.

In this series, we discuss a technique to find either the minima or the roots of a chaotic, unsmooth, or discrete function. A root-finding technique that works well for continuous, differentiable functions is successfully adapted and applied to piece-wise constant functions with an infinite number of discontinuities. It even works if the function has no root:…

ContinueAdded by Vincent Granville on October 23, 2021 at 6:30pm — No Comments

*Source: see last section in this article*

During the October 4, 2021 great Facebook outage, which lasted for over 6 hours, making all FB properties (including Instagram, Snapshot, and even internal tools employees at FB use to communicate between themselves or even to enter the building) were down. Twitter's…

ContinueAdded by Vincent Granville on October 5, 2021 at 8:30pm — No Comments

*Source: see last section in this article*

Of course this question begs for the answer that it is both an art and a science. I view it more like craftsmanship. This article discusses my opinion on the subject.

We need to start by defining what machine learning is, or more precisely, what kind of work it…

ContinueAdded by Vincent Granville on October 3, 2021 at 2:00pm — No Comments

It is often said that data science jobs are for seasoned professionals, and many job ads still show a preference for a profile with a PhD, with years of experience. Yet, many corporate employers have been disillusioned about the value that a PhD brings to the company. Likewise, many professionals, especially among those who just completed a PhD and…

ContinueAdded by Vincent Granville on September 25, 2021 at 11:00am — No Comments

This question is raised on occasion. Salaries are not increasing as fast as they used to, though this is natural for any discipline reaching some maturity. Some job seekers claim it is not that easy anymore to find a job as a data scientist. Some employers have complained about the costs associated with a data science team, and ROI expectations not…

ContinueAdded by Vincent Granville on September 12, 2021 at 6:30pm — No Comments

This article focuses on the machine learning aspects of the problem, and the use of pattern recognition techniques leading to interesting, new findings about twin primes. Twin primes are prime numbers *p* such that *p* + 2 is also prime. For instance, 3 and 5, or 29 and 31. A famous, unsolved and old mathematical conjecture states that…

Added by Vincent Granville on September 7, 2021 at 6:30am — No Comments

*Dynamical system used in weather prediction (see here)*

We are dealing here with random variables recursively defined by *X**n*+1 =…

Added by Vincent Granville on August 26, 2021 at 7:00pm — No Comments

These Fourier series can be considered as bivariate time series (*X*(*t*), *Y*(*t*)) where *t* is the time, *X*(*t*) is a weighted sum of cosine terms of arbitrary periods, and *Y*(*t*) is the same sum, except that cosine is replaced by sine. The orbit at time *t* is…

Added by Vincent Granville on August 17, 2021 at 8:00pm — No Comments

This article is part of a new series featuring problems with solution, to help you hone your machine learning and pattern recognition skills. Try to solve this problem by yourself first, before looking at the solution. Today's problem also has an intriguing mathematical appeal and solution: this allows you to check if your solution found using machine…

ContinueAdded by Vincent Granville on July 28, 2021 at 8:30pm — No Comments

This is not a discussion as to whether the data is flawed or not, or whether we are comparing apples to oranges or not (the way statistics are gathered in different countries). These are of course fundamental questions, but here I will only use data (provided by Google) that everyone seem to more or less agree with, and I am not questioning it…

ContinueAdded by Vincent Granville on July 18, 2021 at 7:30pm — 1 Comment

The original version of the central limit theorem (CLT) assumes *n* independently and identically distributed (i.i.d.) random variables *X*1, ..., *Xn*, with finite variance. Let *Sn* = *X…*

Added by Vincent Granville on July 15, 2021 at 7:30pm — No Comments

*Source: here*

If you are wondering how much a data scientist earns, whether you are a hiring manager or looking for a job, there are plenty of websites…

ContinueAdded by Vincent Granville on July 7, 2021 at 7:49pm — No Comments

This is part of a series featuring the following aspects of machine learning:

- Mathematics, simulations, benchmarking algorithms based on synthetic data (in short,…

Added by Vincent Granville on June 19, 2021 at 7:26am — No Comments

In this article, I describe the various steps involved in managing a machine learning process from beginning to end. Depending on which company you work for, you may or may not be involved in all the steps. In larger companies, you typically focus on one or two specialized aspects of a project. In small companies, you may be involved in all…

ContinueAdded by Vincent Granville on June 12, 2021 at 7:00pm — No Comments

As a machine learning professional, I have worked for several startups ranging from zero to 600 employees, as well as companies such as eBay, Wells Fargo, Visa and Microsoft. Here I share my experience. A brief summary can be found in my conclusions, at the bottom of this article.

It is not easy to define what a startup is. The first…

ContinueAdded by Vincent Granville on June 3, 2021 at 6:30pm — 1 Comment

In this article, I illustrate the concept of asymmetric key with a simple example. Rather than discussing algorithms such as RSA, (still widely used, for instance to set up a secure website) I focus on a system easier to understand, based on random permutations. I discuss how to generate these random permutations and compound them, and how to…

ContinueAdded by Vincent Granville on June 1, 2021 at 7:30pm — No Comments

Many of us have solid foundations in math or have an interest in learning more, and are passionate about solving difficult problems during our free time. Of course, most of us are not professional mathematicians, but we may bring some value to help solve some of the most challenging mathematical conjectures, especially the ones that can be…

ContinueAdded by Vincent Granville on May 25, 2021 at 7:30pm — 1 Comment

This is part of a series featuring the following aspects of machine learning:

- Mathematics, simulations, benchmarking algorithms based on synthetic data (in short, experimental data science)
- Opinions, for instance about the value of a PhD in our field, or the use of some…

Added by Vincent Granville on May 19, 2021 at 6:26pm — No Comments

*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…

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

*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…

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

- A New Machine Learning Optimization Technique - Part I
- Lessons to be Learned from the Facebook Outage
- Is Machine Learning an Art, a Science or Something Else?
- Machine Learning Career: Pros and Cons of Having a PhD
- Are Data Scientists Becoming Obsolete?
- Machine Learning Perspective on the Twin Prime Conjecture
- The Inverse Problem in Random Dynamical Systems

- 88 percent of all integers have a factor under 100
- 29 Statistical Concepts Explained in Simple English - Part 1
- Machine Learning Summarized in One Picture
- Data Science Summarized in One Picture
- Deep Learning versus Machine Learning in One Picture
- The Mathematics of Machine Learning
- Big Data and Data Science. Some reflections on compensation levels

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