Python

Exploring GLMs with Python

A few months ago Philipp Berens and I ran a six week course introducing the Generalised Linear Model to graduate students. We decided do run the course in Python and to use the IPython Notebook to present the lectures. You can view the lecture notes here and get the source code here.

The six lectures were:

  1. Introduction by us, then student group presentations of a points of significance article that we hoped would provide a refresher on basic statistics.
  2. Finishing off student presentations (which took too long in the first week), followed by an introduction to Python, dataframes and exploratory plotting.
  3. Design matrices
  4. Interactions
  5. ANOVA and link functions
  6. Current issues in statistical practice, in which we touched on things like exploratory vs confirmatory data analysis, p-hacking, and the idea that statistics is not simply a cookbook one can mechanically follow.

What worked

  • In general the feedback suggests that most students felt they benefitted from the course. Many reported that they enjoyed using the notebook and working through the course materials with a few exercises themselves.
  • The main goal of the course was to give students a broad understanding of how GLMs work and how many statistical procedures can be thought of as special cases of the GLM. Our teaching evaluations suggest that many people felt they achieved this.
  • The notebooks allow tying the theory and equations very concretely to the computations one performs to do the analysis. I think many students found this helpful, particularly in working through the design matrices

What didn’t

  • Many students felt the course was too short for the material that we wanted to cover. I agree.
  • Some students found the lectures (for which weeks 2–5 involved me working through notebooks and presenting extra material) boring.
  • Despite the niceness of the Anaconda distribution, Python is unfortunately still not as easy to set up as (for example) MATLAB across different environments (primarily Windows, some OSX). We spent more time than we would have liked troubleshooting issues (mainly to do with different Windows versions not playing nicely with other things).
  • We didn’t spend a lot of time discussing the homework assignments in class.
  • Some students (graduate students in the neural behavioural school) are more familiar with MATLAB and strongly preferred that we teach the course using that.

If I were to run the course again

I think the main thing I would change if I ran the course again would be to have it run longer. As a “taste test” I think six weeks was fine, but to really get into the materials would require more lectures.

I also think it would be beneficial to split the content into lectures and practicals. I think the IPython notebooks in the way I used them would be excellent for teaching practical / small class tutorials, but that the lectures probably benefit from higher-level overviews and less scrolling over code*.

I would also plan the homework projects better. One student suggested that rather than having the introduction presentations at the beginning of the course, it would be nice to have the last lecture dedicated to students running through their analysis of a particular dataset in the notebook. I think that’s a great idea.

Finally, I would ignore requests to do the course in MATLAB. Part of why we wanted to use Python or R to do the course was to equip students with tools that they could continue using (for free) if they leave the university environment. Perhaps this is more valuable to undergraduates than PhD students (who already have some MATLAB experience), but I think it’s good for those students to get exposed to free alternatives as well. Plus, the IPython notebooks are just, well, pretty boss.

*I know you can hide cells using the slide mode, but I found slide mode in general quite clunky and so I opted not to use it.

High-level plotting in Python

If you have read my older blog posts, you know I’m a fan of R’s ggplot2 library for exploratory data analysis. It allows you to examine many views onto data, creating summaries over different variables right there as you plot. I gave a short tutorial here. Once you understand how the library works, it’s a very powerful way of quickly seeing patterns in large datasets.

Moving over to Python

The past few months have seen me ramp up my Python useage (as I preempted almost a year ago). This is for a variety of reasons, but mostly (a) Python is a general programming language, so you can essentially do anything in it without it being a massive hack; (b) the scientific computing packages available for Python are generally super awesome; (c) it seems to me to be poised to replace Matlab as the lingua franca of neuroscience / vision research — at least, much more so than R. See Tal Yarkoni’s blog for a related discussion. Of course, it’s also free and open source.

What I’m still kind of missing in Python is a nice high-level plotting library like ggplot2. Certainly, there are many in the works, but in playing around I’ve found that none of them can match R’s ggplot2 yet.

Amphibious assault

Of the libraries I’ve tried (main competitor is yhat’s ggplot port), my go-to library for plotting in Python is hands-down Seaborn. Developed largely by Michael Waskom, a graduate student in Cog Neuro at Stanford, it has the prettiest plots, and also the best ideas for high-level functionality.

Speeding up Seaborn?

Unfortunately, compared to R’s ggplot2, Seaborn data summary functions are slow. As an example, I’ll show you a summary plot using the simulated data from my R tutorials.

We want to summarise our (simulated) subjects’ detection performance as a function of stimulus contrast, for each spatial frequency. In R, my code looks like this:

    library(ggplot2)
    setwd('~/Dropbox/Notebooks/')
    dat <- read.csv('contrast_data.csv')
    summary(dat)

    plot_fun <- function(){
      fig <- ggplot(data = dat, aes(x=contrast, y=correct, colour=factor(sf))) +
        stat_summary(fun.data = "mean_cl_boot") + 
        scale_x_log10() + scale_y_continuous(limits = c(0,1)) + 
        facet_wrap( ~ subject, ncol=3)  +  
        stat_smooth(method = "glm", family=binomial())
      print(fig)
    }

    system.time(plot_fun())

This takes about 3 seconds (2.67) to return the following plot:

<a href="https://tomwallisblog.files.wordpress.com/2014/10/ggplot_timing.png"><img src="https://tomwallisblog.files.wordpress.com/2014/10/ggplot_timing.png&quot; alt="ggplot_timing" width="600" height="485" class="aligncenter size-full wp-image-374" /></a>

EDIT: for some reason WordPress is being silly and won't let me actually show this picture. Suffice to say it looks substantively similar to the plot below

Let's contrast this to Seaborn. First the code:

# do imports
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
import ggplot

dat = pd.read_csv('contrast_data.csv')

# make a log contrast variable (because Seaborn can't auto-log an axis like ggplot):
dat['log_contrast'] = np.log(dat['contrast'])

# set some styles we like:
sns.set_style("white")
sns.set_style("ticks")
pal = sns.cubehelix_palette(5, start=2, rot=0, dark=0.1, light=.8, reverse=True)

%%timeit
fig = sns.lmplot("log_contrast", "correct", dat,
x_estimator=np.mean,
col="subject",
hue='sf',
col_wrap=3,
logistic=True,
palette=pal,
ci=95);

(note that the above lines were run in an ipython notebook, hence the %%timeit magic operator).

Seaborn takes… wait for it… 2 minutes and 11 seconds to produce the following plot:

seaborn_2min

(I’m using Python 3.3.5, Anaconda distribution 2.1.0, Seaborn 0.4.0.)

Note also that both packages are doing 1000 bootstraps by default (as far as I’m aware), so I’m pretty sure they’re doing equivalent things.

What can be done?

This is obviously not a positive factor for my switch from R to Python, and I’m hoping it’s just that I’ve done something wrong. However, another explanation is that whatever Seaborn is using to do the bootstrapping or logistic model fitting is just far less optimised than ggplot2’s backend in R.

The nice thing about open source software is that we can help to make this better. So if you’re a code guru who’s reading this and wants to contribute to the scientific computing world moving ever faster to Python, go fork the github repo now!

Update

After I posted this, I opened an issue on Github asking the developers about the slow times. Turns out that the ci flag in sns.lmplot specifies confidence intervals for the logistic regression, which is also bootstrapped. Bootstrapping a logistic regression takes a while; setting ci=False means that Seaborn now takes about 7 seconds to produce that plot instead of 2 minutes.

So, hooray for Seaborn and for awesome open source developers!

Guest Post: Matlab versus Pandas for data analysis

Annelie Muehler is an undergraduate student who is about to finish a 2 month internship in our group. She has been working with me conducting psychophysical experiments, and we have been creating stimuli using python. As part of getting used to scientific python Annelie learned to use Pandas, a package that essentially gives you R’s data frames in Python. The following compares the code to do a simple analysis in Matlab and Python. While it’s possible there are ways to improve the Matlab implementation (perhaps using the statistics toolbox?), it’s noteworthy that these weren’t taught in Annelie’s course.

A comparison of Matlab and Pandas for a simple data analysis

As part of my undergraduate studies in cognitive psychology and neuroscience, I did a water maze experiment in an advanced biology/neuroscience lab course using mice. For this experiment, I had ten mice that did four trials of the experiment over a six day period. The point of this experiment is for the mice to be able to find the platform in the water with increasing speed as they complete more trials. This is because they learn where the platform is. The water maze experiment is one of the behavioural experiments used in mice and rats to test for the ability to learn. Later we used this data while we were learning Matlab in another lab class as a basis for learning data analysis.

During my internship at the Centre for Integrative Neuroscience in Tuebingen, Germany, I reanalyzed this data using pandas in python as a way to learn pandas, giving me a direct comparison of Matlab and pandas. There are definitely some very nice things about pandas. First, you are able to define your own index and column names that are shown surrounding the matrix in a format similar to a table in a word processing document or excel file. This was one of the most frustrating things for me in Matlab because in Matlab you have a dataset and then another variable which contains a list of strings that corresponded to the column names so that you can look them up there.

Table_example_blog

An example of the format in which tables are seen in pandas using the mice data. The table is stored in a variable called rdata.

In pandas, reading data in and out in is easy with the pd.read_csv() and rdata.to_csv function. As you can see in the image above, the mice data is structured so that the indices represent the row number, the other columns are:

  • Trials which represents the trial number and is numbered from one to four for each trial in each day
  • Animal is the animal number which is in the range one to ten
  • Day stands for the day number and is numbered from one to six
  • Swimming Time represents the amount of time it took the mouse to find the platform in the water maze experiment.

I find it easier to work with the table labeled in this way as opposed to having a different variable with the labels of the columns, as we had done in Matlab. Also pandas has great functions
such as:

  • rdata.head() which shows the top rows of the dataframe
  • rdata.describe() which gives the count, mean, standard deviation and other statistics of the dataframe (not the most useful for this specific dataframe)
  • rdata.sort(columns = 'Animal') which sorts the data by a specific column, in this case the column Animal.

As you can see above, pandas (and python in general) has object-oriented functions. These work by using the name of the object, in this case rdata, adding a period and then typing the function. This will show you the result of the function but generally not change the actual object unless the object is equated with the function (as in rdata = rdata.sort(columns = 'Animal').

The idea of the analysis was the find the average swimming time per day across animals to see if there was any improvement as the mice learned the task. In Matlab we did this by:

1.

for i=1:nday
rows_day(:,i)=find(rdata(:,3)==i);
end

This created a dataset in which the rows for each day were identified.

2.

for i=1:nday
time_day(:,i)=rdata(rows_day(:,i),5);
end

Using the data set from step 1, we are able to get a new data set where the swimming time of each trial is listed for each day across animals.

3.

m_day=mean(time_day);
f=figure;
a=axes;
plot(m_day);
ylabel('Swimming Time (s)')
xlabel('Experimental Day')
set(a,'xtick',1:nday)
title('Average swimming time (s) per day across animals')

This results in this simple line graph:

mean_day_mat

Graph output from Matlab
Here’s the same thing in pandas.

1.

import pandas as pd

The usual importing at the beginning of each python script.

2.

m_day = rdata.groupby('Day')['Swimming Time'].mean()
m_day = pd.DataFrame({'Swimming Time (s)':m_day, 'Experimental Day': range(1,7)})

Groupby is a useful command that will group the data by day (parentheses) according to Swimming Time (square brackets). This eliminates sorting out the rows by day using a for loop as is done in the Matlab code above and allows you to group your data according to different variables in your data frame. The .mean() operator at the end tells pandas that you want to compute the means on the grouped data.

3.

m_day.plot(style='b-', x='Experimental Day', y='Swimming Time (s)', title='Average swimming time (s) per day across animals')

There are other python plot functions that may be a bit more elaborate but in the spirit of doing everything in pandas I decided to show the pandas version. This results in this simple line graph, identical to the one above:

mean_day_py

Graph output from Pandas

Figures can be easily saved in pandas using:

fig = plot.get_figure()

fig.savefig()
Of course this is a very simple example of data analysis, but I think it does outline some of the benefits of pandas. The nicest thing in my opinion is the ease with which you can manipulate the data frame and the ability to select columns by their name. The groupby function is very useful and can be used to groupby multiple columns or to group multiple columns.

In my opinion, pandas is a much simpler and convenient way to work with and manipulate data.

My current direction in scientific computing

During my PhD I learned to program in Matlab. I’d never done any programming before that, and I found it to be a rewarding experience. As is typical for people in vision science, I did pretty much everything in Matlab. Stimuli were generated and presented to human subjects using the CRS Visage (in my PhD; programming this thing can be hell) and now the excellent Psychtoolbox. Early on in my PhD I also moved away from SPSS to doing data analysis in Matlab, too.

An early project in my postdoc (see here) involved some more sophisticated statistical analyses than what I had done before. For this, Matlab was an absolute pain. For example, the inability (in base Matlab) to have named columns in a numerical matrix meant that my code contained references to column numbers throughout. This meant that if I wanted to change the order or number of variables going into the analysis I had to carefully check all the column references. Ugly, and ripe for human error.

Cue my switch to R. For statistical analyses R is pretty damn excellent. There are thousands of packages implementing pretty much every statistical tool ever conceived, often written by the statistician who thought up the method. Plus, it does brilliant plotting and data visualisation. Add the ability to define a function anywhere, real namespaces and the excellent R Studio IDE and I was hooked. I would try to avoid using Matlab again for anything on the analysis side but some light data munging (this is also wrapped up in my preference for science in open software).

For several years now I’ve been doing pretty much everything in R. For our latest paper, I also did my best to make the analysis fully reproducible by using knitr, a package that lets you include and run R analyses in a LaTeX document. You can see all the code for reproducing the analysis, figures and paper here. I’m going to work through the work flow that I used to do this in the next few blog posts.

While R is great for stats and plotting, unfortunately I’m not going to be able to fully replace Matlab with R. Why? First, last I checked, R’s existing tools for image processing are pretty terrible. A typical image processing task I might do to prepare an experiment is take an image and filter it in the Fourier domain (say, to limit the orientations and spatial frequencies to a specific band). I spent about a day trying to do this in R a year or so ago, and it was miserable. Second, R has no ability to present stimuli to the screen with any degree of timing or spatial precision. In fact, that would be going well outside its intended purpose (which is usually a bad idea – see Matlab).

So my “professional development” project for this year is to learn some Python, and test out the PsychoPy toolbox. In addition I’m interested in the data analysis and image processing capabilities of Python – see for example scikit-learn, scikit-image and pandas. I’ve had some recent early success with this, which I’ll share in a future post. It would be so great to one day have all my scientific computing happen in a single, powerful, cross platform, open and shareable software package. I think the signs point to that being a Python-based set of tools.