Metadata-Version: 2.1
Name: shallowgibbs-doublebackpropagation
Version: 1.0.0
Summary: Shallow Gibbs Double Backpropagation
Home-page: https://github.com/kgalahassa/pottscompleteshrinkage
Author: Alejandro, Murua and Alahassa, Nonvikan Karl-Augustt
Author-email: alahassa@dms.umontreal.ca
License: GNU General Public License v3.0
Description: 
        # shallowgibbs-doublebackpropagation
        Double Backpropagation Algorithm -- Implementation with the Shallow Gibbs Model
        
        # Double Backpropagation with the Shallow Gibbs Model
        
        
        ## Installation
        Install using pip
        ```pip install shallowgibbs-doublebackpropagation```
        
        ## Requirements
        * Python 3.6 or greater
        * scipy
        * tensorflow
        * pandas
        * numpy
        * joblib
        * scikit-learn
        
        ## Usage
        Import the Shallow Gibbs Double Backpropagation module
        ```import shallowgibbs.doublebackpropagation as SGDBS```
        You need to load some initial predictions from the Shallow Gibbs Model, or any alike-Structured Model.
        The model requires as parameters: the weigths matrix (W), the biases (b), and the response covariance matrix (Sigma).
        The model framework backpropagation is updated per observation using: 
        
        
        ```math
        MSE\left(y_{i}-\hat{y}_{i}\right)=\|y_{i}-\hat{y}_{e s t, i}\|^{2})
        ```
        
        starting from ``` \hat{\psi}_{0} ``` with the equations:
        
        ```math
        \begin{gathered}
        \hat{\psi}_{1, i} \longleftarrow \hat{\psi}_{0}-\epsilon_{\psi, 0} \frac{\partial M S E\left(y_{i}-\hat{y}_{e s t, i}\right)}{\partial \psi} \\
        \hat{\psi}_{t, i} \longleftarrow \hat{\psi}_{t-1, i}-\epsilon_{\psi, t-1} \frac{\partial M S E\left(y_{i}-\hat{y}_{e s t}, i\right)}{\partial \psi}
        \end{gathered}
        ```
        
        where ``` \psi ``` is the set of parameters (w,b,Sigma) in our case. They are two additional equations that complete those above
        explained in reference [2] and well introduced in [1]. There are about the Training data, and test data predictions update. Please read 
        reference [2] and the Jupyter Notebook for a guide note of usage and application. 
        
        
        ## Pypi Project Page
         https://pypi.org/project/shallowgibbs-doublebackpropagation/1.0.0/
        
        ## Notebook Page
         https://github.com/kgalahassa/shallowgibbs-doublebackpropagation-notebook
        
        ## References
        [1] Muua, Alejandro, Alahassa, Nonvikan Karl-Augustt. The Shallow Gibbs Network, Double Backpropagation and Differential Machine learning, ScienceOpen Preprints (2021).
         https://www.scienceopen.com/document?vid=9aab283e-130f-4922-accb-20bef8faff9f
         
         
        [2] Alejandro Murua, Nonvikan Karl-Augustt Alahassa. Double Back-Propagation and Differential Machine Learning. The Ninth Annual Canadian Statistics Student Conference (CSSC), Jun 2021, Ottawa, Canada. (hal-03265399)
         https://hal.archives-ouvertes.fr/hal-03265399
        
Keywords: Shallow Gibbs,Neural Network,Double Backpropagation
Platform: UNKNOWN
Classifier: Programming Language :: Python :: 3
Classifier: License :: OSI Approved :: GNU Lesser General Public License v3 (LGPLv3)
Classifier: Operating System :: OS Independent
Description-Content-Type: text/markdown
