Is Machine Learning In Wolfram Mathematica As Strong As Python?

Introduction

There are many weblog posts comparing R and Python for data scientific discipline but in that location are only a few most Wolfram vs. Python. In this post I volition bear witness some differences between Wolfram and Python and presume that you are familiar with Python but not with Wolfram. Python is now the well-nigh popular language for information scientific discipline projects, while the Wolfram Linguistic communication is rather a niche language in this business.

The Wolfram Language has been around for over xxx Years, therefore it is really older than R and Python. The Wolfram language was previously known equally Mathematica, which is the primary platform for the Wolfram language, besides the Wolfram Cloud and Wolfram Script. Wolfram is widely used in academia, especially in physics and fiscal analytics. Although I estimate the share is dropping as well there as Python gets more and more popular.

My first feel with Mathematica was during an undergraduate Maths class where I was immediately impressed past the interactive 3D plots. Back than information technology was version 5.4, while at the time of writing this mail the version number is 11.3 with 12 coming soon. Each major release adds a lot of new functions - in total there are currently near 5000 of them. In Mathematica everything is included from the kickoff and there is no need for import, equally all functions are immediately available. If Python comes with batteries included Mathematica comes with the whole bombardment factory. This ways there are no extra packages needed for most of the work, although an in-official package Repository exists.

Wolfram Inquiry, the company behind Mathematica and everything with "Wolfram" in its name, tries to establish that Mathematica is capable of Multiparadigm Data Science. In addition they have announced a Wolfram Information Science Platfrom which I presume to be some kind of cloud service with a lot of automated and pre-defined modules. The platform is "coming soon" for almost four years.

However, let's go back to the basics of the Wolfram language. The general principle is that each function is very high level and automated as much as possible. For case the Classify[] function chooses the method automatically for yous, but if yous want yous tin can also set it manually to something like Method -> "RandomForest".

The Wolfram Language is very consistent, between functions and besides over time. Thirty year old lawmaking even so works in the latest version. This is not a small achievement (because the differences between Python 2 and three) and can mainly be attributed to Stephen Wolfram, the Benevolent Dictator for Life (BDL) for Mathematica and the Wolfram linguistic communication. In dissimilarity to Pyhton's Guido van Rossum who recently resigned I look Stephen Wolfram to be BDL actually for life. You can come across Stephen Wolfram in action during their live-streamed developer meetings.

So lets talk about the elephant in the room: the price. Mathematica is not free, its actually quite expensive and costs about 3545€ for ane license of the standard desktop version. As usual they offer discounts for academia, students (160€) and beginning ups. If y'all want to develop a so called EnterpriseCDF that allows to run your code in the free Mathematica Actor and admission files and databases with information technology, the price is about 10k€. Since Mathematica comes with all functions from the get-go, there is no demand to purchase additional "Toolboxes" like in Matlab.

At that place is a possibility to try Wolfram for free, since every Raspberry Pi comes with Mathematica pre-installed. Although the basic functionality is the aforementioned, Notebooks are more than powerful in the full version and there are of form the speed limitations of the Raspberry Pi.

Examples

In the following sections I briefly show some representative examples. If you want to know more than you tin have a look at http://world wide web.wolfram.com/language/fast-introduction-for-programmers/en/ where you get an overview of the differences compared to Python and the costless volume "An Uncomplicated Introduction to the Wolfram Language" by Stephen Wolfram.

Basic syntax

Everything in the Wolfram language is a symbolic expression, like numbers, strings, images, interfaces, code, etc. And so there are no "undefined variables":

Even Plus is a symbol.

          Plus[2,iii]

Of class you can also write it like this:

          2 + 3

Mathematica automatically does the spacing for you as you lot type.

Or you can besides use Utilize to, yes, use the office:

          Utilise[Plus, {2, 3}]

or in short form

          Plus @@ {2,3}

So Mathematica encourages functional programming with Map[] or @ or Apply, Nest, Fold and and so on. This becomes specially powerful when using pure functions # similar to lambda expressions in Python.

Lists in Mathematica are written inside {} and the alphabetize starts at ane, as it should in every language everywhere and all the time.

          listing = {i, 2, iii} firstelement = listing[[i]] firstelement = Part[listing, ane] firstelement = Beginning[list] firstelement = First@list

The double foursquare brackets are comparable to the brackets in Python. They are the short version of the Part function similar to + existence the short version of Plus and @ being the curt version of Map.

For complex code yous nest functions inside functions which leads to a lot of [], but fortunately Mathematica formats it on the fly in a meaningful way. Nonetheless Python code is easier to read.

A short illustrative example

In the following instance I will use the built-in data to plot the population of the v closest cities near our company location in Älvdalen, Sweden.

Screenshot of Mathematica’s auto suggestion. — Screenshot of Mathematica's auto suggestion.

In the beginning line I use natural language to ask for Älvdalen, which returns an Entitiy. There are many different types of entities, similar "AdministrativeDivision", "Dinosaur", "Glacier", "Airport" or "ZipCode" and each has a unique prepare of meaningful properties, similar Population for Cities. Wolfram comes with born knowledge, the same that powers WolframAlpha. Even the rather pocket-sized "cities" around united states of america are available.

In In[9] I used a pure function # to excerpt the population of the city Entity. The population comes with units which are fully integrated in the Wolfram Linguistic communication. Then finally I plot a bar nautical chart of the populations.

Notebook and Dynamic and Dispense

The popular notebook format was invented by Stephen Wolfram and even so to-date the notebook on Mathematica is more than powerful compared to Jupyter notebooks. For instance, Mathematica does have more formatting possibilities and a powerful suggestion bar. Although I wish it would support Markdown, which it currently doesn't.

With Dynamic you can brand programming even more interactive, like in this example:

This can by applied to any symbol and with a few lines of lawmaking you lot can get a pretty useful tool, for case for data exploration or to interact with your trained model and you lot can build a uncomplicated GUI in minutes. In my experience this helps a lot in understanding the model and the problem ameliorate, since you get a more than intuitive understanding. Manipulate is a more than high level role and you tin build a GUI in just one line when wrapping your trained model in it.

Mathematica’s Manipulate in action. — Mathematica's Dispense in action.

In Jupyter notebooks you can use ipywidgets which I haven't really tested yet.

Dataset

The Wolfram language has something like to a pandas data-frame, called a dataset.

While its similar some syntax is closer to SQL.

          titanic[Select[#age > 29 &]] titanic[GroupBy["sex"]]

I work a lot with datasets only still I need to consult the documentation a lot. An a simple task such every bit adding a new cavalcade can be tricky:

          titanic[All, Append[#, "age+2" -> #age + two] &]

And so I would say pandas wins because it is just as powerful and easier to utilise. As well datasets tin can be slower to work with, especially for big and nested datasets an Association is much faster. It seems like this might modify in the next release of Mathematica.

Motorcar Learning

The Wolfram language comes with congenital-in functions which use ML like ImageIdentify LanguageIdentify FindTextualAnswer and high level functions to railroad train your own models similar Classify and Predict for regression and the more lower level functions like FindFit and NetModel.

Lets look at an example for a neural network.

The neural network office uses MxNet equally a backend and is similar in its apply to Keras, although nicer to look at. In general the ML functions in Wolfram have a blackness box feeling to them, although in that location are lower level functions as well. In general you should non blindly trust that the automatic solution provided by Predict and Classify is the one optimal solution. They are often far from that and at best give you lot a base of operations line solution on which to approve on. You can and then always utilize lower level functions to build your own custom ML solution with Wolfram or Python.

Documentation and Community

Mathematica has a very expert system for documentation with all born functions. Also the documentation itself are notebooks, so you lot tin can quickly try something straight inside the documentation.

The documentation in Mathematica is really good, only Python has a much bigger community and it is very probable that you find an answer for exactly your problem. Also yous can learn a lot through sites like Kaggle. The Wolfram/Mathematica community is comparably modest and therefore it is harder to find relevant information, although the Mathematica customs](https://mathematica.stackexchange.com) on stackexchange is really helpful.

Conclusions

At present some bullet points for both languages in no item order.

Wolfram

natural language estimation
blueprint matching is powerful and prominent, for example in function declaration
interactive and very good documentation
consistent
symbolic, you tin pass everything into a role (has a lot of advantages but likewise makes it harder to debug)
more advanced notebooks
no virtual environments and dependencies
works the same in every Bone
most of the fourth dimension at that place is but one obvious mode to do things, for instance plotting
Dynamic and Manipulate functions for more interactivity
built-in cognition
indices start at 1
instant API (although only in the Wolfram Cloud or your own Wolfram Enterprise Cloud)
hard to find a job / hard to recruit people who know Wolfram

Python

"There is a parcel for that"
closer to state of the fine art
lawmaking is easier to read and to maintain
debug messages are ordinarily more helpful
costless
learn from Kaggle
lots of possibilities to deploy a trained model
a lot of online courses, podcasts and other resources
use of google-colab or Kaggle for learning ML without a local GPU
pandas is easier to use than the "Dataset" in Mathematica
big community

Learning some other language is usually benign for your overall understanding of programming. Then learning Wolfram might be a nice addition for yous. We utilize the Wolfram language for quick prototyping of ideas and often come up with interesting combinations of data or characteristic engineering with the congenital-in knowledge of the Wolfram language. In addition a quick Manipulate is fun and tin help a lot to empathise the problem and data better.

In Mathematica with just ane line you can deploy our model equally an API or web-app, although just in the Wolfram infrastructure, which might non fit within your infrastructure or policy. Likewise the loftier level functions Allocate and Predict are too much of a blackness box and even standard scikit acquire algorithms outperform them.

Overall I hope that both languages inspire each other, as the jupyter notebook was certainly inspired past Mathematica. For instance I hope for a consistent notebook like documentation build into jupyter lab. On the other hand Wolfram will accept a difficult time to come if they go on to try to do everything on their own and lock you into their infrastructure.

PS: for discussion please use utilize the medium post