Skip to content
Switch branches/tags

Latest commit


Git stats


Failed to load latest commit information.


pypi MIT License Build Status

pyHSICLasso is a package of the Hilbert Schmidt Independence Criterion Lasso (HSIC Lasso), which is a black box (nonlinear) feature selection method considering the nonlinear input and output relationship. HSIC Lasso can be regarded as a convex variant of widely used minimum redundancy maximum relevance (mRMR) feature selection algorithm.

Advantage of HSIC Lasso

  • Can find nonlinearly related features efficiently.
  • Can find non-redundant features.
  • Can obtain a globally optimal solution.
  • Can deal with both regression and classification problems through kernels.

Feature Selection

The goal of supervised feature selection is to find a subset of input features that are responsible for predicting output values. By using this, you can supplement the dependence of nonlinear input and output and you can calculate the optimal solution efficiently for high dimensional problem. The effectiveness are demonstrated through feature selection experiments for classification and regression with thousands of features. Finding a subset of features in high-dimensional supervised learning is an important problem with many real- world applications such as gene selection from microarray data, document categorization, and prosthesis control.


$ pip install -r requirements.txt
$ python install


$ pip install pyHSICLasso


First, pyHSICLasso provides the single entry point as class HSICLasso()

This class has the following methods.

  • input
  • regression
  • classification
  • dump
  • plot_path
  • plot_dendrogram
  • plot_heatmap
  • get_features
  • get_features_neighbors
  • get_index
  • get_index_score
  • get_index_neighbors
  • get_index_neighbors_score
  • save_param

The input format corresponds to the following formats.

  • MATLAB file (.mat)
  • .csv
  • .tsv
  • numpy's ndarray

Input file

When using .mat, .csv, .tsv, we support pandas dataframe. The rows of the dataframe are sample number. The output variable should have class tag. If you wish to use your own tag, you need to specify the output variables by list (output_list=['tag']) The remaining columns are values of each features. The following is a sample data (csv format).


For multi-variate output cases, you can specify the output by using the list (output_list). See Sample code for details.

Save results to a csv file

If you want to save the feature selection results in csv file, please call the following function:

>>> hsic_lasso.save_param()

To get rid of specific covariates effect

In biology applications, we may want to get rid of the effect of some covariates such as gender and/or age. In such cases, we can pre-specify the covariates X in classification or regression functions as

>>> hsic_lasso.regression(5,covars=X)

>>> hsic_lasso.classification(10,covars=X)

Please check the example/ for details.

To handle large number of samples

HSIC Lasso scales well with respect to the number of features d. However, the vanilla HSIC Lasso requires O(dn^2) memory space and may run out the memory if the number of samples n is more than 1000. In such case, we can use the block HSIC Lasso which requires only O(dnBM) space, where B << n is the block parameter and M is the permutation parameter to stabilize the final result. This can be done by specifying B and M parameters in the regression or classification function. Currently, the default parameters are B=20 and M=3, respectively. If you wish to use the vanilla HSIC Lasso, please use B=0 and M=1.


>>> from pyHSICLasso import HSICLasso
>>> hsic_lasso = HSICLasso()

>>> hsic_lasso.input("data.mat")

>>> hsic_lasso.input("data.csv")

>>> hsic_lasso.input("data.tsv")

>>> hsic_lasso.input(np.array([[1, 1, 1], [2, 2, 2]]), np.array([0, 1]))

You can specify the number of subset of feature selections with arguments regression and classification.

>>> hsic_lasso.regression(5)

>>> hsic_lasso.classification(10)

About output method, it is possible to select plots on the graph, details of the analysis result, output of the feature index. Note, to run the dump() function, it needs at least 5 features in the dataset.

>>> hsic_lasso.plot()
# plot the graph

>>> hsic_lasso.dump()
============================================== HSICLasso : Result ==================================================
| Order | Feature      | Score | Top-5 Related Feature (Relatedness Score)                                          |
| 1     | 1100         | 1.000 | 100          (0.979), 385          (0.104), 1762         (0.098), 762          (0.098), 1385         (0.097)|
| 2     | 100          | 0.537 | 1100         (0.979), 385          (0.100), 1762         (0.095), 762          (0.094), 1385         (0.092)|
| 3     | 200          | 0.336 | 1200         (0.979), 264          (0.094), 1482         (0.094), 1264         (0.093), 482          (0.091)|
| 4     | 1300         | 0.140 | 300          (0.984), 1041         (0.107), 1450         (0.104), 1869         (0.102), 41           (0.101)|
| 5     | 300          | 0.033 | 1300         (0.984), 1041         (0.110), 41           (0.106), 1450         (0.100), 1869         (0.099)|
>>> hsic_lasso.get_index()
[1099, 99, 199, 1299, 299]

>>> hsic_lasso.get_index_score()
array([0.09723658, 0.05218047, 0.03264885, 0.01360242, 0.00319763])

>>> hsic_lasso.get_features()
['1100', '100', '200', '1300', '300']

>>> hsic_lasso.get_index_neighbors(feat_index=0,num_neighbors=5)
[99, 384, 1761, 761, 1384]

>>> hsic_lasso.get_features_neighbors(feat_index=0,num_neighbors=5)
['100', '385', '1762', '762', '1385']

>>> hsic_lasso.get_index_neighbors_score(feat_index=0,num_neighbors=5)
array([0.9789888 , 0.10350618, 0.09757666, 0.09751763, 0.09678892])

>>> hsic_lasso.save_param() #Save selected features and its neighbors 


If you use this softwawre for your research, please cite the following two papers: Original HSIC Lasso and its block counterparts.

  title={High-dimensional feature selection by feature-wise kernelized lasso},
  author={Yamada, Makoto and Jitkrittum, Wittawat and Sigal, Leonid and Xing, Eric P and Sugiyama, Masashi},
  journal={Neural computation},
  publisher={MIT Press}

  title={Block HSIC Lasso: model-free biomarker detection for ultra-high dimensional data},
  author={Climente-Gonz{\'a}lez, H{\'e}ctor and Azencott, Chlo{\'e}-Agathe and Kaski, Samuel and Yamada, Makoto},
  publisher={Oxford University Press}




HSIC Lasso based algorithms

Applications of HSIC Lasso

  • Takahashi, Y., Ueki, M., Yamada, M., Tamiya, G., Motoike, I., Saigusa, D., Sakurai, M., Nagami, F., Ogishima, S., Koshiba, S., Kinoshita, K., Yamamoto, M., Tomita, H. Improved metabolomic data-based prediction of depressive symptoms using nonlinear machine learning with feature selection. Translational Psychiatry volume 10, Article number: 157 (2020).



Name : Makoto Yamada (Kyoto University/RIKEN AIP), Héctor Climente-González (RIKEN AIP)

E-mail :


Name : Hirotaka Suetake (RIKEN AIP)

E-mail :