I have a data set called Data, with 30 scaled and centered features and 1 outcome with column name OUTCOME, referred to 700k records, stored in data.table format. I computed its PCA, and observed that its first 8 components account for the 95% of the variance. I want to train a random forest in h2o, so this is what I do:
Data.pca=prcomp(Data,retx=TRUE) # compute the PCA of Data
Data.rotated=as.data.table(Data.pca$x)[,c(1:8)] # keep only first 8 components
Data.dump=cbind(Data.rotated,subset(Data,select=c(OUTCOME))) # PCA dataset plus outcomes for training
This way I have a dataset Data.dump where I have 8 features that are rotated on the PCA components, and at each record I associated its outcome.
First question: is this rational? or do I have to permute somehow the outcomes vector? or the two things are unrelated?
Then I split Data.dump in two sets, Data.train for training and Data.test for testing, all as.h2o. The I feed them to a random forest:
rf=h2o.randomForest(training_frame=Data.train,x=1:8,y=9,stopping_rounds=2,
ntrees=200,score_each_iteration=T,seed=1000000)
rf.pred=as.data.table(h2o.predict(rf,Data.test))
What happens is that rf.pred seems not so similar to the original outcomes Data.test$OUTCOME. I tried to train a neural network as well, and did not even converge, crashing R.
Second question: is it because I am carrying on some mistake from the PCA treatment? or because I badly set up the random forest? Or I am just dealing with annoying data?
I do not know where to start, as I am new to data science, but the workflow seems correct to me.
Thanks a lot in advance.
The answer to your second question (i.e. "is it the data, or did I do something wrong") is hard to know. This is why you should always try to make a baseline model first, so you have an idea of how learnable the data is.
The baseline could be h2o.glm(), and/or it could be h2o.randomForest(), but either way without the PCA step. (You didn't say if you are doing a regression or a classification, i.e. if OUTCOME is a number or a factor, but both glm and random forest will work either way.)
Going to your first question: yes, it is a reasonable thing to do, and no you don't have to (in fact, should not) involve the outcomes vector.
Another way to answer your first question is: no, it unreasonable. It may be that a random forest can see all the relations itself without needing you to use a PCA. Remember when you use a PCA to reduce the number of input dimensions you are also throwing away a bit of signal, too. You said that the 8 components only capture 95% of the variance. So you are throwing away some signal in return for having fewer inputs, which means you are optimizing for complexity at the expense of prediction quality.
By the way, concatenating the original inputs and your 8 PCA components, is another approach: you might get a better model by giving it this hint about the data. (But you might not, which is why getting some baseline models first is essential, before trying these more exotic ideas.)
Related
Working with a dataset of ~200 observations and a number of variables. Unfortunately, none of the variables are distributed normally. If it possible to extract a data subset where at least one desired variable will be distributed normally? Want to do some statistics after (at least logistic regression).
Any help will be much appreciated,
Phil
If there are just a few observations that skew the distribution of individual variables, and no other reasons speaking against using a particular method (such as logistic regression) on your data, you might want to study the nature of "weird" observations before deciding on which analysis method to use eventually.
I would:
carry out the desired regression analysis (e.g. logistic regression), and as it's always required, carry out residual analysis (Q-Q Normal plot, Tukey-Anscombe plot, Leverage plot, also see here) to check the model assumptions. See whether the residuals are normally distributed (the normal distribution of model residuals is the actual assumption in linear regression, not that each variable is normally distributed, of course you might have e.g. bimodally distributed data if there are differences between groups), see if there are observations which could be regarded as outliers, study them (see e.g. here), and if possible remove them from the final dataset before re-fitting the linear model without outliers.
However, you always have to state which observations were removed, and on what grounds. Maybe the outliers can be explained as errors in data collection?
The issue of whether it's a good idea to remove outliers, or a better idea to use robust methods was discussed here.
as suggested by GuedesBF, you may want to find a test or model method which has no assumption of normality.
Before modelling anything or removing any data, I would always plot the data by treatment / outcome groups, and inspect the presence of missing values. After quickly looking at your dataset, it seems that quite some variables have high levels of missingness, and your variable 15 has a lot of zeros. This can be quite problematic for e.g. linear regression.
Understanding and describing your data in a model-free way (with clever plots, e.g. using ggplot2 and multiple aesthetics) is much better than fitting a model and interpreting p-values when violating model assumptions.
A good start to get an overview of all data, their distribution and pairwise correlation (and if you don't have more than around 20 variables) is to use the psych library and pairs.panels.
dat <- read.delim("~/Downloads/dput.txt", header = F)
library(psych)
psych::pairs.panels(dat[,1:12])
psych::pairs.panels(dat[,13:23])
You can then quickly see the distribution of each variable, and the presence of correlations among each pair of variables. You can tune arguments of that function to use different correlation methods, and different displays. Happy exploratory data analysis :)
I am using the h2o package to train a GBM for a churn prediction problem.
all I wanted to know is what influences the size of the fitted model saved on disk (via h2o.saveModel()), but unfortunately I wasn't able to find an answer anywhere.
more specifically, when I tune the GBM to find the optimal hyperparameters (via h2o.grid()) on 3 non-overlapping rolling windows of the same length, I obtain models whose sizes are not comparable (i.e. 11mb, 19mb and 67mb). the hyperparameters grid is the same, and also the train set sizes are comparable.
naturally the resulting optimized hyperparameters are different across the 3 intervals, but I cannot see how this can produces such a difference in the model sizes.
moreover, when I train the actual models based on those hyperparameters sets, I end up with models with different sizes as well.
any help is appreciated!
thank you
ps. I'm sorry but I cannot share any dataset to make it reproducible (due to privacy restrictions)
It’s the two things you would expect: the number of trees and the depth.
But it also depends on your data. For GBM, the trees can be cut short depending on the data.
What I would do is export MOJOs and then visualize them as described in the document below to get more details on what was really produced:
http://docs.h2o.ai/h2o/latest-stable/h2o-genmodel/javadoc/index.html
Note the 60 MB range does not seem overly large, in general.
If you look at the model info you will find out things about the number of trees, their average depth, and so on. Comparing those between the three best models should give you some insight into what is making the models large.
From R, if m is your model, just printing it gives you most of that information. str(m) gives you all the information that is held.
I think it is worth investigating. The cause is probably that two of those data windows are relatively clear-cut, and only a few fields can define the trees, whereas the third window of data is more chaotic (in the mathematical sense), and you get some deep trees being made as it tries to split that apart into decision trees.
Looking into that third window more deeply might suggest some data engineering you could do, that would make it easier to learn. Or, it might be a difference in your data. E.g. one column is all NULL in your 2016 and 2017 data, but not in your 2018 data, because 2018 was the year you started collecting it, and it is that extra column that allows/causes the trees to become deeper.
Finally, maybe the grid hyperparameters are unimportant as regards performance, and this a difference due to noise. E.g. you have max_depth as a hyperparameter, but the influence on MSE is minor, and noise is a large factor. These random differences could allow your best model to go to depth 5 for two of your data sets (but 2nd best model was 0.01% worse but went to depth 20), but go to depth 30 for your third data set (but 2nd best model was 0.01% worse but only went to depth 5).
(If I understood your question correctly, you've eliminated this as a possibility, as you then trained all three data sets on the same hyperparameters? But I thought I'd include it, anyway.)
I have a question about LASSO. I'm getting crazy because it is something that I can not solve only according to my background. I'm a biologist.
Briefly I run LASSO using the R library "penalized". In particular I used the opt1D function with around 500 simulations on a data.frame (numerical) of around 30 columns that are my biomarkers (gene expression). I want to test and 3000 rows that are people of which around 50 are tumours and all the others are normals.
Unfortunately by using L1 regularization, all and really all coefficients of 500 simulations are 0. If I check L2 matrix of coefficients they are close to 0. Now my point is that I cannot think that all my biomarkers are not able to distinguish between Normals and Tumors.
I don't know if what I have done is all I can to check for the discriminatory potential of my molecules. Is there something else I can do to understand why are they all 0 and also is there something else I can do to verify that really they are not able to stratify my cohort?
Did you consider fitting your data without penalization before using regularization? L1 regularization will naturally result in a significant number of zero coefficients.
As a side note I would first run PCA/PCoA and see whether or not your genes separate according to your class variable. This could save you some time and allow you to trim your data set to those genes that show the greatest differences across your class variable. Also if you have relatively little experience with R I would suggest using a linear modeling package such as Limma since it has excellent documentation and many examples that are easy to follow.
I am working with a dataset of roughly 1.5 million observations. I am finding that running a regression tree (I am using the mob()* function from the party package) on more than a small subset of my data is taking extremely long (I can't run on a subset of more than 50k obs).
I can think of two main problems that are slowing down the calculation
The splits are being calculated at each step using the whole dataset. I would be happy with results that chose the variable to split on at each node based on a random subset of the data, as long as it continues to replenish the size of the sample at each subnode in the tree.
The operation is not being parallelized. It seems to me that as soon as the tree has made it's first split, it ought to be able to use two processors, so that by the time there are 16 splits each of the processors in my machine would be in use. In practice it seems like only one is getting used.
Does anyone have suggestions on either alternative tree implementations that work better for large datasets or for things I could change to make the calculation go faster**?
* I am using mob(), since I want to fit a linear regression at the bottom of each node, to split up the data based on their response to the treatment variable.
** One thing that seems to be slowing down the calculation a lot is that I have a factor variable with 16 types. Calculating which subset of the variable to split on seems to take much longer than other splits (since there are so many different ways to group them). This variable is one that we believe to be important, so I am reluctant to drop it altogether. Is there a recommended way to group the types into a smaller number of values before putting it into the tree model?
My response comes from a class I took that used these slides (see slide 20).
The statement there is that there is no easy way to deal with categorical predictors with a large number of categories. Also, I know that decision trees and random forests will automatically prefer to split on categorical predictors with a large number of categories.
A few recommended solutions:
Bin your categorical predictor into fewer bins (that are still meaningful to you).
Order the predictor according to means (slide 20). This is my Prof's recommendation. But what it would lead me to is using an ordered factor in R
Finally, you need to be careful about the influence of this categorical predictor. For example, one thing I know that you can do with the randomForest package is to set the randomForest parameter mtry to a lower number. This controls the number of variables that the algorithm looks through for each split. When it's set lower you'll have fewer instances of your categorical predictor appear vs. the rest of the variables. This will speed up estimation times, and allow the advantage of decorrelation from the randomForest method ensure you don't overfit your categorical variable.
Finally, I'd recommend looking at the MARS or PRIM methods. My professor has some slides on that here. I know that PRIM is known for being low in computational requirement.
I have a very large data set that I extract from a data warehouse. To download the data set to the box where I want to run lme4 takes a long time. I would like to know if I could process the data into a covariance matrix, download that data (which is much smaller), and use that as the data input to lme4. I have done something similar to this for multiple regression models using SAS, and am hoping I can create this type of input for lme4.
Thanks.
I don't know of any way to use the observed covariance matrix to fit an lmer model. But if the goal is to reduce data set size in order to speed up analysis, there may be simpler approaches. For example, if you don't need the conditional modes of the random effects, and you have a very large sample size, then you might try fitting the model to progressively larger subsets of the data until the estimates of the fixed effects and the covariance matrix of the random effects 'stabilize'. This approach has worked well in my experience, and has been discussed by others:
http://andrewgelman.com/2012/04/hierarchicalmultilevel-modeling-with-big-data/
Here's another quotation:
"Related to the “multiple model” approach are simple approximations that speed the computations. Computers are getting faster and faster—but models are getting more and more complicated! And so these general tricks might remain important. A simple and general trick is to break the data into subsets and analyze each subset separately. For example, break the 85 counties of radon data randomly into three sets of 30, 30, and 25 counties, and analyze each set separately." Gelman and Hill (2007), p.547.