Re: making a markovian "mad lib"

[trippledubs]

I'll have a go

for (@{$data}) {
    my $key = $_->[0];
    my $last_element = $#{$_};
    my $random = $_->[rand($#{$_}) + 1];
    $vars{$key} =  $random;
}

A more concise way:

%vars = map { $_->[0],$_->[rand($#{$_}) + 1] } @{$data};

You could represent like:

$story = {
      protaganist => [ 'al debaran','narrator','japh','gilligan' ],
      dog => [ 'my pretty pitty' ],
};

or

data/protaganist.txt
al debaran
the narrator
japh

data/trials.txt
adventures
bedraengisse

[Aldebaran]

I'll have a go

Your response seems to work, thank you very much. Indeed, it helped me to understand the syntax involved. I used the more compact version and got the behaviours I was looking for. I'll put output and source between readmore tags.

Read more... (5 kB)

So I'm happy with this as an intermediate result but started puzzling on what I was coding towards. I wanted to throw the ball to the dog and have that repeat through probabilistic methods. The repeated events were hard to extricate causally. If I tried to represent the scenario with object oriented methods, what would the "objects" be? The story, the things in the story, the state of the things in the story, the Animals as with _Intermediate Perl_? Wherein does it show Markovian nature?

After wrestling with that for a few days whilst distracted by the US div I college men's basketball tournament, I decided, wait a sec, this tournament with its "bracketology" is the type of creature I'm looking for. So I'm shifting the story from being about the dog chasing the ball to ten guys on a court chasing a ball like their lives depend on it. I'm redefining the problem here a bit and would like to change the subject to reflect that. It doesn't take long for code to get longer, so I will use readmore tags:

Read more... (8 kB)

Also, I'm fishing for any way to re-imagine this problem. I'm gonna have to create a dozen hodge-podge arrays, and the tournament is always a 2**6 thing.*

Thanks for your comment,

*except for "first four" games

[bliako]

The "markovian principle" is nothing more than the following simple tenet:

next state depends (= is influenced) only on current state

The context is a random process which outputs symbols (or it being in a "state"), one after another. For example, the process is "weather" during a single hour (i.e. 1 hour=1 weather state), with 3 states: "rain", "sunny", "dry-cloudy". And the outcome of this process is something like "rain"->"rain"->"sunny"->"dry-cloudy" ...

If that was a "markovian process" then we could describe it simply by a "transition matrix" which is a convenient way to convey the information of what the probability of "next" state is given "current" state in the form of a 2d array often called a stochastic matrix:

            rain   sunny   dry-cloudy
rain         0.6    0.2      0.2
sunny        0.3    0.5      0.2
dry-cloudy   0.4    0.3      0.3

In the above array, row represents current state and column the next state, e.g. the probability of rain when now is raining is 0.6, the prob of dry-cloudy when now is sunny is 0.2 etc. The important property of the above matrix is that the probabilities of all the possible events from a current state must sum to 1: all rows sum to 1. Why? If we are now in current state of "rain" we have 3 possible outcomes. And so their probabilities must sum to one because one of them will happen with absolute certainty (as far as our model goes).

Similarly, one can use multi-dimensional arrays in order to model a random process whose next state depends on n-previous states. It will not be "markovian" but we can use the same tools.

So, the most important thing so far, forgetting about markov property etc, is that a random process outputs from a finite set of symbols with a probability depending on n-previous symbols and that can be modeled using a transition matrix as described above. In this matrix all the probabilities of the possible events from a current state must sum to 1.

Another useful tool (equivalent to the transition matrix) in modelling or visualising such random processes (of finite number of events) is a Graph, see the diagram here: Markov_chain.

Graph or transition matrix, once you built one by observing the weather for too long and finally estimating the transition probabilities, you can use it to simulate your random process. And make it produce random symbols.

The Graph or matrix can also be constructed by hand from imagination. Feed that information to your simulator in order to run the random process. That's probably how a computer game would calculate the weather in Mars.

I can not help you with your basketball model because I am not acquainted at all with these "big dances", "east", "west" etc. but perhaps you can rubber-duck it and in more general terms.

bw, bliako

[trippledubs]

So I'm happy with this as an intermediate result but started puzzling on what I was coding towards. I wanted to throw the ball to the dog and have that repeat through probabilistic methods. The repeated events were hard to extricate causally. If I tried to represent the scenario with object oriented methods, what would the "objects" be? The story, the things in the story, the state of the things in the story, the Animals as with _Intermediate Perl_? Wherein does it show Markovian nature?

I didn't see any probability calculations in your script that I looked at. You asked for equiprobable. Bliako uses a corpus to build up probability tables, you used a template with some variables. So, from my very limited, but now less so by reading through n-dimensional statistical analysis of DNA sequences (or text, or ...), you need some input to build up those probability tables. If I understand correctly: for some input, some text probably follows some other text. Then for some other (or same) input, you replace the text based on those probabilities. In sports, some team beats some other team with some frequency.

So if you want to utilize Bliakos methods you need a corpus that relates. Like, previous scores. You are using rankings (seeds), but that will just give you what you already have. It's not going to increase the accuracy if ranked 1 probably beats ranked 2. You need a corpus with scores or something. Then you might be able to bet the spread.

Bliako's solution aims to be more general in that, the n-gram is configurable, as well as what separates the n-grams. You have to have an input that matches that criteria or hammer it into that. Team X vs Team Y will not be read the same as Team Y vs Team X. And it's not going to account for degrees, only the probability of a sequence. Degrees like, if team X beats Y by a whole lot. Or what is the average point difference, things like that. So if you had a corpus like

Virginia: 40 Duke 60 (Duke)
Virginia: 50 Duke 70 (Duke)
Virginia: 80 Duke 70 (Virginia)

With n-gram=2 and separator being 'space and then some digits' it follows that (Duke) succeeds Virginia: Duke 2/3 of the time. Those are the kind of probabilities Bliako is using, pretty sure.

[Aldebaran]

I didn't see any probability calculations in your script that I looked at. You asked for equiprobable.

I did. That was meant to start things off, to get on the proverbial scoreboard. They still work for the naive use of appositives, which remains a component of this output. The equaprobable outcomes do sum to one, so we aren't too far afield of bliako's development with cumulative probablity. I've included another way to generate the probabilities now. The working version of what I have now follows with abridged output and source:

Read more... (13 kB)

Thanks for your comments,