I'm trying to run the hlda algorytmm and producing a descriptive hierarchy of the input documents. The problem is I'm running diverse parameters configs and trying to understand how it works in an "empirical way", because I can not match the ones that are being used in the original papers (I understand it's a different team). E.g. alpha in Mallet seems to be eta in the paper, but I'm not very sure. Besides, I can not know the boundaries for each of them. I mean, the range of possible values for each parameter.
In the source code, there is some help:
double alpha; // smoothing on topic distributions
double gamma; // "imaginary" customers at the next
double eta; // smoothing on word distributions.
First, I used the default values: alpha=10.0; gamma=1.0; eta = 0.1;
Then, I tryed running the algorythm by changing the values and interpret the results, but I can't understand the meaning of them. E.g. I think changing gamma (in Mallet) has an effect on the customers decition: to start a new node in the tree or to be placed in an existing one. So, if I set gamma = 0.5, less nodes should be produced, because 0.5 is half the probability of the default one, right? But the results with gamma=1 give me 87 nodes, and with gamma=0.5, it returns 98! And then, I'm asking me something new: is that a probability? I was trying to find the range of possible values in these two papers, but I didn't find them:
Hierarchical Topic Models andthe Nested Chinese Restaurant Process
The Nested Chinese Restaurant Process and BayesianNonparametric Inference of Topic Hierarchies
I know I could be missing something, because I don't have the a good background on this, but that's why I'm asking here, maybe someone already had this problem and can help me understanding those limits.
Thanks in advance!
It may be helpful to run multiple times with each hyperparameter setting. I suspect that gamma does not have a big influence on the final number of topics, and that what you are seeing could just be typical variability in the sampling process.
In my experience the parameter that has by far the strongest influence on the number of topics is actually eta, the topic-word smoothing.
Related
Firstly, I am totally out of my expertise zone so please bear with me.
I developed a fluid dynamic engine with 5 exposed parameters (say A,B,C,D,E). When you give this engine these 5 parameters, it does magic and give out a value 'Z'.
I want to write a script which can explore which combinations of A-E give lowest (or close to lowest) value of Z.
I know optimization algorithm exists, but from all of my search for examples, they use some function.
So I guess my function would simply be minimize Z? But where do A-E go?
Not really an answer, but some questions and ideas that might help you think through the best way to address this. We have no understanding of how big a range of values needs to be explored for those parameters, or how Z behaves, so this is very vague...
If you look at the values of Z for given values of A...E, does the value of Z jump around a lot for small changes on the parameter values, or does the Z value change reasonably smoothly?
If the Z value is not too eratic you could try some kind of gradient descent approach using calculated values of Z for some values of the parameters to approximate the gradient - suppose changing the value of 'A' from 1 to 2 gives a better change in the Z value than a similar size change in the other parameters, then try other values of A while keeping the other parameters fixed until you find a value of A that gives the best value of Z. Then try changing the other parameter values to see which one gives the steepest descent and try to find some better value for that parameter. Repeat this process until you can't find any improvement and you will have found a (local) minimum. You could then start at a different place in your parameter space and try again - you will probably find several local minima, and may just choose the best of those. Not provably optimal but may be good enough. Of course you can get clever and use things like conjugate gradients, Newton-Raphson or similar if Z is smooth enough.
If the Z values are very eratic, then you might have to just do some sampling of the possible combinations of A...E to get values of Z and choose the best you can find. Again you might do that in some systematic way (e.g. points on a grid in your parameter space) or entirely at random, or a combination of both.
If you find that there are 'clusters' of good solutions with similar values of the parameters then maybe some kind of local search would help - the idea is that there is often a better solution in the local neighbourhood of a known good solution. So maybe try perturbing your parameter values a bit from a known solution to see if that can lead to a better solution - either by some gradient descent method or by random sampling.
Unfortunately, if your Z calculation is complex, then any method using it as a black box will likely be slow as it will need to be re-evaluated many times.
You could use a Genetic Algorithm, where your chromosomes are formed with the 5 candidate values of the variables you have to optimize, to minimize Z, and your optimization/fitness "function" is the simulation itself outputting Z.
Other viable alternatives are Particle Swarm Optimization algorithm or Ant Colony Optimization. All of those are usable algortihms for that kind of optimization problem.
I am creating a machine learning model that essentially returns the correctness of one text to another.
For example; “the cat and a dog”, “a dog and the cat”. The model needs to be able to identify that some words (“cat”/“dog”) are more important/significant than others (“a”/“the”). I am not interested in conjunction words etc. I would like to be able to tell the model which words are the most “significant” and have it determine how correct text 1 is to text 2, with the “significant” words bearing more weight than others.
It also needs to be able to recognise that phrases don’t necessarily have to be in the same order. The two above sentences should be an extremely high match.
What is the basic algorithm I should use to go about this? Is there an alternative to just creating a dataset with thousands of example texts and a score of correctness?
I am only after a broad overview/flowchart/process/algorithm.
I think TF-IDF might be a good fit to your problem, because:
Emphasis on words occurring in many documents (say, 90% of your sentences/documents contain the conjuction word 'and') is much smaller, essentially giving more weight to the more document specific phrasing (this is the IDF part).
Ordering in Term Frequency (TF) does not matter, as opposed to methods using sliding windows etc.
It is very lightweight when compared to representation oriented methods like the one mentioned above.
Big drawback: Your data, depending on the size of corpus, may have too many dimensions (the same number of dimensions as unique words), you could use stemming/lemmatization in order to mitigate this problem to some degree.
You may calculate similiarity between two TF-IDF vector using cosine similiarity for example.
EDIT: Woops, this question is 8 months old, sorry for the bump, maybe it will be of use to someone else though.
and thanks for reading my thread.
I have read some of the previous posts on formatting/normalising input data for a Neural Network, but cannot find something that addresses my queries specifically. I apologise for the long post.
I am attempting to build a radial basis function network for analysing horse racing data. I realise that this has been done before, but the data that I have is "special" and I have a keen interest in racing/sportsbetting/programming so would like to give it a shot!
Whilst I think I understand the principles for the RBFN itself, I am having some trouble understanding the normalisation/formatting/scaling of the input data so that it is presented in a "sensible manner" for the network, and I am not sure how I should formulate the output target values.
For example, in my data I look at the "Class change", which compares the class of race that the horse is running in now compared to the race before, and can have a value between -5 and +5. I expect that I need to rescale these to between -1 and +1 (right?!), but I have noticed that many more runners have a class change of 1, 0 or -1 than any other value, so I am worried about "over-representation". It is not possible to gather more data for the higher/lower class changes because thats just 'the way the data comes'. Would it be best to use the data as-is after scaling, or should I trim extreme values, or something else?
Similarly, there are "continuous" inputs - like the "Days Since Last Run". It can have a value between 1 and about 1000, but values in the range of 10-40 vastly dominate. I was going to scale these values to be between 0 and 1, but even if I trim the most extreme values before scaling, I am still going to have a huge representation of a certain range - is this going to cause me an issue? How are problems like this usually dealt with?
Finally, I am having trouble understanding how to present the "target" values for training to the network. My existing results data has the "win/lose" (0 or 1?) and the odds at which the runner won or lost. If I just use the "win/lose", it treats all wins and loses the same when really they're not - I would be quite happy with a network that ignored all the small winners but was highly profitable from picking 10-1 shots. Similarly, a network could be forgiven for "losing" on a 20-1 shot but losing a bet at 2/5 would be a bad loss. I considered making the results (+1 * odds) for a winner and (-1 / odds) for a loser to capture the issue above, but this will mean that my results are not a continuous function as there will be a "discontinuity" between short price winners and short price losers.
Should I have two outputs to cover this - one for bet/no bet, and another for "stake"?
I am sorry for the flood of questions and the long post, but this would really help me set off on the right track.
Thank you for any help anyone can offer me!
Kind regards,
Paul
The documentation that came with your RBFN is a good starting point to answer some of these questions.
Trimming data aka "clamping" or "winsorizing" is something I use for similar data. For example "days since last run" for a horse could be anything from just one day to several years but tends to centre in the region of 20 to 30 days. Some experts use a figure of say 63 days to indicate a "spell" so you could have an indicator variable like "> 63 =1 else 0" for example. One clue is to look at outliers say the upper or lower 5% of any variable and clamp these.
If you use odds/dividends anywhere make sure you use the probabilities ie 1/(odds+1) and a useful idea is to normalize these to 100%.
The odds or parimutual prices tend to swamp other predictors so one technique is to develop separate models, one for the market variables (the market model) and another for the non-market variables (often called the "fundamental" model).
Question after BIG edition :
I need to built a ranking using genetic algorithm, I have data like this :
P(a>b)=0.9
P(b>c)=0.7
P(c>d)=0.8
P(b>d)=0.3
now, lets interpret a,b,c,d as names of football teams, and P(x>y) is probability that x wins with y. We want to build ranking of teams, we lack some observations P(a>d),P(a>c) are missing due to lack of matches between a vs d and a vs c.
Goal is to find ordering of team names, which the best describes current situation in that four team league.
If we have only 4 teams than solution is straightforward, first we compute probabilities for all 4!=24 orderings of four teams, while ignoring missing values we have :
P(abcd)=P(a>b)P(b>c)P(c>d)P(b>d)
P(abdc)=P(a>b)P(b>c)(1-P(c>d))P(b>d)
...
P(dcba)=(1-P(a>b))(1-P(b>c))(1-P(c>d))(1-P(b>d))
and we choose the ranking with highest probability. I don't want to use any other fitness function.
My question :
As numbers of permutations of n elements is n! calculation of probabilities for all
orderings is impossible for large n (my n is about 40). I want to use genetic algorithm for that problem.
Mutation operator is simple switching of places of two (or more) elements of ranking.
But how to make crossover of two orderings ?
Could P(abcd) be interpreted as cost function of path 'abcd' in assymetric TSP problem but cost of travelling from x to y is different than cost of travelling from y to x, P(x>y)=1-P(y<x) ? There are so many crossover operators for TSP problem, but I think I have to design my own crossover operator, because my problem is slightly different from TSP. Do you have any ideas for solution or frame for conceptual analysis ?
The easiest way, on conceptual and implementation level, is to use crossover operator which make exchange of suborderings between two solutions :
CrossOver(ABcD,AcDB) = AcBD
for random subset of elements (in this case 'a,b,d' in capital letters) we copy and paste first subordering - sequence of elements 'a,b,d' to second ordering.
Edition : asymetric TSP could be turned into symmetric TSP, but with forbidden suborderings, which make GA approach unsuitable.
It's definitely an interesting problem, and it seems most of the answers and comments have focused on the semantic aspects of the problem (i.e., the meaning of the fitness function, etc.).
I'll chip in some information about the syntactic elements -- how do you do crossover and/or mutation in ways that make sense. Obviously, as you noted with the parallel to the TSP, you have a permutation problem. So if you want to use a GA, the natural representation of candidate solutions is simply an ordered list of your points, careful to avoid repitition -- that is, a permutation.
TSP is one such permutation problem, and there are a number of crossover operators (e.g., Edge Assembly Crossover) that you can take from TSP algorithms and use directly. However, I think you'll have problems with that approach. Basically, the problem is this: in TSP, the important quality of solutions is adjacency. That is, abcd has the same fitness as cdab, because it's the same tour, just starting and ending at a different city. In your example, absolute position is much more important that this notion of relative position. abcd means in a sense that a is the best point -- it's important that it came first in the list.
The key thing you have to do to get an effective crossover operator is to account for what the properties are in the parents that make them good, and try to extract and combine exactly those properties. Nick Radcliffe called this "respectful recombination" (note that paper is quite old, and the theory is now understood a bit differently, but the principle is sound). Taking a TSP-designed operator and applying it to your problem will end up producing offspring that try to conserve irrelevant information from the parents.
You ideally need an operator that attempts to preserve absolute position in the string. The best one I know of offhand is known as Cycle Crossover (CX). I'm missing a good reference off the top of my head, but I can point you to some code where I implemented it as part of my graduate work. The basic idea of CX is fairly complicated to describe, and much easier to see in action. Take the following two points:
abcdefgh
cfhgedba
Pick a starting point in parent 1 at random. For simplicity, I'll just start at position 0 with the "a".
Now drop straight down into parent 2, and observe the value there (in this case, "c").
Now search for "c" in parent 1. We find it at position 2.
Now drop straight down again, and observe the "h" in parent 2, position 2.
Again, search for this "h" in parent 1, found at position 7.
Drop straight down and observe the "a" in parent 2.
At this point note that if we search for "a" in parent one, we reach a position where we've already been. Continuing past that will just cycle. In fact, we call the sequence of positions we visited (0, 2, 7) a "cycle". Note that we can simply exchange the values at these positions between the parents as a group and both parents will retain the permutation property, because we have the same three values at each position in the cycle for both parents, just in different orders.
Make the swap of the positions included in the cycle.
Note that this is only one cycle. You then repeat this process starting from a new (unvisited) position each time until all positions have been included in a cycle. After the one iteration described in the above steps, you get the following strings (where an "X" denotes a position in the cycle where the values were swapped between the parents.
cbhdefga
afcgedbh
X X X
Just keep finding and swapping cycles until you're done.
The code I linked from my github account is going to be tightly bound to my own metaheuristics framework, but I think it's a reasonably easy task to pull the basic algorithm out from the code and adapt it for your own system.
Note that you can potentially gain quite a lot from doing something more customized to your particular domain. I think something like CX will make a better black box algorithm than something based on a TSP operator, but black boxes are usually a last resort. Other people's suggestions might lead you to a better overall algorithm.
I've worked on a somewhat similar ranking problem and followed a technique similar to what I describe below. Does this work for you:
Assume the unknown value of an object diverges from your estimate via some distribution, say, the normal distribution. Interpret your ranking statements such as a > b, 0.9 as the statement "The value a lies at the 90% percentile of the distribution centered on b".
For every statement:
def realArrival = calculate a's location on a distribution centered on b
def arrivalGap = | realArrival - expectedArrival |
def fitness = Σ arrivalGap
Fitness function is MIN(fitness)
FWIW, my problem was actually a bin-packing problem, where the equivalent of your "rank" statements were user-provided rankings (1, 2, 3, etc.). So not quite TSP, but NP-Hard. OTOH, bin-packing has a pseudo-polynomial solution proportional to accepted error, which is what I eventually used. I'm not quite sure that would work with your probabilistic ranking statements.
What an interesting problem! If I understand it, what you're really asking is:
"Given a weighted, directed graph, with each edge-weight in the graph representing the probability that the arc is drawn in the correct direction, return the complete sequence of nodes with maximum probability of being a topological sort of the graph."
So if your graph has N edges, there are 2^N graphs of varying likelihood, with some orderings appearing in more than one graph.
I don't know if this will help (very brief Google searches did not enlighten me, but maybe you'll have more success with more perseverance) but my thoughts are that looking for "topological sort" in conjunction with any of "probabilistic", "random", "noise," or "error" (because the edge weights can be considered as a reliability factor) might be helpful.
I strongly question your assertion, in your example, that P(a>c) is not needed, though. You know your application space best, but it seems to me that specifying P(a>c) = 0.99 will give a different fitness for f(abc) than specifying P(a>c) = 0.01.
You might want to throw in "Bayesian" as well, since you might be able to start to infer values for (in your example) P(a>c) given your conditions and hypothetical solutions. The problem is, "topological sort" and "bayesian" is going to give you a whole bunch of hits related to markov chains and markov decision problems, which may or may not be helpful.
Y
I have 6 parameters for which I know maxi and mini values. I have a complex function that includes the 6 parameters and return a 7th value (say Y). I say complex because Y is not directly related to the 6 parameters; there are many embeded functions in between.
I would like to find the combination of the 6 parameters which returns the highest Y value. I first tried to calculate Y for every combination by constructing an hypercube but I have not enough memory in my computer. So I am looking for kinds of markov chains which progress in the delimited parameter space, and are able to overpass local peaks.
when I give one combination of the 6 parameters, I would like to know the highest local Y value. I tried to write a code with an iterative chain like a markov's one, but I am not sure how to process when the chain reach an edge of the parameter space. Obviously, some algorythms should already exist for this.
Question: Does anybody know what are the best functions in R to do these two things? I read that optim() could be appropriate to find the global peak but I am not sure that it can deal with complex functions (I prefer asking before engaging in a long (for me) process of code writing). And fot he local peaks? optim() should not be able to do this
In advance, thank you for any lead
Julien from France
Take a look at the Optimization and Mathematical Programming Task View on CRAN. I've personally found the differential evolution algorithm to be very fast and robust. It's implemented in the DEoptim package. The rgenoud package is another good candidate.
I like to use the Metropolis-Hastings algorithm. Since you are limiting each parameter to a range, the simple thing to do is let your proposal distribution simply be uniform over the range. That way, you won't run off the edges. It won't be fast, but if you let it run long enough, it will do a good job of sampling your space. The samples will congregate at each peak, and will spread out around them in a way that reflects the local curvature.