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Vincent Granville's Blog – February 2019 Archive (5)

New Perspectives on Statistical Distributions and Deep Learning

In this data science article, emphasis is placed on science, not just on data. State-of-the art material is presented in simple English, from multiple perspectives: applications, theoretical research asking more questions than it answers, scientific computing, machine learning, and algorithms. I attempt here to lay the foundations of a new statistical technology, hoping that it will plant the seeds for further research on a topic with a broad range of potential…

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Added by Vincent Granville on February 23, 2019 at 11:00am — No Comments

A Plethora of Original, Not Well-Known Statistical Tests

Many of the following statistical tests are rarely discussed in textbooks or in college classes, much less in data camps. Yet they help answer a lot of different and interesting questions. I used most of them without even computing the underlying distribution under the null hypothesis, but instead, using simulations to check whether my assumptions were plausible or not. In short, my approach to statistical testing is is model-free, data-driven. Some are easy to implement even in Excel. Some…

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Added by Vincent Granville on February 13, 2019 at 7:00pm — No Comments

Machine Learning Glossary

For background to this post, please see Learn Machine Learning Coding Basics in a weekend. Here,we present the glossary that we use for the coding and the mindmap attached to these classes and upcoming book. About 80 terms are included in the glossary, covering Ensembles, Regression, Classification,…

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Added by Vincent Granville on February 12, 2019 at 12:31pm — No Comments

Alternatives to Logistic Regression

Logistic regression (LR) models estimate the probability of a binary response, based on one or more predictor variables. Unlike linear regression models, the dependent variables are categorical. LR has become very popular, perhaps because of the wide availability of the procedure in software. Although LR is a good choice for many situations, it doesn't work well for all situations. For example:

  • In propensity score…
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Added by Vincent Granville on February 7, 2019 at 3:23pm — No Comments

From Infinite Matrices to New Integration Formula

This is another interesting problem, off-the-beaten-path. It ends up with a formula to compute the integral of a function, based on its derivatives solely. 

For simplicity, I'll start with some notations used in the context of matrix theory, familiar to everyone: T(f) = g, where f and g are vectors, and T a square matrix. The notation T(f) represents the product between the matrix T, and the vector f. Now, imagine that the…

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Added by Vincent Granville on February 3, 2019 at 5:30pm — 1 Comment

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