[scikit-learn] Need for multioutput multivariate algorithm for Random Forest in Python (using Mahalanobis distance)

Nicolas Hug niourf at gmail.com
Sat Feb 15 08:54:29 EST 2020 

> For my knowledge’s sake, could you please inform me about the 
> technique being employed now to take advantage of the correlations 
> between targets? Is it the Mahalanobis distance or some other metric? 
> In other words, could you please give me a hint as to the underlying 
> reason why the single output predictions differ from the multioutput 
> predictions?

I don't know much more than what's already in the doc that I linked to. 
Namely, the best split is the chosen to minimize the *average* criteria 
across all outputs, instead of just using a single output. You'll find 
more details in the code.

About the docs: we generally try to write all the useful info about the 
estimators in the "User Guide" section 
(https://scikit-learn.org/stable/modules/ensemble.html#forests-of-randomized-trees). 
In this case you can find a link to the multi-output handling. Sometimes 
the info is instead in the docstrings. That's not always perfect though, 
and the link might not have been there when you first looked. We're 
working hard to keep on improving the docs. But there's so much info 
that it's easy to miss some...


Welcome back to python!


On 2/14/20 8:47 PM, Paul Chike Ofoche via scikit-learn wrote:
>
> Many thanks Nicolas and Andreas.
>
> I appreciate your taking the time and effort to look into the issue 
> that I raised and for pointing me to the documentation. It is quite 
> pleasant to know that scikit-learn’s RandomForestRegressor handles 
> multioutput cases. This issue has been very important to me and was 
> the sole reason that I switched from Python to R for my research in 
> the Fall of 2018 and have seldom used Python since then.
>
> I got convinced about my earlier stance when reading a documentation 
> such as 
> https://scikit-learn.org/stable/modules/multiclass.html#multioutput-regression 
> which explained that the “MultiOutputRegressor fits one regressor per 
> target and cannot take advantage of correlations between targets”, 
> although I am aware that this is different from the RandomForestRegressor.
>
>
> Inline image
>
>
> I was wondering whether this multioutput handling capability of the 
> RandomForestRegressor has been added recently. In order to verify, I 
> went on a fact-finding mission by re-running the exact same codes I 
> had in 2018 and noticed quite a number of changes. I guess that many 
> moons have passed since then!
>
> For instance, sklearn.cross_validation has been deprecated since when 
> last I used it in 2018 (and replaced by sklearn.model_selection). 
> Also, such errors as:
>
> i. ValueError: Expected 2D array, got scalar array instead:
>
> array=6.5.
>
> Reshape your data either using array.reshape(-1, 1) if your data has a 
> single feature or array.reshape(1, -1) if it contains a single sample.
>
> and
>
> ii. DataConversionWarning: A column-vector y was passed when a 1d 
> array was expected. Please change the shape of y to (n_samples,), for 
> example using ravel().
>
> when passing a *scalar* and a *column-vector y* respectively are 
> entirely new from when last I made use of Python’s 
> RandomForestRegressor. Previously, they worked just fine without 
> throwing out any errors. I know that the “multioutputs” were handled 
> back in 2018 (I actually tested this capability back then), but I 
> assumed that the regressors were fit per target i.e. that there was no 
> correlation between targets.
>
> Today, for comparison, I generated some random target outputs (three 
> columns) and using the same *random_state*, I ran the all-inclusive 
> multioutput prediction (with all three output targets simultaneously 
> vs. re-running each output prediction one at a time). The results are 
> different, implying that some form of correlation takes place amongst 
> the multioutput targets, when predicted together. (For completeness, I 
> display the first 28 predicted output values, from the multioutput 
> prediction as well as the single output predictions.)
>
>
> Results from the multioutput prediction of the targets (capturing 
> their correlations).
>
> Inline image
>
>
> Results from the individual prediction of each single output target.
>
> Inline image
>
>
> For my knowledge’s sake, could you please inform me about the 
> technique being employed now to take advantage of the correlations 
> between targets? Is it the Mahalanobis distance or some other metric? 
> In other words, could you please give me a hint as to the underlying 
> reason why the single output predictions differ from the multioutput 
> predictions? I am curious to know as this would finally fully quench 
> my appetite after nearly two years. I will have to retrace my steps 
> and get back to the good old Python ways (again). Thank you.
>
> Highest regards,
> Paul
>
>
>
> On Friday, February 14, 2020, 07:00:35 a.m. CST, Nicolas Hug 
> <niourf at gmail.com> wrote:
>
>
> Hi Paul,
>
> The way multioutput is handled in decision trees (and thus in the 
> forests) is described in 
> https://scikit-learn.org/stable/modules/tree.html#multi-output-problems. 
> As you can see, the correlation between the output values *is* taken 
> into account.
>
> Can you explain what you would like to modify there?
>
> Nicolas
>
> On 2/14/20 7:37 AM, Paul Chike Ofoche via scikit-learn wrote:
> Scikit-learn random forest does *not *handle the multi-output case, 
> but only maps to each output one at a time, thereby not accounting for 
> the correlation between multi-outputs, which is what the Mahalanobis 
> distance does. I, as well as other researchers have observed this 
> issue for as much as two years. Could there be a solution to implement 
> it in RandomForest, since Python already has a function that computes 
> Mahalanobis distances?
>
>
> On Thursday, February 13, 2020, 10:15:11 PM CST, Andreas Mueller 
> <t3kcit at gmail.com> <mailto:t3kcit at gmail.com> wrote:
>
>
>
>
> On 2/9/20 12:21 PM, Paul Chike Ofoche via scikit-learn wrote:
>
> Hello all,
>
> My name is Paul and I am enthused about data science. I have been 
> using Python and other programming languages for close to two years. 
> There is an issue that I have been facing since I began applying 
> Python to the analysis of my research work.
>
>
> My question has remained unanswered for months. Has anybody not run 
> into the need to work with data whereby the regression results are a 
> multiple output, in which the output parameters are correlated with 
> each other? This is called a multi-output multivariate problem. A 
> version of random forest that handles multiple outputs is referred to 
> as the multivariate random forest. It is implemented in the 
> programming language, R (see attached reference documentation below).
>
> The scikit-learn random forest actually handles this. It doesn't use 
> the mahalanobis distance but that seems like a simple preprocessing step.
>
>>
>> Till date, there exists no such package in Python. My question is 
>> whether anybody knows how to go about implementing this. The random 
>> forest univariate regression case utilizes the Euclidean distance as 
>> the measurement criteria, whereas the multivariate regression case 
>> uses the Mahalanobis distance, which takes into account the 
>> inter-relationships between the multiple outputs. I have inquired 
>> about an equivalent capability in Python for many years, but it has 
>> still not been addressed. Such a multivariate random forest mode is 
>> very applicable to the type of research and analysis that I do. Could 
>> someone help, please?
>>
>> Thank you,
>>
>> Paul Ofoche
>>
>> PS: This is an important need for multivariate output analysis as a 
>> technique to solving practical research problems. Here are some 
>> posted questions by various other Python users concerning this same 
>> issue.
>>
>> *https://datascience.stackexchange.com/questions/21637/code-for-multivariate-random-forest-in-python-r*
>>
>> Multi-output regression 
>> <https://stackoverflow.com/questions/49391637/multi-output-regression>
>>
>>
>>
>> 	
>>
>>
>> 	
>>
>>
>>     Multi-output regression
>>
>> I have been looking in to Multi-output regression the last view 
>> weeks. I am working with the scikit learn packag...
>>
>> <https://stackoverflow.com/questions/49391637/multi-output-regression>
>>
>>
>>
>>
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