Reading scientific pages on Kindle

When reading science (math) pages, the large screen (2K or 4K) is the best,

but I would like to have the whole library of papers in my pocket on Kindle.

I can send via email a PDF of any page to Kindle, but the PDF reading on a small Kindle device is awful. 

The same on Kindle Scribe might be a bit better, but in the end, I want font-scalable ePub.

Let's take an example from the following Wikipedia page as it has nice mathematics:

https://en.wikipedia.org/wiki/Spherical_coordinate_system

Pretty much every tool I have tried does convert HTML but fails to convert the math,

in-line LaTEX math seems to work fine, 

but the vector-graphic .svg does not:

I do have to consider that MAYBE it is the viewer that does not display Vector Graphics (.svg)!

Here is a list of tools I have tried:

WebToEpub Chrome extension

• Shows tables nicely
• shows images nicely
• converts LaTEX math YES
• SVG NO, shows them as "?", it might be the viewer's problem, I tried a few
• Calibre E-book viewer
• Kindle 7-inch 2022
• Apple Books
• Apple Preview - does not open ePub

EpubPress

• Creates a table of Contents with each Web page included, useless if converting a single page
• fails to convert table borders
• converts LaTEX fine
• drops (does not display) the Vector Graphics (.svg) 

dotEpub

• in the non-immerse mode, you can view the first few images only
• results in an error on Apple books
• fails to convert table borders
• converts LaTEX math YES
• on Kindle: SPELLS OUT the SVG formula, not good.
• in Calibre E-book viewer shows SVG nicely!

Summary 

1. Use print-to-PDF and view it in MacOS Preview on a big screen
2. If you read a long MATH and NO-image page, use dotEpub and read in the Calibre E-book viewer
3. If you want images, but you do not care for SVG math, WebTOEpub is best.

Sorry, no winning here.

View Kindle Scribe on Amazon: https://amzn.to/4db51Q7

How to write a Math or Data Science eBook?

When studying, I like to take notes, usually, I do it on my Blog, but often I use Jupyter notebooks which I commit to GitHub. If I am writing a paper I use Google Docs. Having my writing in 3 different places is not optimal. 

On top of that, using math formulas complicates things as it is not supported everywhere.

Example of a formula written using LaTeX:

$$ LogLoss = - \frac{1}{n} \sum_{i=1}^{n}
( y_i \cdot log(\hat{y_i}) + ( 1 - y_i ) \cdot \log(1 - \hat{y_i}) ) $$

So, how should I write a Math, or a Data Science, eBook?

First, publishing papers as PDF is most common, I read tons of them, but they are hard to digest unless you print them, or view them on a big screen. I do not want to sit in front of the computer any longer than I already do.  I like using Kindle reader, so an eBook format is much more user-friendly. I can set font sizes, and spacing, take notes, etc. The PDFs on Kindle are a really bad experience. Also, I would like to distribute my papers over the Amazon Kindle store (for free or not). Not everyone has a university or a work subscription to access papers on ieee.org, sciencedirect.com, proquest.com, etc.

Below, I will investigate different approaches and hopefully, come to a good conclusion.

How to send documents to Kindle:

• Every Kindle account has an associated (secret) email, you can attach a file to it and it will show in your Kindle.
• Make sure the file name is human-readable!
• HTML (export from Jupyter Lab) sent to Kindle:
• PRO:
• it is readable, good for text-only pages
• CON:
• LaTeX is not converted to math formulas
• Images are missing
• PDF (of the same HTML) sent to Kindle:
• PRO:
• images show up
• LaTeX formulas show up
• good enough to publish a "paper"
• CON:
• still the problem with PDF in general -- no font size adjustment
• ePUB (of the same HTML) sent to Kindle:
• conversion is done with convertio.co
• PRO
• font adjustable
• plots included
• CONS:
• missing images
• LaTeX not converted to math formulas 
• conversion with  calibre-ebook.com
• 
  

Is Blogger (Blogspot) good for writing papers and articles?

Pro:

• searchable 
• easy to manage and edit
• use of tags (labels) for finding related articles
• support for LaTeX math notation

Cons: 

• No good ways to "clean" export to ePub, PDF, or Markdown
• I could write embedded JavaScript in Blogger that creates "print" version of article text only

Using Jupyter Notebook

Pro:

• inline and current code (Julia, Python)
• incline and current plots 
• export to HTML, PDF, Markdown with pandoc.org/

Cons

• no spellcheck while writing (Grammarly)

• conda install -c conda-forge jupyterlab-spellchecker

• GitHub Diff is garbage

How to install brew?

/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/HEAD/install.sh)"

How to install pandoc? 

[see reference 5]

brew install pandoc

[see reference 1]

Using Markdown

Pros:

• GitHub diff is readable

Using Google Docs

Pros:

• Available on all devices, online and offline

[see reference 2]

References

1. https://towardsdatascience.com/transform-jupyter-notebook-to-an-ebook-ef3a9d32ac4f
2. https://workspace.google.com/marketplace/app/autolatex_equations/850293439076
3. https://tug.org/mactex/mactex-download.html
4. https://nbconvert.readthedocs.io/en/latest/install.html#installing-tex
5. https://pandoc.org/installing.html
6. 
   

LaTex

 

https://tex.stackexchange.com/questions/13865/how-to-use-latex-on-blogspot

<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js">
MathJax.Hub.Config({
 extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
 jax: ["input/TeX", "output/HTML-CSS"],
 tex2jax: {
     inlineMath: [ ['$','$'], ["\\(","\\)"] ],
     displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
 },
 "HTML-CSS": { availableFonts: ["TeX"] }
});
</script> 

Regression - Machine Learning with Python - IBM AI Engineering certificate program on Coursera

Machine Learning with Python

Please note that the Mathematic formulas (LaTex script) DO NOT show on the MOBILE phone, to read this post please use the desktop Chrome browser.

All images are copyrighted by IBM.

https://www.coursera.org/learn/machine-learning-with-python/home/week/1

Definitions:

Machine learning is a subfield of computer science that gives "computers the ability to learn without being explicitly programmed."

Machine Learning tries to train on a large quantity of data and derive solutions to cases not encountered during the training.

AI, a subset of machine Learning, tries to make computers intelligent with vision, language, creativity, etc.

Deep Learning is a subset of AI, where computers learn and make decisions on their own.

The course covers:

• Regression / Estimation
• predicting continuous values
• Classification
• predicting the item class or category
• Clustering
• finding the structure of the data, summarization
• Association
• finding co-occurring items or events
• Anomaly detection
• discovering abnormal or unusual cases
• Sequence mining
• predicting next events; e.g. click stream (Markov Model, HMM)
• Dimension Reduction
• reducing the size of the data (PCA)
• Recommendation Systems
• discovering preferences

Software tools:

• Scikit Learn
• algorithms for machine learning
• SciPy
• signal processing, optimization, statistics, etc.
• NumPy
• arrays, dictionaries, data structures, etc.
• MatPlotLib
• 2D and 3D plotting
• Pandas
• high-performance data structures, data importing, manipulation, and analysis, numerical tables and time-series

Projects:

• Cancer detection
• Economic trends
• Customer churn
• Recommendation engines
• more

Example:

Benign or malignant?

Pipeline:

1. Data Preprocessing
2. Train vs Test data split
3. Algorithm Setup
4. Model Fitting
5. Prediction
6. Evaluation
7. Model Export

scikit-learn functions

Supervised vs Unsupervised Algorithms

Supervised learning is using a "labeled" data set.

data column = feature

data row = observation

There are 2 types of "supervised" learning:

• Classification
• Regression

The unsupervised model draws conclusions on unlabeled data.

Unsupervised techniques:

• Dimension reduction
• Density estimation
• Market basket analysis
• Clustering
• Discovering structure
• Summarization
• Anomaly detection

 

Linear Regression

Introduction to Regression

https://www.coursera.org/learn/machine-learning-with-python/lecture/AVIIM/introduction-to-regression

Simple Linear Regression

https://www.coursera.org/learn/machine-learning-with-python/lecture/r0vEE/simple-linear-regression

Data:

• X: independent variable
• explanatory variables
• can be measured on a categorical or continuous scale
• Y: dependent variable 
• which we try to predict
• needs to be continuous and cannot be a discrete value

Types of regression models:

• Simple regression  (1 feature vs the dependent variable)
• simple linear regression
• simple non-linear regression
• Multiple regression   (comparing 2+ features)
• multiple linear regression
• multiple non-linear regression 

Applications:

• sales forecasting
• satisfaction analysis
• price estimation
• employment income

Regression algorithms:

• ordinal regression
• poison regression
• fast forest quantile regression
• Linear, Polynomial, Lasso, Stepwise, Ridge regression
• Bayesian linear regression
• Neural network regression
• Boosted decision tree regression
• KNN (K-nearest neighbors)

Fit line:

• it is a polynomial written as $ ŷ=\theta_0 + \theta_1 x_1  $ 
• where 
• y is a particular, observed, dependent variable (i.e. emissions )
• $ \hat{y} $, or y "hat" is the response variable or predicted value (ideal value on fitted regression line)
• $  \theta_0 $ y-intercept of the line
• $ \theta_1 $ is the slope or gradient of the line
• $  x_1  $ is the independent variable or a single predictor (i.e engine size in liters)
• $ \theta_0  $ and $  \theta_1 $ are also called the coefficients of the equation

Error

The difference between the ŷ and y is the error.

The mean of the squared sum of errors (differences) formula:

$$ MSE = \frac{1}{n} \sum_{i=1} ^{n} \left( y_i - ŷ_i \right)^2 $$

Objective:
We have to find the best parameters $ \theta_0 $ and $ \theta_1 $ to minimize the MSE. 

Options to find $ \theta_0 $ and $ \theta_1 $:

• mathematical approach
• optimization approach

$$
\theta_1 =
\frac{
\sum_{i=1} ^{s}
\left( x_i - \bar{x} \right) 
\left( y_i - \bar{y} \right) 
}{
\sum_{i=1} ^{s}
\left( x_i - \bar{x} \right)^2 
}
$$

where:

• s = n  , or number of observations (rows in the table)
• $ \bar{x} = \frac{\sum_{i=1} ^{n} \left( x_i \right)  }{n}  $ or, x "bar" is mean of x
• $ \bar{y} = \frac{\sum_{i=1} ^{n} \left( y_i \right)  }{n}  $ or,  y "bar" is mean of y

Conclusions for Linear Regression:

• very fast
• no parameter tuning
• easy to interpret

Model Evaluation in Regression Models

https://www.coursera.org/learn/machine-learning-with-python/lecture/2WZdq/model-evaluation-in-regression-models

Calculate the Error:

$$
\hat{y} =
\frac{1}{n} 
\sum_{j=1}^{n}   
|    y_j - \hat{y}_j     |
$$

Understanding the difference:

• train and test on the same data
• High training accuracy is not necessarily a good thing
• Overfitting
• memorized the input to output data and produced a non-generalized model
• aka: rote learning
• provides bad results for the input data that the model was not trained on
• train and test on the split data

Wrong "Out of Sample Accuracy" is the percentage of correct predictions that the model makes on data that the model has NOT been trained on.

"Out of Sample Accuracy" is the accuracy of an overly trained model (which may capture noise and produced a non-generalized model)

Evaluation:

• testing on the portion of the test data (not split, not randomized)
• high "training accuracy"
• low "out of sample" accuracy
• testing on the split data (randomized)
• more accurate evaluation for "out of sample" accuracy
• highly dependent on which data is selected

K-fold cross-validation

Evaluation Metrics in Regression Models

https://www.coursera.org/learn/machine-learning-with-python/lecture/5SxtZ/evaluation-metrics-in-regression-models

Error definition:

The difference between observed data points ($ y_i $) and the fitted trend (regression) line values ($ \hat{y} $).

Mean Absolute Error (MAE):    

• easy to understand

$$
MAE =
\frac{1}{n}
\sum_{j=1}^{n}
    | \hspace{0.5em}
      y_j - \hat{y}_j
    \hspace{0.5em} |
$$

Mean Squared Error (MSE):

• more commonly used
• stresses the large errors, exponentially increasing them (hence $ error^2 $)

$$
MSE =
\frac{1}{n}
\sum_{j=1}^{n}
    \left(
      y_j - \hat{y}_j
    \right)^2
$$

Root Mean Squared Error (RMSE):

• MOST commonly used
• interpretable in the same units as the response vector, or y-units, easy to relate the information

$$
RMSE =
\sqrt{
  \frac{1}{n}
  \sum_{j=1}^{n}
      \left(
        y_j - \hat{y}_j
      \right)^2
}
$$


Relative Absolute Error (RAE):

• aka: residual sum of squares
• normalizes the value by dividing the derived error by the mean error

$$
RAE =
\frac
{
  \sum_{j=1}^{n}
      |
        y_j - \hat{y}_j
      |
}{
  \sum_{j=1}^{n}
      |
        y_j - \bar{y}
      |
}
$$

Relative Absolute Error (RSE):

• widely used by the data community to calculate $ R^2 $
• $ R^2 = 1- RSE $
• it is a popular metric of your model: shows how close the data values are to the fitted regression line
• the higher the $ R^2 $ the better the model fits your data

$$
RAE =
\frac
{
  \sum_{j=1}^{n}
      \left(
        y_j - \hat{y}_j
      \right)^2
}{
  \sum_{j=1}^{n}
      \left(
        y_j - \bar{y}
      \right)^2
}
$$

You should do your own investigation of when to use each error estimation method.

Lab: Simple Linear Regression (1hr)

https://www.coursera.org/learn/machine-learning-with-python/ungradedLti/X7V0r/lab-simple-linear-regression

At this point, I decided that adding about 1 hour of setup work will be beneficial in the long run:

• create a private GitHub repo for the University of London CS that will include a directory for this certification:
  https://github.com/UkiDLucas/UoL_CS
• Install Anaconda Python environment with Jupyter Notebook, etc. 
  https://uki.blogspot.com/2018/10/conda-environment-as-jupyter-notebook.html
• locally this looks like this:
  
  

_REPOS/UoL_CS/IBM_AI_Eng/ML_Python/ML0101EN-Reg-Simple-Linear-Regression-Co2.ipynb

Multiple Linear Regression

https://www.coursera.org/learn/machine-learning-with-python/lecture/0y8Cq/multiple-linear-regression

When should I use Multiple Linear Regression?

- When there are multiple dependent variables and EACH independent variable has a linear correlation with the dependent variable.

• Most of the applications of Linear Regression use multiple variables.

$$  \hat{y} = \theta_0 + \theta_1 x_1 + \theta_2 x_2 + ... + \theta_n x_n $$

$$  \hat{y} = \theta^T  X $$

$$  \theta^T = \left[ \theta_0, \theta_1, \theta_2, ... \right] $$

 

$$
X = \begin{bmatrix}
1 \\
x_1 \\
x_2 \\
x_3 \\
\vdots
\end{bmatrix}
$$

Where:

• $  \hat{y} $ is a "dot" product of two vectors $ \theta^T  X $, 
• in one-dimensional space, it is an equation of a line
• in two-dimensional space, it is a plane
• in multi-dimensional space, it is a hyper-plane
• $ \theta^T  $ is the n-by-1 vector of unknown parameters in the multi-dimensional space, 
• traditionally it is shown as transpose $ \theta $, 
• it is also called: 
• the vector of parameters, 
• vector of coefficients, 
• or the weight vector of the regression equation
• T indicates "transpose" (see reference 4)
• X is the feature set vector
• the first element of X is 1, an intercept, or bias parameter

We have to optimize the parameters $ \theta $ in $  \hat{y} = \theta^T  X $ to result in the fewest errors.

• For example, let's assume:
• for a given set of parameters we get the result for row 1:
• $  \hat{y}_1 $ = 140
• from the observation dataset, we see
• $  y_1 $ = 196
• hence:
• $  y_1 - \hat{y} $ = 196 -140 = 56 
• which is called residual error for a single observation
• or distance from the regression line

We can use the Means Square Error formula to calculate the error for all the observations:

$$
MSE =
\frac{1}{n}
\sum_{j=1}^{n}
    \left(
      y_j - \hat{y}_j
    \right)^2
$$

Methods to find optimal coefficients:

• Ordinary Least Squares
• Linear algebra operations
• it takes a long time for large datasets (10k+ rows)
• Scikit-learn uses the plain Ordinary Least Squares method
• Optimization Approach
• Gradient Decent
• a proper approach for the large data sets

Concerns:

• multiple linear regression may give you a better predictive model
• avoid overfitting
• convert variables to continuous numbers
• analyze the relationships between dependent and independent variables
• use scatterplots to check for linearity, if there is no dependency then do not use it

Lab: Multiple Linear Regression

https://www.coursera.org/learn/machine-learning-with-python/ungradedLti/EkvC6/lab-multiple-linear-regression

Non-Linear (Polynomial) Regression

Non-linear regression is a method to model the non-linear relationship between the independent variables 𝑥x and the dependent variable 𝑦y. Essentially any relationship that is not linear can be termed as non-linear and is usually represented by the polynomial of 𝑘k degrees (maximum power of 𝑥x). For example:

$$ 𝑦 = 𝑎𝑥^3 + 𝑏𝑥^2 + 𝑐𝑥 + 𝑑 $$

Non-linear functions can have elements like exponentials, logarithms, fractions, etc. For example:
$$ 𝑦 = log(𝑥) $$

$$  \hat{y} = \frac{ \theta_0 }{ 1 + \theta_1^ \left( x -  \theta_2 \right) } $$

We can have a function that's even more complicated such as :

$$ 𝑦 = log(𝑎𝑥^3 + 𝑏𝑥^2 + 𝑐𝑥 + 𝑑) $$

How do we know whether the problem is linear or non-linear?

• inspect data visually
• fit non-linear model
• transform your data

Exponential (hockey stick) functions:

$$  \hat{y} =
\theta_0
+ \theta_1
\theta_2^x
$$

Logarithmic (inverse hockey stick) Regression

$$  \hat{y} =
\log{
  \left(
     \theta_0
  + \theta_1 x
  + \theta_2 x^2 
  + \theta_3 x^3 
 \right)
 }
$$

In the case below, 

$$  \hat{y} =  
\theta_0
+ \theta_1  
\log{x}
$$

Quadratic (parabolic) Regression

$$  \hat{y} =
\theta_0
+ \theta_1 x
+ \theta_2 x^2
$$

in the example below:

$$  \hat{y} =
\theta_0 * 0
+ \theta_1 x * 0
+ \theta_2 x^2
$$

Cubic (s-curve) Polynomial (3rd degree) Regression

$$  \hat{y} =
\theta_0
+ \theta_1 x
+ \theta_2 x^2
+ \theta_3 x^3
$$

Logistic Regression (sigmoid curve)

generic:

$$ Y = a + \frac{b}{1+ c^{(X-d)}} $$

Specific below:

$$ Y = \hat{y} = 0 + \frac{-3}{1 + 3^{(X-2)}} $$

Given the 3rd-degree polynomial equation:

$$
x_1 = x \\
x_2 = x^2 \\
x_3 = x^3
$$

The model is converted to a simple (special case of multiple) linear regression:

$$  \hat{y} =
\theta_0
+ \theta_1 x_1
+ \theta_2 x_2
+ \theta_3 x_3
$$

Least Squares is a method of estimating unknown parameters in a linear regression model by 
minimizing the sum of the squares of the differences between $ y $ and  $\hat{y} $.

Please continue to Classification:
https://uki.blogspot.com/2022/10/classification.html

References

1. https://oeis.org/wiki/List_of_LaTeX_mathematical_symbols
2. https://tex.stackexchange.com/questions/13865/how-to-use-latex-on-blogspot
3. Special Characters (i.e. Greek) LaTex https://uki.blogspot.com/search/label/Jupyther%20Lab
4. https://en.wikipedia.org/wiki/Transpose
   
5. https://www.atqed.com/latex-column-vector