
“the” “dog” 1*a+ 2*b = 1*2 + 2*1 = 4
“cat” 1*2 + 1*1 = 3
“sloth” 0*2 + 1*1 = 1
“memer” 2*2 + 8*1 = 12
“a” “bunny” 2*2 + 0*1 = 4
New Model (constructed with Model 1 weighing twice as much as Model 2)
Prefix Prediction Frequency
“the” “dog” 1*a+ 2*b = 1*2 + 2*1 = 4
“cat” 1*2 + 1*1 = 3
“sloth” 0*2 + 1*1 = 1
“memer” 2*2 + 8*1 = 12
“a” “bunny” 2*2 + 0*1 = 4
In the new CombinedModel,
After the prefix “the”
How much more likely is “memer” predicted than “cat”?
In CombinedModel.java
Constructor takes in 2 WordModels, and 2 weights
public CombinedModel (WordModel model1, WordModel model2, int a, int b);
You only need to implement one method:
public String generateNext(ArrayList<String> prefix);
To predict the next word.
In CombinedModel.java
Hint 1: you can call any public method in WordModel, but which
method actually gives you a “distribution of words”?
Hint 2: you can comfortably write this in 40 ish lines of code, if it gets
super long, something might be wrong
How to check if you combined the distribution correctly?
Something to think about for the next assignment:
In a world where strings do not have a length() method, how
would you count how many characters are in a string?

PSA 7 – Generating Text with Markov Language Model
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