Statistical and mathematical python

Kinda hate R, because it as much as it is a statistical dream, it is a programming nightmare? Is MATLAB too expensive when you try to run it on your cloud server farm and you’re anyway vaguely suspicious that they get kickback from the companies that sell RAM because otherwise why does it eat all your memory like that? Love the speed of C++ but have a nagging feeling that you should not need to recompile your code to do exploratory data analysis? Like the idea of Julia, but wary of depending on yet another bloody language, let along one without the serious corporate backing or history of the other ones I mentioned?

Python has a different set of warts to those other options. Its statistical library support is narrower than R - probably comparable to MATLAB. It is, however, generally fast-ish and nicer to debug, and integrates general programming tasks well — web servers, academic blogs, neural networks, weird art projects, online open workbooks

The matrix mathematics side of python is not so comprehensive as MATLAB, mind. The core matrix libraries, numpy and scipy, do what you want mostly, but when, for example, you really need some fancy spline type you read about on the internet, or you want someone to have really put in some effort on ensuring such-and-such a recursive filter is stable, you might find you need to do it yourself.

OTOH, it’s ubiquitous and free, free, free so you don’t need to worry about stupid licensing restrictions, and the community is enormous, so it’s pretty easy to answer any questions you may have.

But in any case, you don’t need to choose. Python interoperates with all these other languages, and indeed, makes a specialty of gluing stuff together.

Aside: A lot of useful machine-learning-type functionality, which I won’t discuss in detail here here, exists in the python deep learning toolkits such as Tensorflow and Theano; you might want to check those pages too. Also graphing is a whole separate issue, as is optimisation.

In recent times, a few major styles have been ascendant in the statistical python scene.

DataFrame-style ecosystem

pandas plus statsmodels look a lot more like R, but stripped down. On the minus side, they lack some language features of R (e.g. regression formulae are not first class language features). On the plus side, they lack some language features of R, such as the object model being a box of turds, and copy-by-value semantics, and broken reference counting and hating kittens.

Then again, there is no ggplot2 and a smaller selection of implemented algorithms compared to R, so you don’t get this stuff for free.

  • pandas is more-or-less a dataframe class for python. Lots of nice things are built on this, such as …

  • statsmodels, which is more-or-less R, but Python. Implements

    • Linear regression models
    • Generalized linear models
    • Discrete choice models
    • Robust linear models
    • Many models and functions for time series analysis
    • Nonparametric estimators
    • A wide range of statistical tests
    • etc
  • patsy implements a formula language for pandas. This does lots of things, but most importantly, it

    • builds design matrices (i.e. it knows how to represent z~x^2+x+y^3 as a matrix, which only sounds trivial if you haven’t tried it)
    • statefully preconditions data (e.g. constructs data transforms that will correctly normalise the test set as well as the training data.)

Matrix-style ecosystem

scikit-learn exemplifies a machine-learning style, with lots of abstract feature construction and predictive-performance style model selection built around homogeneously-typed (only floats, only ints) matrices instead of dataframes. This style wil be more familiar to MATLAB users than to R users.

  • pycaret

    is an open source, low-code machine learning library in Python that allows you to go from preparing your data to deploying your model within seconds in your choice of notebook environment.

  • scikit-learn (sklearn to its friends) is the flagship of this fleet. It is fast, clear and well-designed. I enjoy using it for implementing ML-type tasks. It has various algorithms such as random forests and linear regression and Gaussian processes and reference implementations of many algorithms, both à la mode and passé. Although I miss sniff glmnet in R for lasso regression.

  • Tensorflow includes a sklearn-like API in its library.

  • SciKit-Learn Laboratory

    SKLL (pronounced “skull”) provides a number of utilities to make it simpler to run common scikit-learn experiments with pre-generated features.

  • Sklearn-pandas

    …provides a bridge between sklearn’s machine learning methods and pandas-style Data Frames.

    In particular, it provides:

    • a way to map DataFrame columns to transformations, which are later recombined into features

    • a way to cross-validate a pipeline that takes a pandas DataFrame as input.

  • libROSA, the machine listening library is more or less in this school.

  • kernel-regression I should check out. Claims to supplement the convolution kernel algorithms in sklearn.

  • pystruct aims at being an easy-to-use structured learning and prediction library.”

    Currently it implements only max-margin methods and a perceptron, but other algorithms might follow. The learning algorithms implemented in PyStruct have various names, which are often used loosely or differently in different communities. Common names are conditional random fields (CRFs), maximum-margin Markov random fields (M3N) or structural support vector machines.

The new fusion: xarray

xarray is a system which labels arrays, leading to a

Xarray introduces labels in the form of dimensions, coordinates and attributes on top of raw NumPy-like multidimensional arrays, which allows for a more intuitive, more concise, and less error-prone developer experience.

This data model is borrowed from the netCDF file format, which also provides xarray with a natural and portable serialization format. NetCDF is very popular in the geosciences, and there are existing libraries for reading and writing netCDF in many programming languages, including Python.

This system seems to be a developing lingua franca for the differentiable learning frameworks. Somewhat similar to the matrix-style interface of the scikit-learn, but weirder, is the computation-flow-graph-style of the differentiable learning libraries such as pytorch and Tensorflow, and the variational approximation / deep learning communities.

ArviZ is a Python package for exploratory analysis of Bayesian models. Includes functions for posterior analysis, data storage, sample diagnostics, model checking, and comparison.

The goal is to provide backend-agnostic tools for diagnostics and visualizations of Bayesian inference in Python, by first converting inference data into xarray objects. See here for more on xarray and ArviZ usage and here for more on InferenceData structure and specification.

Time series

Suddenly there is a big pile of time series packages, whcih might be useful. They tend to be based on time series classification and feature extraction which I… am sure is useful for something but I have personally never needed.

See tslearn

tslearn is a Python package that provides machine learning tools for the analysis of time series. This package builds on (and hence depends on) scikit-learn, numpy and scipy libraries.

It relates to a bunch of other time series tools:


It automatically calculates a large number of time series characteristics, the so called features. Further the package contains methods to evaluate the explaining power and importance of such characteristics for regression or classification tasks.


Cesium is an end-to-end machine learning platform for time-series, from calculation of features to model-building to predictions. Cesium has two main components - a Python library, and a web application platform that allows interactive exploration of machine learning pipelines. Take control over the workflow in a Python terminal or Jupyter notebook with the Cesium library, or upload your time-series files, select your machine learning model, and watch Cesium do feature extraction and evaluation right in your browser with the web application.

Interoperation with other languages, platforms


Direct API calls

You can do this using rpy2.ipython

%load_ext rpy2.ipython

%R library(robustbase)
%Rpush yy xx
%R mod <- lmrob(yy ~ xx);
%R params <- mod$coefficients;
%Rpull params

See the Revolutions blog, or Josh Devlin’s tips for more of that.

Counterintuitively this is remarkably slow. I have experienced much greater speed in saving data to the file system in one language then loading it in another. For that, see the next

via the filesystem

Much faster, weirdly, and better documented. Recommended. Try feather, which is based on Apache arrow.

import pandas as pd
import feather

path = 'my_data.feather'
feather.write_dataframe(df, path)
df = feather.read_dataframe(path)

path <- "my_data.feather"
write_feather(df, path)
df <- read_feather(path)

If that doesn’t work, try hdf5 or protobuf or whatever. There are many options. hdf5 seems to work well for me.


See pycall from julia.


e.g. for performance or invoking external binaries.

See compiling python.

Displaying numbers legibly

Easy, but documentation is hard to find.


Sven Marnach distills everything adroitly:


means “with 4 decimal points, align x to fill 10 columns”.

All conceivable alternatives are displayed at


How I set my numpy arrays to be displayed big and informative:

  linewidth=85, precision=4,
  suppress=True, threshold=500)

Reset to default:

np.set_printoptions(edgeitems=3, infstr='inf',
  linewidth=75, nanstr='nan', precision=8,
  suppress=False, threshold=1000, formatter=None)

There are a lot of ways to do this one.

See also np.array_str for one-off formatting.


Use a known-good project structure

cookiecutter data science.

Local random number generator state

Seeding your RNG can be a pain in the arse, especially if you are interfacing with an external library that doesn’t have RNG state passing in the API. So, use a context manager. Here’s one that works for numpy-based code:

from numpy.random import get_state, set_state, seed

class Seed(object):
  context manager for reproducible seeding.

  >>> with Seed(5):
  >>>   print(np.random.rand())

  def __init__(self, seed):
    self.seed = seed
    self.state = None

  def __enter__(self):
    self.state = get_state()

  def __exit__(self, exc_type, exc_value, traceback):

Exercise for the student: make it work with the default RNG also

Miscellaneous learning resources

Numerical tours of signal processing in python.

Miscellaneous tools

  • hypertools is a generic dimensionality reduction toolkit. Is this worthwhile?
  • Bonus scientific computation is also available through GSL, most easily via CythonGSL
  • agate is a stats package is not designed for high performance but for ease of use and reproducibility for journalists.
  • savez makes persisting arrays fast and efficient per default. Use that, if you are talking to other python processes.
  • biopython is a whole other world of phylogeny and bio-data wrangling. I’m not sure if it adheres to one of the aforementioned schools or not. Should check.
  • more options for speech/string analysis at natural language processing.