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Vincent Granville's Blog (1,568)

Fascinating Facts About Complex Random Variables and the Riemann Hypothesis

Orbit of the Riemann zeta function in the complex plane (see also here)

Despite my long statistical and machine learning career both in academia and in…

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Added by Vincent Granville on May 9, 2021 at 8:00am — 1 Comment

What I Learned From 25 Years of Machine Learning

Source: here

Here is what I learned from practicing machine learning in business settings for over two decades, and prior to that in the academia. Back in the nineties, it was known as computational…

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Added by Vincent Granville on May 3, 2021 at 9:00pm — No Comments

More Machine Learning Tricks, Recipes, and Statistical Models

Source for picture: here

The first part of this list was published…

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Added by Vincent Granville on April 29, 2021 at 6:57pm — No Comments

Unusual Opportunities for AI, Machine Learning, and Data Scientists

Here some off-the-beaten-path options to consider, when looking for a first job, a new job or extra income by leveraging your machine learning experience. Many were offers that came to my mailbox at some point in the last 10 years, mostly from people looking at my LinkedIn profile. Thus the importance of growing your network and visibility, write…

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Added by Vincent Granville on April 19, 2021 at 4:30pm — No Comments

Simple Machine Learning Approach to Testing for Independence

We describe here a methodology that applies to any statistical test, and illustrated in the context of assessing independence between successive observations in a data set. After reviewing a few standard approaches, we discuss our methodology, its benefits, and drawbacks. The data used here for illustration purposes, has known theoretical…

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Added by Vincent Granville on April 7, 2021 at 9:00pm — No Comments

A Plethora of Machine Learning Tricks, Recipes, and Statistical Models

Source: See article #5, in section 1

Part 2 of this short series focused on fundamental techniques, see here. In this Part 3, you will find several…

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Added by Vincent Granville on April 5, 2021 at 6:59pm — No Comments

Defining and Measuring Chaos in Data Sets: Why and How, in Simple Words

There are many ways chaos is defined, each scientific field and each expert having its own definitions. We share here a few of the most common metrics used to quantify the level of chaos in univariate time series or data sets. We also introduce a new, simple definition based on metrics that are familiar to everyone. Generally speaking, chaos…

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Added by Vincent Granville on March 28, 2021 at 3:00pm — No Comments

Hurwitz-Riemann Zeta And Other Special Probability Distributions

Source: here

In my previous article here, I discussed a…

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Added by Vincent Granville on March 21, 2021 at 8:30pm — No Comments

An Easy Way to Solve Complex Optimization Problems in Machine Learning

Source: here

There are numerous examples in machine learning, statistics, mathematics and deep learning, requiring an algorithm to solve some complicated equations: for instance, maximum likelihood…

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Added by Vincent Granville on March 7, 2021 at 6:30pm — No Comments

A Plethora of Machine Learning Articles: Part 2

Source:…

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Added by Vincent Granville on March 3, 2021 at 4:44pm — No Comments

A Plethora of Machine Learning Articles: Part 1

Source: see here

In Part 1 of this short series, I have included the most interesting articles that I wrote in the last few years. This part focuses on the business analytics / BI /…

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Added by Vincent Granville on February 21, 2021 at 2:30pm — No Comments

Maximum runs in Bernoulli trials: simulations and results

Bernoulli trials are random experiments with two possible outcomes: "yes" and "no" (in the case of polls),  "success" and "failure" (in the case of gambling or clinical trials). The trials are independent from each other: for instance tossing a coin multiple times, or testing the success of a new drug against a specific…

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Added by Vincent Granville on February 15, 2021 at 11:00pm — No Comments

More Surprising Math Images

To zoom in on any picture, click on the image to get a higher resolution.

This a follow up to my previous article here, where you can find additional, very different images, the theory behind it, and relevance to machine learning techniques. What is surprising is that all these images were produced with a formula with a single parameter λ, and…

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Added by Vincent Granville on February 7, 2021 at 7:30pm — No Comments

Beautiful Mathematical Images

To zoom in on any picture, click on the image to get a higher resolution.

Figure 1: The pillow basins (see section 3)

The topic discussed here is closely related to optimization techniques in machine…

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Added by Vincent Granville on February 2, 2021 at 10:30am — 1 Comment

Can a Diploma from a Lower Ranking University Hurt your Data Science Career Prospects?

Here I specifically discuss the case of a PhD degree from a third-tier university, though to some extent, it also applies to master degrees. Many professionals joining companies such as Facebook, Microsoft, or Google in a role other than a programmer, typically have a PhD degree, although there are many exceptions. It is still possible to learn data science on the job, especially if you have a quantitative background (say in physics or engineering) and have experience working with serious…

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Added by Vincent Granville on January 28, 2021 at 7:16pm — 1 Comment

Moving Averages: Natural Weights, Iterated Convolutions, and Central Limit Theorem

Convolution is a concept well known to machine learning and signal processing professionals. In this article, we explain in simple English how a moving average is actually a discrete convolution, and we use this fact to build weighted moving averages with natural weights that at the limit, have a Gaussian behavior guaranteed by the Central Limit Theorem. Moving averages are nothing more than blurring filters for signal processing experts, with a Gaussian-like kernel in the case discussed…

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Added by Vincent Granville on January 25, 2021 at 5:00pm — No Comments

Machine Learning / Stats / BI: Mini Translation Dictionary

Here I provide translations for various important terms, to help professionals from related backgrounds better understand each other. In particular, machine learning professionals versus statisticians.

Source for picture:…

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Added by Vincent Granville on January 18, 2021 at 9:12pm — No Comments

Deep visualizations to Help Solve Riemann's Conjecture

This is the second part of my article Spectacular Visualization: The Eye of the Riemann Zeta Function, focusing on the most infamous unsolved mathematical conjecture, one that has a $1 million dollar price attached to it. I used the word deep not in the sense of deep neural networks, but because the implications of these…

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Added by Vincent Granville on January 5, 2021 at 9:00pm — No Comments

Spectacular Visualization: The Eye of the Riemann Zeta Function

We discuss here one of the most famous unsolved mathematical conjectures of all times, one among seven that has a $1 million award attached to it, see here. It is known as the Riemann Hypothesis and abbreviated as RH. Of course I did not solve it (yet), but the material presented here offers a new…

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Added by Vincent Granville on January 2, 2021 at 11:30am — No Comments

Opening a New Restaurant in Covid Times

I am a data scientist, and decided to open a restaurant last November, 10 days before the governor in my state banned dining-in (who knows for how long) and customers were already rare. Some data scientists in managerial positions dream about exiting the corporate world and envied me, at least before the Covid, when I told them my plan.

Here I explore the options and opportunities available, and this article reflects my optimism. I will also discuss analytics in some detail. The…

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Added by Vincent Granville on December 22, 2020 at 9:44pm — No Comments

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