I am working on an LSTM to generate music. My input data will be a BooleanTensor of size 88xLx3, 88 being the amount of available notes, L being the length of each "piece" which will be in the order of 1k - 10k (TBD), and 3 being the parts for "lead melody", "accompaniment", and "bass". A value of 0 would symbolize that that specific note is not being played by that part (instrument) at that time, and a 1 would symbolize that it is.
The problem is that each entry of a BooleanTensor takes 1 byte of space in memory instead of 1 bit, which wastes a lot of valuable GPU memory.
As a solution I thought of packing each BooleanTensor to a ByteTensor (uint8) of size 11xLx3 or 88x(L/8)x3.
My question is: Would packing the data as such have an effect on the learning and generation of the LSTM or would the ByteTensor-based data and model be equivalent to their BooleanTensor-based counterparts in practice?
I wouldn't really care about the fact that the input is taking X instead of Y number of bits, at least when it comes to GPU memory. Most of it is occupied by the network's weights and intermediate outputs, which will likely be float32 anyway (maybe float16). There is active research on training with lower precision (even binary training), but based on your question, it seems completely unnecessary. Lastly, you can always try Quantization to your production models, if you really need it.
With regards to the packing: it can have an impact, especially if you do it naively. The grouping you're suggesting doesn't seem to be a natural one, therefore it may be harder to learn patterns from the grouped data than otherwise. There'll always be workarounds, but then this answer become an opinion because it is almost impossible to antecipate what could work; an opinion-based questions/answer are off-topic around here :)
Related
I am fine-tuning a BERT model on a labeled dataset with many documents longer than the 512 token limit set by the tokenizer.
Since truncating would lose a lot of data I would rather use, I started looking for a workaround. However I noticed that simply splitting the documents after 512 tokens (or another heuristic) and creating new entries in the dataset with the same label was never mentioned.
In this answer, someone mentioned that you would need to recombine the predictions, is that necessary when splitting the documents?
Is this generally considered bad practice or does it mess with the integrity of the results?
You have not mentioned if your intention is to classify, but given that you refer to an article on classification I will refer to an approach where you classify the whole text.
The main question is - which part of the text is the most informative for your purpose - or - in other words - does it make sense to use more than the first / last split of text?
When considering long passages of text, frequently, it is enough to consider the first (or last) 512 tokens to correctly predict the class in substantial majority of cases (say 90%). Even though you may loose some precision, you gain on speed and performance of the overall solution and you are getting rid of a nasty problem of figuring out the correct class out of a set of classifications. Why?
Consider an example of text 2100 tokens long. You split it by 512 tokens, obtaining pieces: 512, 512, 512, 512, 52 (notice the small last piece - should you even consider it?). Your target class for this text is, say, A, however you get the following predictions on the pieces: A, B, A, B, C. So you have now a headache to figure out the right method to determine the class. You can:
use majority voting but it is not conclusive here.
weight the predictions by the length of the piece. Again non conclusive.
check that prediction of the last piece is class C but it is barely above the threshold and class C is kinda A. So you are leaning towards A.
re-classify starting the split from the end. In the same order as before you get: A, B, C, A, A. So, clearly A. You also get it when you majority vote combining all of the classifications (forward and backward splits).
consider the confidence of the classifications, e.g. A: 80, B: 70, A: 90, B: 60, C: 55% - avg. 85% for A vs. 65% for B.
reconfirm the correction of labelling of the last piece manually: if it turns out to be B, then it changes all of the above.
then you can train an additional network to classify out of the raw classifications of pieces. Getting again into trouble of figuring out what to do with particularly long sequences or non-conclusive combinations of predictions resulting in poor confidence of the additional classification layer.
It turns out that there is no easy way. And you will notice that text is a strange classification material exhibiting all of the above (and more) issues while typically the difference in agreement between the first piece prediction and the annotation vs. the ultimate, perfect classifier is slim at best.
So, spare the effort and strive for simplicity, performance, and heuristic... and clip it!
On details of the best practices you should probably refer to the article from this answer.
I am working on a problem for which we aim to solve with deep Q learning. However, the problem is that training just takes too long for each episode, roughly 83 hours. We are envisioning to solve the problem within, say, 100 episode.
So we are gradually learning a matrix (100 * 10), and within each episode, we need to perform 100*10 iterations of certain operations. Basically we select a candidate from a pool of 1000 candidates, put this candidate in the matrix, and compute a reward function by feeding the whole matrix as the input:
The central hurdle is that the reward function computation at each step is costly, roughly 2 minutes, and each time we update one entry in the matrix.
All the elements in the matrix depend on each other in the long term, so the whole procedure seems not suitable for some "distributed" system, if I understood correctly.
Could anyone shed some lights on how we look at the potential optimization opportunities here? Like some extra engineering efforts or so? Any suggestion and comments would be appreciated very much. Thanks.
======================= update of some definitions =================
0. initial stage:
a 100 * 10 matrix, with every element as empty
1. action space:
each step I will select one element from a candidate pool of 1000 elements. Then insert the element into the matrix one by one.
2. environment:
each step I will have an updated matrix to learn.
An oracle function F returns a quantitative value range from 5000 ~ 30000, the higher the better (roughly one computation of F takes 120 seconds).
This function F takes the matrix as the input and perform a very costly computation, and it returns a quantitative value to indicate the quality of the synthesized matrix so far.
This function is essentially used to measure some performance of system, so it do takes a while to compute a reward value at each step.
3. episode:
By saying "we are envisioning to solve it within 100 episodes", that's just an empirical estimation. But it shouldn't be less than 100 episode, at least.
4. constraints
Ideally, like I mentioned, "All the elements in the matrix depend on each other in the long term", and that's why the reward function F computes the reward by taking the whole matrix as the input rather than the latest selected element.
Indeed by appending more and more elements in the matrix, the reward could increase, or it could decrease as well.
5. goal
The synthesized matrix should let the oracle function F returns a value greater than 25000. Whenever it reaches this goal, I will terminate the learning step.
Honestly, there is no effective way to know how to optimize this system without knowing specifics such as which computations are in the reward function or which programming design decisions you have made that we can help with.
You are probably right that the episodes are not suitable for distributed calculation, meaning we cannot parallelize this, as they depend on previous search steps. However, it might be possible to throw more computing power at the reward function evaluation, reducing the total time required to run.
I would encourage you to share more details on the problem, for example by profiling the code to see which component takes up most time, by sharing a code excerpt or, as the standard for doing science gets higher, sharing a reproduceable code base.
Not a solution to your question, just some general thoughts that maybe are relevant:
One of the biggest obstacles to apply Reinforcement Learning in "real world" problems is the astoundingly large amount of data/experience required to achieve acceptable results. For example, OpenAI in Dota 2 game colletected the experience equivalent to 900 years per day. In the original Deep Q-network paper, in order to achieve a performance close to a typicial human, it was required hundres of millions of game frames, depending on the specific game. In other benchmarks where the input are not raw pixels, such as MuJoCo, the situation isn't a lot better. So, if you don't have a simulator that can generate samples (state, action, next state, reward) cheaply, maybe RL is not a good choice. On the other hand, if you have a ground-truth model, maybe other approaches can easily outperform RL, such as Monte Carlo Tree Search (e.g., Deep Learning for Real-Time Atari Game Play Using Offline Monte-Carlo Tree Search Planning or Simple random search provides a competitive approach to reinforcement learning). All these ideas a much more are discussed in this great blog post.
The previous point is specially true for deep RL. The fact of approximatting value functions or policies using a deep neural network with millions of parameters usually implies that you'll need a huge quantity of data, or experience.
And regarding to your specific question:
In the comments, I've asked a few questions about the specific features of your problem. I was trying to figure out if you really need RL to solve the problem, since it's not the easiest technique to apply. On the other hand, if you really need RL, it's not clear if you should use a deep neural network as approximator or you can use a shallow model (e.g., random trees). However, these questions an other potential optimizations require more domain knowledge. Here, it seems you are not able to share the domain of the problem, which could be due a numerous reasons and I perfectly understand.
You have estimated the number of required episodes to solve the problem based on some empirical studies using a smaller version of size 20*10 matrix. Just a caution note: due to the curse of the dimensionality, the complexity of the problem (or the experience needed) could grow exponentially when the state space dimensionalty grows, although maybe it is not your case.
That said, I'm looking forward to see an answer that really helps you to solve your problem.
Im wondering if there is a general rule of thumb for population sizing. Ive read in a book that 2x the chromosome length is a good starting point. Am i correct in assuming then that if i had an equation with 5 variables, i should have a population of 10?
Im also wondering if the following is correct:
Larger Population Size.
Pros:
Larger diversity so more likely to pick up on traits which return a good fitness.
Cons:
Requires longer to process.
vs
Smaller Population Size.
Pros:
Larger number of generations experienced per unit time.
Cons:
Mutation will have to be more prominent in order to compensate for smaller population??
EDIT
A little additional info, say i have an equation which has 5 unknown parameters. For each parameter i have anywhere between 10-50 values i would like to try assign to each of these variables. So for example
variable1 = 20 different values
variable2 = 15 different values
...
I thought a GA would be a decent approach to such a problem as the search space is quite large, ie worst case for the above would be 312,500,000 permutations (unless i have screwed up?) n!/(n-k)! where n = 50 and k = 1 => 50 * 50 * 50 * 50 * 50
unfortunately the number of parameters/range of values to check can vary alot so i was looking for some sort of rule of thumb as to how large i should set the population.
Thanks for ur help + if there is any more info you need/prefer to discuss in one of the chatrooms, just give me a shout.
I'm not sure where you read that 2x the chromosome length is a good starting point, but I'm guessing it's a book that concentrated on larger problems.
If you only have five variables, a genetic algorithm is probably not the right choice for converging upon a solution. With a chromosome length of five you're probably going to find that you very quickly reach a non-deterministic(this will change in subsequent runs) local minimum and slowly iterate around that space until you find the true local minimum.
However, if you are insistent on using a GA I would suggest abandoning that rule of thumb for this problem and really think about starting population as a measure of how far from the final solution you expect a random solution to be.
The reason that many rule of thumbs is dependent on chromosome length is because that's a decent proxy for this, if I have a hundred variables, and given randomly generating dna sequence is going to be further from ideal than if I had only one variable.
Additionally, if you're worried about computation intensity I'm going to go ahead and say that it shouldn't be an issue since you're dealing with such a small solution set. I think a better rule of thumb for smaller sets like this would be along the lines of:
(ln(chromosome_length*(solution_space/granularity)/mutation_rate))^2
Probably with a constant thrown in to scale for the particular problem.
It's definitely not a great rule of thumb (no rule is) but here's my logic for it:
Chromosome length is just a proxy for size of solution space, so taking into account the size of the solution space will necessarily increase the accuracy of this proxy
A smaller mutation rate necessitates a larger population size to compensate for the fact that you are more prone to get caught in local minima
Any rule of thumb should scale logarithmically since a genetic algorithm is akin to a tree search of your solution space.
The squared term was mostly the result of trying this out, but it looks like the logarithmic scaling was a little aggressive, though the general shape seemed right.
However I think a better choice would be to start at a reasonable number (100) and try iterating up and down until you find a population size that seems to balance accuracy with execution speed.
As with most genetic algorithm parameters population size is highly dependant on the problem. There are certain factors that can help to point in the direction of whether you should have a large or small population size but a lot of the time testing different values against a known solution before running it on your problem is a good idea (if this is possible of course).
A population size of 10 does seem rather small though. You say you have an equation with five variables. Is your problem represented by a chromosome of 5 values? It seems small for a chromosome and if this is the case it's likely that using a genetic algorithm may not be the best way to solve the problem. Perhaps if you give a bit more detail on your problem and how you are representing it people may have a better idea of how to advise you.
I'd also add that your cons for large and small population sizes aren't exactly correct. A larger population size does take longer to process than a small one but since it can often solve the problem quicker then overall the processing time isn't necessarily longer. gain, it's highly dependant on the problem. With a smaller population size mutation shouldn't have to be more prominent. Mutation is generally used to stop the genetic algorithm from becoming stuck in a local maximum and should usually be a very small value. A small population is more likely to become stuck in a local maximum but if you have a mutation value which is too high you may be nullifying the natural improvement of the genetic algorithm.
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Is there a rule-of-thumb for how to best divide data into training and validation sets? Is an even 50/50 split advisable? Or are there clear advantages of having more training data relative to validation data (or vice versa)? Or is this choice pretty much application dependent?
I have been mostly using an 80% / 20% of training and validation data, respectively, but I chose this division without any principled reason. Can someone who is more experienced in machine learning advise me?
There are two competing concerns: with less training data, your parameter estimates have greater variance. With less testing data, your performance statistic will have greater variance. Broadly speaking you should be concerned with dividing data such that neither variance is too high, which is more to do with the absolute number of instances in each category rather than the percentage.
If you have a total of 100 instances, you're probably stuck with cross validation as no single split is going to give you satisfactory variance in your estimates. If you have 100,000 instances, it doesn't really matter whether you choose an 80:20 split or a 90:10 split (indeed you may choose to use less training data if your method is particularly computationally intensive).
Assuming you have enough data to do proper held-out test data (rather than cross-validation), the following is an instructive way to get a handle on variances:
Split your data into training and testing (80/20 is indeed a good starting point)
Split the training data into training and validation (again, 80/20 is a fair split).
Subsample random selections of your training data, train the classifier with this, and record the performance on the validation set
Try a series of runs with different amounts of training data: randomly sample 20% of it, say, 10 times and observe performance on the validation data, then do the same with 40%, 60%, 80%. You should see both greater performance with more data, but also lower variance across the different random samples
To get a handle on variance due to the size of test data, perform the same procedure in reverse. Train on all of your training data, then randomly sample a percentage of your validation data a number of times, and observe performance. You should now find that the mean performance on small samples of your validation data is roughly the same as the performance on all the validation data, but the variance is much higher with smaller numbers of test samples
You'd be surprised to find out that 80/20 is quite a commonly occurring ratio, often referred to as the Pareto principle. It's usually a safe bet if you use that ratio.
However, depending on the training/validation methodology you employ, the ratio may change. For example: if you use 10-fold cross validation, then you would end up with a validation set of 10% at each fold.
There has been some research into what is the proper ratio between the training set and the validation set:
The fraction of patterns reserved for the validation set should be
inversely proportional to the square root of the number of free
adjustable parameters.
In their conclusion they specify a formula:
Validation set (v) to training set (t) size ratio, v/t, scales like
ln(N/h-max), where N is the number of families of recognizers and
h-max is the largest complexity of those families.
What they mean by complexity is:
Each family of recognizer is characterized by its complexity, which
may or may not be related to the VC-dimension, the description
length, the number of adjustable parameters, or other measures of
complexity.
Taking the first rule of thumb (i.e.validation set should be inversely proportional to the square root of the number of free adjustable parameters), you can conclude that if you have 32 adjustable parameters, the square root of 32 is ~5.65, the fraction should be 1/5.65 or 0.177 (v/t). Roughly 17.7% should be reserved for validation and 82.3% for training.
Last year, I took Prof: Andrew Ng’s online machine learning course. His recommendation was:
Training: 60%
Cross-validation: 20%
Testing: 20%
Well, you should think about one more thing.
If you have a really big dataset, like 1,000,000 examples, split 80/10/10 may be unnecessary, because 10% = 100,000 examples may be just too much for just saying that model works fine.
Maybe 99/0.5/0.5 is enough because 5,000 examples can represent most of the variance in your data and you can easily tell that model works good based on these 5,000 examples in test and dev.
Don't use 80/20 just because you've heard it's ok. Think about the purpose of the test set.
Perhaps a 63.2% / 36.8% is a reasonable choice. The reason would be that if you had a total sample size n and wanted to randomly sample with replacement (a.k.a. re-sample, as in the statistical bootstrap) n cases out of the initial n, the probability of an individual case being selected in the re-sample would be approximately 0.632, provided that n is not too small, as explained here: https://stats.stackexchange.com/a/88993/16263
For a sample of n=250, the probability of an individual case being selected for a re-sample to 4 digits is 0.6329.
For a sample of n=20000, the probability is 0.6321.
It all depends on the data at hand. If you have considerable amount of data then 80/20 is a good choice as mentioned above. But if you do not Cross-Validation with a 50/50 split might help you a lot more and prevent you from creating a model over-fitting your training data.
Suppose you have less data, I suggest to try 70%, 80% and 90% and test which is giving better result. In case of 90% there are chances that for 10% test you get poor accuracy.
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I am using LibSVM to classify some documents. The documents seem to be a bit difficult to classify as the final results show. However, I have noticed something while training my models. and that is: If my training set is for example 1000 around 800 of them are selected as support vectors.
I have looked everywhere to find if this is a good thing or bad. I mean is there a relation between the number of support vectors and the classifiers performance?
I have read this previous post but I am performing a parameter selection and also I am sure that the attributes in the feature vectors are all ordered.
I just need to know the relation.
Thanks.
p.s: I use a linear kernel.
Support Vector Machines are an optimization problem. They are attempting to find a hyperplane that divides the two classes with the largest margin. The support vectors are the points which fall within this margin. It's easiest to understand if you build it up from simple to more complex.
Hard Margin Linear SVM
In a training set where the data is linearly separable, and you are using a hard margin (no slack allowed), the support vectors are the points which lie along the supporting hyperplanes (the hyperplanes parallel to the dividing hyperplane at the edges of the margin)
All of the support vectors lie exactly on the margin. Regardless of the number of dimensions or size of data set, the number of support vectors could be as little as 2.
Soft-Margin Linear SVM
But what if our dataset isn't linearly separable? We introduce soft margin SVM. We no longer require that our datapoints lie outside the margin, we allow some amount of them to stray over the line into the margin. We use the slack parameter C to control this. (nu in nu-SVM) This gives us a wider margin and greater error on the training dataset, but improves generalization and/or allows us to find a linear separation of data that is not linearly separable.
Now, the number of support vectors depends on how much slack we allow and the distribution of the data. If we allow a large amount of slack, we will have a large number of support vectors. If we allow very little slack, we will have very few support vectors. The accuracy depends on finding the right level of slack for the data being analyzed. Some data it will not be possible to get a high level of accuracy, we must simply find the best fit we can.
Non-Linear SVM
This brings us to non-linear SVM. We are still trying to linearly divide the data, but we are now trying to do it in a higher dimensional space. This is done via a kernel function, which of course has its own set of parameters. When we translate this back to the original feature space, the result is non-linear:
Now, the number of support vectors still depends on how much slack we allow, but it also depends on the complexity of our model. Each twist and turn in the final model in our input space requires one or more support vectors to define. Ultimately, the output of an SVM is the support vectors and an alpha, which in essence is defining how much influence that specific support vector has on the final decision.
Here, accuracy depends on the trade-off between a high-complexity model which may over-fit the data and a large-margin which will incorrectly classify some of the training data in the interest of better generalization. The number of support vectors can range from very few to every single data point if you completely over-fit your data. This tradeoff is controlled via C and through the choice of kernel and kernel parameters.
I assume when you said performance you were referring to accuracy, but I thought I would also speak to performance in terms of computational complexity. In order to test a data point using an SVM model, you need to compute the dot product of each support vector with the test point. Therefore the computational complexity of the model is linear in the number of support vectors. Fewer support vectors means faster classification of test points.
A good resource:
A Tutorial on Support Vector Machines for Pattern Recognition
800 out of 1000 basically tells you that the SVM needs to use almost every single training sample to encode the training set. That basically tells you that there isn't much regularity in your data.
Sounds like you have major issues with not enough training data. Also, maybe think about some specific features that separate this data better.
Both number of samples and number of attributes may influence the number of support vectors, making model more complex. I believe you use words or even ngrams as attributes, so there are quite many of them, and natural language models are very complex themselves. So, 800 support vectors of 1000 samples seem to be ok. (Also pay attention to #karenu's comments about C/nu parameters that also have large effect on SVs number).
To get intuition about this recall SVM main idea. SVM works in a multidimensional feature space and tries to find hyperplane that separates all given samples. If you have a lot of samples and only 2 features (2 dimensions), the data and hyperplane may look like this:
Here there are only 3 support vectors, all the others are behind them and thus don't play any role. Note, that these support vectors are defined by only 2 coordinates.
Now imagine that you have 3 dimensional space and thus support vectors are defined by 3 coordinates.
This means that there's one more parameter (coordinate) to be adjusted, and this adjustment may need more samples to find optimal hyperplane. In other words, in worst case SVM finds only 1 hyperplane coordinate per sample.
When the data is well-structured (i.e. holds patterns quite well) only several support vectors may be needed - all the others will stay behind those. But text is very, very bad structured data. SVM does its best, trying to fit sample as well as possible, and thus takes as support vectors even more samples than drops. With increasing number of samples this "anomaly" is reduced (more insignificant samples appear), but absolute number of support vectors stays very high.
SVM classification is linear in the number of support vectors (SVs). The number of SVs is in the worst case equal to the number of training samples, so 800/1000 is not yet the worst case, but it's still pretty bad.
Then again, 1000 training documents is a small training set. You should check what happens when you scale up to 10000s or more documents. If things don't improve, consider using linear SVMs, trained with LibLinear, for document classification; those scale up much better (model size and classification time are linear in the number of features and independent of the number of training samples).
There is some confusion between sources. In the textbook ISLR 6th Ed, for instance, C is described as a "boundary violation budget" from where it follows that higher C will allow for more boundary violations and more support vectors.
But in svm implementations in R and python the parameter C is implemented as "violation penalty" which is the opposite and then you will observe that for higher values of C there are fewer support vectors.