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  • 03_Linear_Regression
    • 01_Using_the_Matrix_Inverse_Method
    • 02_Implementing_a_Decomposition_Method
    • 03_Tensorflow_Way_of_Linear_Regression
    • 04_Loss_Functions_in_Linear_Regressions
    • 05_Implementing_Deming_Regression
    • 07_Implementing_Elasticnet_Regression
    • 08_Implementing_Logistic_Regression

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03_Linear_Regression/01_Using_the_Matrix_Inverse_Method/readme.md

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# Graph of linear fit
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![Matrix Inverse Method](https://github.com/nfmcclure/tensorflow_cookbook/blob/master/03_Linear_Regression/images/01_Inverse_Matrix_Method.png "Matrix Inverse Method")
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![Matrix Inverse Method](../images/01_Inverse_Matrix_Method.png "Matrix Inverse Method")

03_Linear_Regression/02_Implementing_a_Decomposition_Method/readme.md

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# Graph of linear fit
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![Cholesky decomposition](https://github.com/nfmcclure/tensorflow_cookbook/blob/master/03_Linear_Regression/images/02_Cholesky_Decomposition.png "Cholesky decomposition")
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![Cholesky decomposition](../images/02_Cholesky_Decomposition.png "Cholesky decomposition")

03_Linear_Regression/03_Tensorflow_Way_of_Linear_Regression/readme.md

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# Graph of Loss Function
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![Regression Loss](https://github.com/nfmcclure/tensorflow_cookbook/blob/master/03_Linear_Regression/images/03_lin_reg_loss.png "Regression Loss")
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![Regression Loss](../images/03_lin_reg_loss.png "Regression Loss")
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# Graph of Linear Fit
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![TF Regression](https://github.com/nfmcclure/tensorflow_cookbook/blob/master/03_Linear_Regression/images/02_Cholesky_Decomposition.png "TF Regression")
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![TF Regression](../images/02_Cholesky_Decomposition.png "TF Regression")

03_Linear_Regression/04_Loss_Functions_in_Linear_Regressions/readme.md

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# Graph of L1 vs L2 Loss Functions
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![L1 and L2 Loss](https://github.com/nfmcclure/tensorflow_cookbook/blob/master/03_Linear_Regression/images/04_L1_L2_loss.png "L1 and L2 Loss")
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![L1 and L2 Loss](../images/04_L1_L2_loss.png "L1 and L2 Loss")
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# Graph of L1 vs L2 Loss Functions (L2 not converging)
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Here is an example of the L2 function not converging. Despite a large learning rate, L1 has converged but L2 has not.
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![L2 Not Converging](https://github.com/nfmcclure/tensorflow_cookbook/blob/master/03_Linear_Regression/images/04_L1_L2_loss2.png "L2 Not Converging")
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![L2 Not Converging](../images/04_L1_L2_loss2.png "L2 Not Converging")
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# Graphical Summary of L1 and L2 with Learning Rates
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Here is a plot of a 1D example of L1 and L2 loss with a small and large learning rate.
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![L1 and L2](https://github.com/nfmcclure/tensorflow_cookbook/blob/master/03_Linear_Regression/images/04_L1_L2_learningrates.png "L1 and L2")
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![L1 and L2](../images/04_L1_L2_learningrates.png "L1 and L2")
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To note:
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03_Linear_Regression/05_Implementing_Deming_Regression/readme.md

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Deming regression, also known as total regression, is regular regression that minimizes the shortest distance to the line. Contrast this to regular regression, in which we aim to minimize the vertical distance between the model output and the y-target values.
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![Deming Regression](https://github.com/nfmcclure/tensorflow_cookbook/blob/master/03_Linear_Regression/images/05_demming_vs_linear_reg.png "Deming Regression")
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![Deming Regression](../images/05_demming_vs_linear_reg.png "Deming Regression")
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# Model
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# Graph of Linear Fit
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![Deming Output](https://github.com/nfmcclure/tensorflow_cookbook/blob/master/03_Linear_Regression/images/05_demming_reg.png "Deming Output")
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![Deming Output](../images/05_demming_reg.png "Deming Output")
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# Implementing Elasticnet Regression
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![Elasticnet Regression Loss](https://github.com/nfmcclure/tensorflow_cookbook/blob/master/03_Linear_Regression/images/07_elasticnet_reg_loss.png "Elasticnet Regression Loss")
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![Elasticnet Regression Loss](../images/07_elasticnet_reg_loss.png "Elasticnet Regression Loss")

03_Linear_Regression/08_Implementing_Logistic_Regression/readme.md

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Running the script should result in a similar loss and accuracy output.
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![Logistic Regression Loss](https://github.com/nfmcclure/tensorflow_cookbook/blob/master/03_Linear_Regression/images/08_logistic_reg_loss.png "Logistic Regression Loss")
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![Logistic Regression Loss](../images/08_logistic_reg_loss.png "Logistic Regression Loss")
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# Accuracy of Train and Test Sets
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![Logistic Regression Accuracy](https://github.com/nfmcclure/tensorflow_cookbook/blob/master/03_Linear_Regression/images/08_logistic_reg_acc.png "Logistic Regression Accuracy")
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![Logistic Regression Accuracy](../images/08_logistic_reg_acc.png "Logistic Regression Accuracy")

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