I was reading a paper about missing values on the Internet and having a problem in interpreting interpreting the meaning of the first sentence highlighted in bold below:
Missing data present various problems. First, the absence of data reduces statistical power, which refers to the probability that the test will reject the null hypothesis when it is false. Second, the lost data can cause bias in the estimation of parameters. Third, it can reduce the representativeness of the samples. Fourth, it may complicate the analysis of the study. Each of these distortions may threaten the validity of the trials and can lead to invalid conclusions.
Hope to hear some explanations.
Firstly, power is the probability of rejecting the null hypothesis when in fact it is false. So, you could say it is the probability of making the correct decision. The absence of data reduces this statistical power, a low sample size of studies, small effects being investigated, or both adversely impacts the likelihood that a statistically significant finding actually reflects a true effect. Meaning let's say if you've 100 samples and because of missing values you discard 40 samples from the dataset, now whatever conclusion you come up with using the remaining 60 samples, you can't be much confident that it reflects a true effect.
Secondly, If you choose to replace those missing values using the mean for example, then you're injecting a sort of bias to the data, actually, however you decide to replace or remove the data, the bias is getting injected. (though certain bias is more plausible in certain situations)
Thirdly, the sentence is quite explanatory itself, those missing values reduce the representativeness of the samples, as you don't have all the info you need about those samples.
Lastly, we can say it (missing values) actually does complicates our study, It's the last thing we would want when working with data, however because of human error and many other sources of errors we often have to deal with these missing values with certain operations.
Related
I'm trying to use H2O's Random Forest for a multinominal classification into 71 classes with 38,000 training set examples. I have one features that is a string that in many cases are predictive, so I want to use it as a categorical feature.
The hitch is that even after canonicalizing the strings (uppercase, stripping out numbers, punctuation, etc.), I still have 7,000 different strings (some due to spelling or OCR errors, etc.) I have code to remove strings that are relatively rare, but I'm not sure what a reasonable cut off value is. (I can't seem to find any help in the documentation.)
I'm also not sure what to due with nbin_cats hyperparameter. Should I make it equal to the number of different categorical variables I have? [added: default for nbin_cats is 1024 and I'm well below that at around 300 different categorical values, so I guess I don't have to do anything with this parameter]
I'm also thinking perhaps if a categorical value is associated with too many different categories that I'm trying to predict, maybe I should drop it as well.
I'm also guessing I need to increase the tree depth to handle this better.
Also, is there a special value to indicate "don't know" for the strings that I am filtering out? (I'm mapping it to a unique string but I'm wondering if there is a better value that indicates to H2O that the categorical value is unknown.)
Many thanks in advance.
High cardinality categorical predictors can sometimes hurt model performance, and specifically in the case of tree-based models, the tree ensemble (GBM or Random Forest) ends up memorizing the training data. The model has a poor time generalizing on validation data.
A good indication of whether this is happening is if your string/categorical column has very high variable importance. This means that the trees are continuing to split on this column to memorize the training data. Another indication is if you see much smaller error on your training data than on your validation data. This means the trees are overfitting to the training data.
Some methods for handling high cardinality predictors are:
removing the predictor from the model
performing categorical encoding [pdf]
performing grid search on nbins_cats and categorical_encoding
There is a Python example in the H2O tutorials GitHub repo that showcases the effects of removing the predictor from the model and performing grid search here.
I'm pretty sure that the answer is no, but wanted to confirm...
When training a neural network or other learning algorithm, we will compute the cost function J(θ) as an expression of how well our algorithm fits the training data (higher values mean it fits the data less well). When training our algorithm, we generally expect to see J(theta) go down with each iteration of gradient descent.
But I'm just curious, would there ever be a value to computing J(θ) against our test data?
I think the answer is no, because since we only evaluate our test data once, we would only get one value of J(θ), and I think that it is meaningless except when compared with other values.
Your question touches on a very common ambiguity regarding the terminology: one between the validation and the test sets (the Wikipedia entry and this Cross Vaidated post may be helpful in resolving this).
So, assuming that you indeed refer to the test set proper and not the validation one, then:
You are right in that this set is only used once, just at the end of the whole modeling process
You are, in general, not right in assuming that we don't compute the cost J(θ) in this set.
Elaborating on (2): in fact, the only usefulness of the test set is exactly for evaluating our final model, in a set that has not been used at all in the various stages of the fitting process (notice that the validation set has been used indirectly, i.e. for model selection); and in order to evaluate it, we obviously have to compute the cost.
I think that a possible source of confusion is that you may have in mind only classification settings (although you don't specify this in your question); true, in this case, we are usually interested in the model performance regarding a business metric (e.g. accuracy), and not regarding the optimization cost J(θ) itself. But in regression settings it may very well be the case that the optimization cost and the business metric are one and the same thing (e.g. RMSE, MSE, MAE etc). And, as I hope is clear, in such settings computing the cost in the test set is by no means meaningless, despite the fact that we don't compare it with other values (it provides an "absolute" performance metric for our final model).
You may find this and this answers of mine useful regarding the distinction between loss & accuracy; quoting from these answers:
Loss and accuracy are different things; roughly speaking, the accuracy is what we are actually interested in from a business perspective, while the loss is the objective function that the learning algorithms (optimizers) are trying to minimize from a mathematical perspective. Even more roughly speaking, you can think of the loss as the "translation" of the business objective (accuracy) to the mathematical domain, a translation which is necessary in classification problems (in regression ones, usually the loss and the business objective are the same, or at least can be the same in principle, e.g. the RMSE)...
Do you know how to intepret RAE and RSE values? I know a COD closer to 1 is a good sign. Does this indicate that boosted decision tree regression is best?
RAE and RSE closer to 0 is a good sign...you want error to be as low as possible. See this article for more information on evaluating your model. From that page:
The term "error" here represents the difference between the predicted value and the true value. The absolute value or the square of this difference are usually computed to capture the total magnitude of error across all instances, as the difference between the predicted and true value could be negative in some cases. The error metrics measure the predictive performance of a regression model in terms of the mean deviation of its predictions from the true values. Lower error values mean the model is more accurate in making predictions. An overall error metric of 0 means that the model fits the data perfectly.
Yes, with your current results, the boosted decision tree performs best. I don't know the details of your work well enough to determine if that is good enough. It honestly may be. But if you determine it's not, you can also tweak the input parameters in your "Boosted Decision Tree Regression" module to try to get even better results. The "ParameterSweep" module can help with that by trying many different input parameters for you and you specify the parameter that you want to optimize for (such as your RAE, RSE, or COD referenced in your question). See this article for a brief description. Hope this helps.
P.S. I'm glad that you're looking into the black carbon levels in Westeros...I'm sure Cersei doesn't even care.
I am working on a project which performs text auto-classification, I have a lot of data set like as below:
Text | CategoryName
xxxxx... | AA
yyyyy... | BB
zzzzz... | AA
then, I will use the above data set to generate a classifier, once new text coming, the classifier can label new text with correct CategoryName
(text is natural language, size between 10-10000)
Now, the problem is, the original data set contains some incorrect data, (E.g. AAA should be labeled as Category AA, but it is labeled as Category BB accidentally ) because these data are classified manually. And I don't know which label is wrong and how many percentages are wrong because I can't review all data manually...
So my question is, what should I do?
Can I find the wrong labels via some automatic way?
How to increase precision and recall when new data coming?
How to evaluate the impact of wrong data? (since I don't know how many percentage data is wrong)
Any other suggestions?
Obviously, there is no easy way to solve your problem - after all, why build a classifier if you already have a system that can detect wrong classifications.
Do you know how much the erroneous classifications affect your learning? If there are only a small percentage of them, they should not hurt the performance much. (Edit. Ah, apparently you don't. Anyway, I suggest you try it out - at least if you can identify a false result when you see one.)
Of course, you could always first train your system and then have it suggest classifications for the training data. This might help you identify (and correct) your faulty training data. This obviously depends on how much training data you have, and if it is sufficiently broad to allow your system to learn correct classification despite the faulty data.
Can you review any of the data manually to find some mislabeled examples? If so, you might be able to train a second classifier to identify mislabeled data, assuming there is some kind of pattern to the mislabeling. It would be useful for you to know if mislabeling is a purely random process (it is just noise in the training data) or if mislabeling correlates with particular features of the data.
You can't evaluate the impact of mislabeled data on your specific data set if you have no estimate regarding what fraction of your training set is actually mislabeled. You mention in a comment that you have ~5M records. If you can correctly manually label a few hundred, you could train your classifier on that data set, then see how the classifier performs after introducing random mislabeling. You could do this multiple times with varying percentages of mislabeled data to see the impact on your classifier.
Qualitatively, having a significant quantity of mislabeled samples will increase the impact of overfitting so it is even more important that you do not overfit your classifier to the data set. If you have a test data set (assuming it also suffers from mislabling), then you might consider training your classifier to less-than-maximal classification accuracy on the test data set.
People usually deal with the problem you a describing by having multiple annotators and computing their agreement (e.g. Fleiss' kappa). This is often seen as the upper bound on the performance of any classifier. If three people give you three different answers, you know the task is quite hard and your classifier stands no chance.
As a side note:
If you do not know how many of your records have been labelled incorrectly, you do not understand one of the key properties of the problem. Select 1000 records at random and spend the day reviewing their labels to get an idea. It really is time well spent. For example, I found I can easily review 500 labelled tweets per hour. Health warning: it is very tedious, but a morning spent reviewing gives me a good idea of how distracted my annotators were. If 5% of the records are incorrect, it is not such a problem. If 50 are incorrect, you should go back you your boss and tell them it can't be done.
As another side note:
Someone mentioned active learning. I think it is worth looking into options from the literature, keeping in mind labels might have to change. You said that it hard.
I'm exploring some of the code examples in Mahout in Action in more detail. I have built a small test that computes the RMS of various algorithms applied to my data.
Of course, multiple parameters impact the RMS, but I don't understand the "unable to recommend in ... cases" message that is generated while running an evaluation.
Looking at StatsCallable.java, this is generated when an evaluator encounters a NaN response; Perhaps not enough data in the training set or the user's prefs to provide a recommendation.
It seems like the RMS score isn't impacted by a very large set of "unable to recommend" cases. Is that assumption correct? Should I be evaluating my algorithm not only on RMS but also the ratio of "unable to recommend" cases versus my overall training set?
I'd appreciate any feedback.
Yes this essentially means there was no data at all on which to base an estimate. That's generally a symptom of data sparseness. It should be rare, and happen only for users with data that's very small or disconnected from others'.
I personally think it's not such a big deal unless it's a really significant percentage (20%+?) I'd worry more if you couldn't generate any recs at all for many users.