Esben Sørig

Can you provide a discussion on how this model would be adjusted to find the w and b parameters (B1 and B0 respectively) in the example detailed in this Wikipedia article?: 
https://en.wikipedia.org/wiki/Logistic_regression#Parameter_estimation

Mario Delgado 

Can you be a bit more specific about what you would like discussed? 

This notebook shows the process of estimating the parameters of the logistic regression model. As stated in the Wikipedia article, these parameters must be found using numerical methods and this notebook shows how that can be done using tensorflow. 

The model example in the wikipedia article has a single covariate (x). In this notebook, I show the generalisation to 2 covariates (x_1, x_2). In my case I therefore have 3 parameters to estimate which I have called b, w_1, w_2. b, and w_1 are equivalent to b_0 and b_1 in the wiki article. 

By clicking the "take a step" button in this notebook, you can step through the numerical optimisation process that optimises the likelihood function (once you have taken enough steps). This way of estimating the parameters is called maximum likelihood estimation.

Is your question how you would do the univariate case?

I've added an option to see the 1 dimensional example like the wiki page. Hope that helps

Thanks.  I've developed a visualization minimizing sigmoidCrossEntropy for the example in the Wikipedia article.

See: https://observablehq.com/d/907eea004b9a540a

To get the same parameters as the Wikipedia example (see: https://en.wikipedia.org/wiki/Logistic_regression#Example ) the pred/truth parameters have to be flipped; as per the API documentation (see: https://js.tensorflow.org/api/latest/#metrics.binaryCrossentropy  )

So the loss function should be:

loss = (pred, truth) => tf.metrics.binaryCrossentropy(truth, pred)

A working notebook illustrating this is here: https://observablehq.com/d/19a4cd23355a326d
 
Note that parameters w_1 (B1) and b (B0) get closer to 1.5,-4.1 (the values in the Wikipedia example) as steps approach 236.

Good catch! Yeah this was a bug on my part