Metadata-Version: 1.0
Name: group-lasso
Version: 1.1.1
Summary: Fast group lasso regularised linear models in a sklearn-style API.
Home-page: UNKNOWN
Author: Yngve Mardal Moe
Author-email: yngve.m.moe@gmail.com
License: MIT
Description: ===========
        Group Lasso
        ===========
        
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        The group lasso [1]_ regulariser is a well known method to achieve structured 
        sparsity in machine learning and statistics. The idea is to create 
        non-overlapping groups of covariates, and recover regression weights in which 
        only a sparse set of these covariate groups have non-zero components.
        
        There are several reasons for why this might be a good idea. Say for example 
        that we have a set of sensors and each of these sensors generate five 
        measurements. We don't want to maintain an unneccesary number of sensors. 
        If we try normal LASSO regression, then we will get sparse components. 
        However, these sparse components might not correspond to a sparse set of 
        sensors, since they each generate five measurements. If we instead use group 
        LASSO with measurements grouped by which sensor they were measured by, then
        we will get a sparse set of sensors.
        
        An extension of the group lasso regulariser is the sparse group lasso
        regulariser [2]_, which imposes both group-wise sparsity and coefficient-wise
        sparsity. This is done by combining the group lasso penalty with the
        traditional lasso penalty. In this library, I have implemented an efficient
        sparse group lasso solver being fully scikit-learn API compliant.
        
        ------------------
        About this project
        ------------------
        This project is developed by Yngve Mardal Moe and released under an MIT 
        lisence. I am still working out a few things so changes might come rapidly.
        
        ------------------
        Installation guide
        ------------------
        Group-lasso requires Python 3.5+, numpy and scikit-learn. 
        To install group-lasso via ``pip``, simply run the command::
        
            pip install group-lasso
        
        Alternatively, you can manually pull this repository and run the
        ``setup.py`` file::
        
            git clone https://github.com/yngvem/group-lasso.git
            cd group-lasso
            python setup.py
        
        -------------
        Documentation
        -------------
        
        You can read the full documentation on 
        `readthedocs <https://group-lasso.readthedocs.io/en/latest/maths.html>`_.
        
        --------
        Examples
        --------
        
        Group lasso regression
        ======================
        
        The group lasso regulariser is implemented following the scikit-learn API,
        making it easy to use for those familiar with the Python ML ecosystem.
        
        .. code-block:: python
        
            import numpy as np
            from group_lasso import GroupLasso
        
            # Dataset parameters
            num_data_points = 10_000
            num_features = 500
            num_groups = 25
            assert num_features % num_groups == 0
        
            # Generate data matrix
            X = np.random.standard_normal((num_data_points, num_features))
        
            # Generate coefficients and intercept
            w = np.random.standard_normal((500, 1))
            intercept = 2
        
            # Generate groups and randomly set coefficients to zero
            groups = np.array([[group]*20 for group in range(25)]).ravel()
            for group in range(num_groups):
                w[groups == group] *= np.random.random() < 0.8
            
            # Generate target vector:
            y = X@w + intercept
            noise = np.random.standard_normal(y.shape)
            noise /= np.linalg.norm(noise)
            noise *= 0.3*np.linalg.norm(y)
            y += noise
        
            # Generate group lasso object and fit the model
            gl = GroupLasso(groups=groups, reg=.05)
            gl.fit(X, y)
            estimated_w = gl.coef_
            estimated_intercept = gl.intercept_[0]
        
            # Evaluate the model
            coef_correlation = np.corrcoef(w.ravel(), estimated_w.ravel())[0, 1]
            print(
                "True intercept: {intercept:.2f}. Estimated intercept: {estimated_intercept:.2f}".format(
                    intercept=intercept,
                    estimated_intercept=estimated_intercept
                 )
            )
            print(
                "Correlation between true and estimated coefficients: {coef_correlation:.2f}".format(
                    coef_correlation=coef_correlation
                 )
            )
            
        .. code-block::
        
            True intercept: 2.00. Estimated intercept: 1.53
            Correlation between true and estimated coefficients: 0.98
        
        
        Group lasso as a transformer
        ============================
        
        Group lasso regression can also be used as a transformer
        
        .. code-block:: python
        
            import numpy as np
            from sklearn.pipeline import Pipeline
            from sklearn.linear_model import Ridge
            from group_lasso import GroupLasso
        
            # Dataset parameters
            num_data_points = 10_000
            num_features = 500
            num_groups = 25
            assert num_features % num_groups == 0
        
            # Generate data matrix
            X = np.random.standard_normal((num_data_points, num_features))
        
            # Generate coefficients and intercept
            w = np.random.standard_normal((500, 1))
            intercept = 2
        
            # Generate groups and randomly set coefficients to zero
            groups = np.array([[group]*20 for group in range(25)]).ravel()
            for group in range(num_groups):
                w[groups == group] *= np.random.random() < 0.8
            
            # Generate target vector:
            y = X@w + intercept
            noise = np.random.standard_normal(y.shape)
            noise /= np.linalg.norm(noise)
            noise *= 0.3*np.linalg.norm(y)
            y += noise
        
            # Generate group lasso object and fit the model
            # We use an artificially high regularisation coefficient since
            #  we want to use group lasso as a variable selection algorithm.
            gl = GroupLasso(groups=groups, group_reg=0.1, l1_reg=0.05)
            gl.fit(X, y)
            new_X = gl.transform(X)
        
        
            # Evaluate the model
            predicted_y = gl.predict(X)
            R_squared = 1 - np.sum((y - predicted_y)**2)/np.sum(y**2)
        
            print("The rows with zero-valued coefficients have now been removed from the dataset.")
            print("The new shape is:", new_X.shape)
            print("The R^2 statistic for the group lasso model is: {R_squared:.2f}".format(R_squared=R_squared))
            print("This is very low since the regularisation is so high."
        
            # Use group lasso in a scikit-learn pipeline
            pipe = Pipeline(
                memory=None,
                steps=[
                    ('variable_selection', GroupLasso(groups=groups, reg=.1)),
                    ('regressor', Ridge(alpha=0.1))
                ]
            )
            pipe.fit(X, y)
            predicted_y = pipe.predict(X)
            R_squared = 1 - np.sum((y - predicted_y)**2)/np.sum(y**2)
        
            print("The R^2 statistic for the pipeline is: {R_squared:.2f}".format(R_squared=R_squared))
        
            
        .. code-block::
        
            The rows with zero-valued coefficients have now been removed from the dataset.
            The new shape is: (10000, 280)
            The R^2 statistic for the group lasso model is: 0.17
            This is very low since the regularisation is so high.
            The R^2 statistic for the pipeline is: 0.72
        
        -----------
        Furher work
        -----------
        The todos are, in decreasing order of importance
        
        1. Python 3.5 compatibility
        
        ----------------------
        Implementation details
        ----------------------
        The problem is solved using the FISTA optimiser [4]_ with a gradient-based 
        adaptive restarting scheme [5]_. No line search is currently implemented, but 
        I hope to look at that later.
        
        Although fast, the FISTA optimiser does not achieve as low loss values as the 
        significantly slower second order interior point methods. This might, at 
        first glance, seem like a problem. However, it does recover the sparsity 
        patterns of the data, which can be used to train a new model with the given 
        subset of the features.
        
        Also, even though the FISTA optimiser is not meant for stochastic 
        optimisation, it has to my experience not suffered a large fall in 
        performance when the mini batch was large enough. I have therefore 
        implemented mini-batch optimisation using FISTA, and thus been able to fit 
        models based on data with ~500 columns and 10 000 000 rows on my moderately 
        priced laptop.
        
        Finally, we note that since FISTA uses Nesterov acceleration, is not a 
        descent algorithm. We can therefore not expect the loss to decrease 
        monotonically.
        
        ----------
        References
        ----------
        
        .. [1] Yuan, M. and Lin, Y. (2006), Model selection and estimation in
           regression with grouped variables. Journal of the Royal Statistical
           Society: Series B (Statistical Methodology), 68: 49-67.
           doi:10.1111/j.1467-9868.2005.00532.x
        
        .. [2] Simon, N., Friedman, J., Hastie, T., & Tibshirani, R. (2013).
            A sparse-group lasso. Journal of Computational and Graphical
            Statistics, 22(2), 231-245.
        
        .. [3] Yuan L, Liu J, Ye J. (2011), Efficient methods for overlapping
           group lasso. Advances in Neural Information Processing Systems
           (pp. 352-360).
        
        .. [4] Beck, A. and Teboulle, M. (2009), A Fast Iterative 
           Shrinkage-Thresholding Algorithm for Linear Inverse Problems.
           SIAM Journal on Imaging Sciences 2009 2:1, 183-202.
           doi:10.1137/080716542  
        
        .. [5] O’Donoghue, B. & Candès, E. (2015), Adaptive Restart for
           Accelerated Gradient Schemes. Found Comput Math 15: 715.
           doi:10.1007/s10208-013-9150-
        
Platform: UNKNOWN
