# Tag: python

## Building your own scikit-learn Regressor-Class: LS-SVM as an example

The world of Machine-Learning (ML) and Artificial Intelligence (AI) is governed by libraries, as the implementation of a full framework from scratch requires a lot of work. ML and data-science engineers and researchers, therefore don’t generally build their own libraries. Instead they use and extend existing libraries written in python or R. One of the most popular current python ML libraries is scikit-learn. This library provides access to scores of ML-models and methods which can be combined at will via the use of a consistent global API.

However, no matter how many models there are included in such a library, chances are that a model you wish to use (or the extension you envision for an existing model) is not implemented.  In such a case, you do not want to write an entire ML framework from scratch, but just create your own model and fit it into the existing framework.  Within the scikit-learn framework this can be done with relative ease, as is explained in this short tutorial. As an example, I will be building a regressor class for the LS-SVM model.

## 1. The ML-model: LS-SVM?

Least-Squares Support Vector Machines is a type of support vector machines (SVM) initially developed some 20 years ago by researchers at the KULeuven (and is still being further developed, funded via several ERC grants). It’s a supervised learning machine learning approach in which a system of linear equations is solved using the kernel-trick.

So how does it work in practice? Assume, we have a data set of data points (xi,yi), with xi the feature vector and yi the target of the data point (or sample) i. Depending on whether you want to perform classification or regression, training the model corresponds to solving the following system of equations (represented in their matrix form as):

Classification: $\begin{bmatrix} 0 & Y^T \\ Y & \Omega + \gamma^{-1}\mathbb{I} \end{bmatrix} \left[ \begin{array}{c} b \\ \alpha \end{array} \right] = \left[ \begin{array}{c} 0 \\ 1 \end{array} \right]$

Regression: $\begin{bmatrix} 0 & 1^T \\ 1 & \Omega + \gamma^{-1}\mathbb{I} \end{bmatrix} \left[ \begin{array}{c} b \\ \alpha \end{array} \right] = \left[ \begin{array}{c} 0 \\ Y \end{array} \right]$

with $Y$ the vector containing all targets yi, $\gamma$ a hyperparameter, and $\Omega_{k,l}$ a kernel function $K(\mathbf{x_k,x_l})$.

Once trained, results are predicted (in case of regression) by solving the following equation: $y(\mathbf{x})=\sum_{k=1}^{N}{\alpha_k K(\mathbf{x_k,x}) + b}$

More details on these can be found in the book of Suykens, or (if you prefer a shorter read) this paper by Dilmen.

The above model is available through the Matlab library developed by the Suykens group, and has been translated to R, but no implementation in the python scikit-learn library is available, therefore we set out to create such an implementation following the scikit-learn API. Our choice to follow the scikit-learn API is twofold: (1) we want our new class to smoothly integrate with the functionalities of the scikit-learn library (I’m building a framework for automated machine learning on this library, hence all my models need to show the same behavior and functionality) and (2) we want to be lazy and implement as little as possible.

## 2. Creating a Simple Regressor Class.

### 2.1. Initialization

Designing this Class, we will make full use of OOP (Similar ideas as in my fortran tutorials), inheriting behavior from scikit-learn base classes. All estimators in scikit-learn are derived from the BaseEstimator Class. The use of this class requires you to define all parameters of your class as keyword arguments in the __init__ function of your class. In return, you get the get_params and set_params methods for free.

As our goal is to create a regressor class, the class also needs to inherit from the  RegressorMixin Class which provides access to the score method used by all scikit-learn regressors. With this, the initial implementation of our LS-SVM regressor class quickly takes shape:

class LSSVMRegression(BaseEstimator, RegressorMixin):
"""
An Least Squared Support Vector Machine (LS-SVM) regression class

Attributes:
- gamma : the hyper-parameter (float)
- kernel: the kernel used (string: rbf, poly, lin)
- kernel_: the actual kernel function
- x : the data on which the LSSVM is trained (call it support vectors)
- y : the targets for the training data
- coef_ : coefficents of the support vectors
- intercept_ : intercept term
"""

def __init__(self, gamma:float=1.0, kernel:str=None, c:float=1.0,
d:float=2, sigma:float=1.0):
self.gamma=gamma
self.c=c
self.d=d
self.sigma=sigma
if (kernel is None):
self.kernel='rbf'
else:
self.kernel=kernel

params=dict()
if (kernel=='poly'):
params['c']=c
params['d']=d
elif (kernel=='rbf'):
params['sigma']=sigma

self.kernel_=LSSVMRegression.__set_kernel(self.kernel,**params)

self.x=None
self.y=None
self.coef_=None
self.intercept_=None

All parameters have a default value in the __init__ method (and with a background in Fortran, I find it very useful to explicitly define the intended type of the parameters). Additionally, the same name is used for the attributes to which they are assigned. The kernel function is provided as a string (here we have 3 possible kernel functions: the linear (lin), the polynomial (poly), and the radial basis function (rbf) ) and linked to a function pointer via the command:

self.kernel_=LSSVMRegression.__set_kernel(self.kernel,**params)

The static private __set_kernel method returns a pointer to the correct kernel-function, which is later-on used during training and fitting.  The get_params, set_params, and score methods, we get for free so no implementation is needed, but you could override them if you wish. (Note that some tutorials recommend against overriding the get_params and set_params methods.)

### 2.2. Fitting and predicting

As our regressor class should be interchangeable with any regressor class available by scikit-learn, we look at some examples to see which method-names are being used for which purpose. Checking the LinearRegression model and the SVR model, we learn that the following methods are provided for both classes:

__init__ Initialize object of the class. Implemented above (ourselves)
get_params Get a dictionary of class parameters. Inherited from BaseEstimator
set_params Set the class parameters via a dictionary. Inherited from BaseEstimator
score Return the R2 value of the prediction. Inherited from RegressorMixin
fit Fit the model. to do
predict Predict using the fitted model. to do

Only the fit and predict methods are still needed to complete our LS-SVM regressor class. The implementation of the equations presented in the previous section can be done in a rather straight forward way using the numpy library.

import numpy as np

def fit(self,X:np.ndarray,y:np.ndarray):
self.x=X
self.y=y
Omega=self.kernel_(self.x,self.x)
Ones=np.array([]*len(self.y))

A_dag = np.linalg.pinv(np.block([
[0, Ones.T ],
[Ones, Omega + self.gamma**-1 * np.identity(len(self.y))]
]))
B = np.concatenate((np.array(),self.y), axis=None)

solution = np.dot(A_dag, B)
self.intercept_ = solution
self.coef_ = solution[1:]

def predict(self,X:np.ndarray)->np.ndarray:
Ker = self.kernel_(X,self.x)
Y=np.dot(self.coef_,Ker.T) +self.intercept_
return Y

Et voilà, all done. With this minimal amount of work, a new regression model is implemented and capable of interacting with the entire scikit-learn library.

## 3. Getting the API right: Running the Model using Scikit-learn Methods.

The LS-SVM model has at least 1 hyperparameter: the $\gamma$ factor and all hyperparameters present in the kernel function (0 for the linear, 2 for a polynomial, and 1 for the rbf kernel). To optimize the hyperparameters, the GridsearchCV Class of scikit-learn can be used, with our own class as estimator.

For the LS-SVM model, which is slightly more complex than the trivial examples found in most tutorials, you will encounter some unexpected behavior. Assume you are optimizing the hyperparameters of an LS-SVM with an rbf kernel: $\gamma$ and $\sigma$.

from sklearn.model_selection import GridSearchCV
...
parameters = {'kernel':('rbf'),
'gamma':[0.001, 0.01, 0.1, 1.0, 10.0, 100.0, 1000.0],
'sigma':[0.001, 0.01, 0.1, 1.0, 10.0, 100.0, 1000.0]}
lssvm = LSSVMRegression()
clf = GridSearchCV(lssvm, parameters)
clf.fit(X, y)
...

When you plot the quality results as a function of $\gamma$, you’ll notice there is very little (or no) variation with regard to $\sigma$. Some deeper investigation shows that the instances of the LSSVMRegression model use different values of the $\gamma$ attribute, however, the $\sigma$ attribute does not change in the kernel function. This behavior is quite odd if you expect the GridsearchCV class to create a new class instance (or object) using the __init__ method for each grid point (a natural assumption within the context of parallelization). In contrast, the GridsearchCV class appears to be modifying the attributes of a set of instances via the set_params method, as can be found in the 2000+ page manual of scikit-learn, or here in the online manual: Scikit-learn manual section of parameter initialization of classes

In programming languages like C/C++ or Fortran, some may consider this as bad practice as it entirely negates the use of your constructor and splits the initialization section. For now, we will consider this a feature of the Python scripting language. This also means that getting a static class function linked to the kernel_ attribute requires us to override the get_params method (initializing attributes in a fit function is just a bridge too far 😉 ).

def set_params(self, **parameters):
for parameter, value in parameters.items():
setattr(self, parameter, value)

params=dict()
if (self.kernel=='poly'):
params['c']=self.c
params['d']=self.d
elif (self.kernel=='rbf'):
params['sigma']=self.sigma
self.kernel_=LSSVMRegression.__set_kernel(self.kernel,**params)

return self

For consistency the get_params method is also overridden. The resulting class is now suitable for use in combination with the rest of the scikit-learn library.

## 4. The LS-SVM Regressor on Github

At the moment of witting no LS-SVM regressor class compatible with the scikit-learn library was available. There are some online references available to Python libraries which claim to have the LS-SVM model included, but these tend to be closed source.  So instead of trying to morph these to fit my framework, I decided to use this situation as an opportunity to learn some more on the implementation of an ML model and the integration of this model in the scikit-learn framework. The resulting model is extended further to deal with the intricacies of my own framework aimed at small datasets, which is beyond the scope of the current tutorial. Since I believe the LS-SVM regressor may be of interest to other users of the scikit-learn library, you can download it from my github-page:

## 5. References

• J.A.K. Suykens et al., “Least Squares Support Vector Machines“, World Scientific Pub. Co., Singapore, 2002 (ISBN 981-238-151-1)
• E. Dilmen and S. Beyhan, “A Novel Online LS-SVM Approach for Regression and Classification”, IFAC-PapersOnLine Volume 50(1), 8642-8647 (2017)
• D. Hnyk, “Creating your own estimator in scikit-learn“, webpage
• T. Book, “Building a custom model in scikit-learn“, webpage
• User guide: create your own scikit-learn estimator“, webpage

DISCLAIMER: Since Python codes depreciate as fast as they are written, links to the scikit-learn library documentation may be indicated as outdated by the time you read this tutorial. Check out the most recent version in that case. Normally, the changes should be sufficiently limited not to impact the conclusions drawn here. However, if you discover a code-breaking update, feel free to mention it here in the comments section.

## Parallel Python in classes…now you are in a pickle

In the past, I discussed how to create a python script which runs your calculations in parallel.  Using the multiprocessing library, you can circumvent the GIL and employing the async version of the multiprocessing functions, calculations are even performed in parallel. This works quite well, however, when using this within a python class you may run into some unexpected behaviour and errors due to the pickling performed by the multiprocessing library.

For example, if the doOneRun function is a class function defined as

class MyClass:
...
def doOneRun(self, id:int):
return id**3
...

and you perform some parallel calculation in another function of your class as

class MyClass:
...
def ParallelF(self, NRuns:int):
import multiprocessing as mp

nproc=10
pool=mp.Pool(processes=nprocs)
drones=[pool.apply_async(self.doOneRun, args=nr) for nr in range(NRuns)]

for drone in drones:
Results.collectData(drone.get())
pool.close()
pool.join()

...

you may run into a runtime error complaining that a function totally unrelated to the parallel work (or even to the class itself) can not be pickled. 😯

So what is going on? In the above setup, you would expect the pool.apply_async function to take just a function pointer to the doOneRun function. However, as it is provided by a the call self.doOneRun, the pool-function grabs the entire class and everything it contains, and tries to pickle it to distribute it to all the processes.  In addition to the fact that such an approach is hugely inefficient, it has the side-effect that any part associated to your class needs to be pickleable, even if it is a class-function of a class used to generate an object which is just a property of the MyClass Class above.

So both for reasons of efficiency and to avoid such side-effects, it is best to make the doOneRun function independent of a class, and even placing it outside the class.

def doOneRun(id:int):
return id**3

class MyClass:
...
def ParallelF(self, NRuns:int):
import multiprocessing as mp

nproc=10
pool=mp.Pool(processes=nprocs)
drones=[pool.apply_async(doOneRun, args=nr) for nr in range(NRuns)]

for drone in drones:
Results.collectData(drone.get())
pool.close()
pool.join()

...

This way you avoid pickling the entire class, reducing initialization times of the processes and the  unnecessary communication-overhead between processes. As a bonus, you also reduce the risk of unexpected crashes unrelated to the calculation performed.

## Parallel Python?

As part of my machine learning research at AMIBM, I recently ran into the following challenge: “Is it possible to do parallel computation using python.” It sent me on a rather long and arduous journey, with the final answer being something like: “very reluctantly“.

Python was designed with one specific goal in mind; make it easy to implement small test programs to see if an idea is worth pursuing. This gave rise to a scripting language with a lot of flexibility, but also with significant limitations, most of which the “intended” user would never meet. However, as a consequence of its success, many are using it going far beyond this original scope (yours truly as well 🙂 ).

Python offers various libraries to parallelize your scripts…most of them wrappers adding minor additional functionality. However, digging down to the bottom one generally ends up at one of the following two libraries: the threading module and the multiprocessing module.

Of course, as with many things python, there is a huge amount of tutorials available with many of great quality.

Programmers experienced in a programming language such as C/C++, Pascal, or Fortran, may be familiar with the concept of multi-threading. With multi-threading, a CPU allows a program to distribute its work over multiple program-threads which can be performed in parallel by the different cores of the CPU (or while a core is idle, e.g., since a thread is waiting for data to be fetched).  One of the most famous API’s for writing multi-threaded applications is OpenMP. In the past I used it to parallelize my Hirshfeld-I implementation and the phonon-module of HIVE.

For Python, there is no implementation of the OpenMP API, instead there is the threading module. This provides access to the creation of multiple threads, each able to perform their own tasks while sharing data-objects. Unfortunately, python has also the Global Interpreter Lock, GIL for short, which allows only a single thread to access the interpreter at a time. This effectively reduces thread-based parallelization to a complex way of running a code in a serial way.

## import multiprocessing

In addition to the threading module, there is also the multiprocessing module. This module side-steps the GIL by creating multiple processes, each having its own interpreter. This however comes at a cost. Firstly, there is a significant computational cost starting the different processes. Secondly, objects are not shared between processes, so additional work is needed to collect and share data.

Using the “Pool” class, things are somewhat simplified, as can be seen in the code-fragment below.  With the pool class one creates a set of threads/processes available for your program. Then through the function apply_async function it is possible to run processes in parallel. (Note that you need to use the “async” version of the function, as otherwise you end up with running things serial …again)

 multiprocessing backbone   import multiprocessing as mp def doOneRun(id:int): #trivial function to run in parallel	return id**3   num_workers=10  #number of processesNRuns=1000      #number of runs of the function doOneRun pool=mp.Pool(processes=num_workers)   # create a pool of processesdrones=[pool.apply_async(doOneRun, args=nr) for nr in range(NRuns)] #and run things in parallel for drone in drones: #and collect the data	Results.collectData(drone.get()) #Results.collectData is a function you write to recombine the separate results into a single result and is not given here. pool.close() #close the pool...no new tasks can be run on any of the processespool.join()  #collapse all threads back into the main thread

## how many cores does my computer have?

If you are used to HPC applications, you always want to get as much out of your machine as possible. With regard to parallelization this often means making sure no CPU cycle is left unused. In the example above we manually selected the number of processes to spawn. However, would it not be nice if the program itself could just set this value to be equal to the number of physical cores accessible?

Python has a large number of functions claiming to do just that. A few of them are given below.

•  multiprocessing.cpu_count(): returns the number of logical cores it can find. So if you have a modern machine with hyper-threading technology, this will return a multiple of the number of physical cores (and you will be over-subscribing your CPU.
• os.cpu_count(): same as multiprocessing.cpu_count().
• psutil.cpu_count(logical=False): This implementation gives the same default behavior, however, the parameter logical allows for this function to return the correct number of cores in a single CPU. Indeed a single CPU. HPC architectures which contain multiples CPUs per node will again return an incorrect number, as the implementation makes use of a python “set”, and as such doesn’t increment for the same index core on a different CPU.

In conclusion, there seems to be no simple way to obtain the correct number of physical cores using python, and one is forced to provide this number manually. (If you do have knowledge of such a function which works in both windows and unix environments and both desktop and HPC architectures feel free to let me know in the comments.)

All in all, it is technically possible to run code in parallel using python, but you have to deal with a lot of python quirks such as GIL.