Python implementation of nonparametric nearest-neighbor-based estimators for divergences between distributions.
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This is a Python implementation of nonparametric divergence estimators.

For an introduction to the method and why you'd want to use it, see

Code homepage:

Code by Dougal J. Sutherland <> based partially on code by Liang Xiong <>.

NOTE: this package will soon be superceded by the more-generic and better-integrated-with-scikit-learn package skl-groups.


This code is written for Python 2.7, with 3.2+ compatability in mind (but not tested). It is known not to work for 2.6, though adding support would not be overly difficult; let me know if you want that.

It is also only tested on Unix-like operating systems (in particular, on OS X, CentOS, and Ubuntu). All of the code except for the actual SVM wrappers should work on Windows, but it's untested. The SVM wrappers should work if you use n_proc=1; if you try to use multiprocessing there it will complain and crash.

If you want to run with more than about a thousand objects, make sure that your numpy and scipy are linked to a fast BLAS/LAPACK implementation like MKL, ACML, or OpenBLAS.

The easiest way to accomplish that is to use a pre-packaged distribution. I use Anaconda. If you're affiliated with an academic institution, you can get the MKL Optimizations add-on for free that links numpy to Intel's fast MKL library. Anaconda (or EPD) also let you avoid having to compile scipy (which takes a long time) and install non-python libraries like hdf5. If so, conda install accelerate install them all.

It's also easiest to install py-sdm through binaries with the conda package manager (part of Anaconda). There are currently only builds on 64-bit OSX and 64-bit Linux, with Python 2.7. To do so:

conda install -c py-sdm

If you don't want to use binaries, there are various complications. See INSTALL.rst for details.

Quick Start Guide for Images

This shows you the basics of how to do classification or regression on images.

Data Format

If you're doing classification, it's easiest if your images are in a single directory containing one directory per class, and images for that class in the directory: root-dir/class-name/image-name.jpg

If you're doing regression, it's easiest to have your images all in a single directory, and a CSV file $target_name.csv with labels of the form:


for each image in the directory (no header).

Extracting Features

This step extracts SIFT features for a collection of images.

The basic command is something like:

extract_image_features --root-dir path-to-root-dir --color hsv feats_raw.h5

for classification, or:

extract_image_features --dirs path-to-root-dir --color hsv feats_raw.h5

for regression.

This by default spawns one process per core to extract features (each of which uses only one thread); this can be controlled with the --n-proc argument.

You're likely to want to use the --resize option if your images are large and/or of widely varying sizes. We typically resize them to be about 100px wide or so.

See --help for more options.

Post-Processing Features

This step handles "blanks," does dimensionality reduction via PCA, adds spatial information, and standardizes features.

The basic command is:

proc_image_features --pca-varfrac 0.7 feats_raw.h5 feats_pca.h5

This by default does a dense PCA; if you have a lot of images and/or the images are large, it'll take a lot of memory. You can reduce memory requirements a lot by replacing the --pca-varfrac 0.7 with something like --pca-k 50 --pca-random, which will do a randomized SVD to reduce dimensionality to 50; you have to specify a specific dimension rather than a percent of variance, though.

If you have a numpy linked to MKL or other fancy blas libraries, it will probably try to eat all your cores during the PCA; the OMP_NUM_THREADS environment variable can limit that.

Again, other options available via --help.


Once you have this, to calculate divergences and run the SVMs in one step you can use a command like:

sdm cv --div-func renyi:.9 -K 5 --cv-folds 10 \
    feats_pca.h5 --div-cache-file feats_pca.divs.h5 \

for cross-validation. This will cache the calculated divergences in feats_pca.divs.h5, and print out accuracy information as well as saving predictions and some other info in This can take a long time, especially when doing divergences.

For regression, the command would look like:

sdm cv --nu-svr --div-func renyi:.9 -K 5 --cv-folds 10 \
    --labels-name target_name
    feats_pca.h5 --div-cache-file feats_pca.divs.h5

This uses --n-proc to specify the number of SVMs to run in parallel during parameter tuning. During the projection phase (which happens in serial), an MKL-linked numpy is likely to spawn many threads; OMP_NUM_THREADS will again control this.

Many more options are available via sdm cv --help.

sdm also supports predicting using a training / test set through sdm predict rather than sdm cv, but there isn't currently code to produce the input files it assumes. If this would be useful for you, let me know and I'll write it....

Precomputing Divergences

If you'd like to try several divergence functions (e.g. different values of alpha or K), it's much more efficient to compute them all at once than to let sdm do them all separately.

(This will hopefully no longer be true once sdm crossvalidates among divergence functions and Ks: issue #12.)

The estimate_divs command does this, using a command along the lines of:

estimate_divs --div-funcs kl renyi:.8 renyi:.9 renyi:.99 -K 1 3 5 10 --
    feats_pca.h5 feats_pca.divs.h5

(where the -- indicates that the -K arguments are done and it's time for positional args.)

Quick Start Guide For General Features

If you don't want to use the image feature extraction code above, you have two main options for using SDMs.

Making Compatible Files

One option is to make an hdf5 file compatible with the output of extract_image_features and proc_image_features, e.g. with h5py. The structure that you want to make is:

/cat1          # the name of a category
  /bag1        # the name of each data sample
    /features  # a row-instance feature matrix
    /label-1   # a scalar dataset with the value of label-1
    /label-2   # scalar dataset with a second label type

Some notes:

  • All of the names except features can be replaced with whatever you like.
  • If you have a single "natural" classification label, it can be convenient to use that for the category, but you can put them all in the same category if you like.
  • The features matrices can have any number of rows but must have the same numbers of columns.
  • Different bags need not have the same labels available, unless you want to use them for training / cross-validating in sdm. Each bag can have any number of labels.

Alternatively, you can use the "per-bag" format, where you make a .npz file (with np.savez) at root-path/cat-name/bag-name.npz with a features matrix and any labels (as above).

Depending on the nature of your features, you may want to run PCA on them, standardize the dimensions, or perform other normalizations. You can do PCA and standardization with proc_image_features, as long as you make sure to pass --blank-handler none --no-add-x --no-add-y so it doesn't try to do image- specific stuff.

You can then use sdm as above.

Using the API

You can also use the API directly. The following shows basic usage in the situation where test data is not available at training time:

import sdm

# train_features is a list of row-instance data matrices
# train_labels is a numpy vector of integer categories

# PCA and standardize the features
train_feats = sdm.Features(train_features)
pca = train_feats.pca(varfrac=0.7, ret_pca=True, inplace=True)
scaler = train_feats.standardize(ret_scaler=True, inplace=True)

clf = sdm.SDC(), train_labels)
# ^ gets divergences and does parameter tuning. See the docstrings for
# more information about options, divergence caches, etc. Caching
# divergences is highly recommended.

# get test_features: another list of row-instance data matrices
# and then process them consistently with the training samples
test_feats = sdm.Features(test_features, default_category='test')
test_feats.pca(pca=pca, inplace=True)
test_feats.normalize(scaler=scaler, inplace=True)

# get test predictions
preds = clf.predict(test_feats)

accuracy = np.mean(preds == test_labels)

To do regression, use clf = sdm.NuSDR() and a real-valued train_labels; the rest of the usage is the same.

If you're running on a nontrivial amount of data, it may be nice to pass status_fn=True and progressbar=True to the constructor to get status information out along the way (like in the CLI).

If test data is available at training time, it's preferable to use .transduct() instead. There's also a .crossvalidate() method.