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Tivadar Danka

30 Sep, 8 tweets, 2 min read

🤔 Should you learn mathematics for machine learning?

Let's do a thought experiment! Imagine moving to a new country without speaking the language and knowing the way of life. However, you have a smartphone and a reliable internet connection.

How do you start exploring?

1/8

With Google Maps and a credit card, you can do many awesome things there: explore the city, eat in nice restaurants, have a good time.

You can do the groceries every day without speaking a word: just put the stuff in your basket and swipe your card at the cashier.

2/8

After a few months, you'll start to pick up some language as well—simple things, like saying greetings or introducing yourself. You are off to a good start!

There are built-in solutions for common tasks that just work. Food ordering services, public transportation, etc.

3/8

However, at some point, they will break down. For instance, you need to call the delivery person who dropped off your package at the wrong door. This requires communication.

You may also want to do more. Get a job, or perhaps even start your own business.

4/8

For that, you need to communicate with others effectively.

Taking time to learn the language when you plan to live somewhere for a few months is unnecessary.

However, if you want to stay there for the rest of your life, it is one of the best investments you can make.

5/8

Now replace the country with machine learning and the language with mathematics.

Fact is, algorithms are written in the language of mathematics. To work with algorithms on a professional level, you have to speak it.

6/8

I know, learning math can be tough.

This is where I come in. As an educator, my mission is to help you going through the world of math as efficiently as possible.

If you are at this stage of your career, I am writing THE book for you: the Mathematics of Machine Learning.

7/8

The early access just launched in September, where I publish one chapter per week, just as I write them.

The whole process is interactive, and I'll be there for you at every step.

Check it out and join the journey!

tivadar.gumroad.com/l/mathematics-…

8/8

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More from @TivadarDanka

Tivadar Danka

@TivadarDanka

29 Sep

I just released a new chapter for the early access of my book, the Mathematics of Machine Learning!

This week, we are diving deep into the geometry of matrices.

What does this have to do with machine learning? Read on to find out. ↓

tivadar.gumroad.com/l/mathematics-…

Matrices are the basic building blocks of learning algorithms.

Multiplying the data vectors with a matrix is equivalent to transforming the feature space. We think about this as a "black box", but there is a lot to discover.

For one, how they change the volume of objects.

This is described by the determinant of the matrix, which is given by

• how the transformation scales the volume,
• and how it changes the orientation of basis vectors.

The determinant is given by the formula below. I am a mathematician, and even I find this intimidating.

Read 5 tweets

Tivadar Danka

@TivadarDanka

21 Sep

You don't need to go to a university to learn machine learning - you can do it from your living room, for completely free.

Here is an extensive list of curated free courses and tutorials, from beginner to advanced. ↓

(Trust me, you want to bookmark this tweet.)

This is how I'll group the courses.

Machine learning
├── Getting started
├── Computer vision
├── NLP
├── Reinforcement learning
└── Applications

Coding
├── Python
├── R
├── Javascript
└── Machine learning frameworks

Let's start!

@3blue1brown

Machine learning
└── Getting started

1. Neural networks (by @3blue1brown)

youtube.com/playlist?list=…

Read 40 tweets

Tivadar Danka

@TivadarDanka

20 Sep

What do you get when you let a monkey randomly smash the buttons on a typewriter?

Hamlet from Shakespeare, of course. And Romeo and Juliet. And every other finite string that is possible.

Don't believe me? Keep reading. ↓

Let's start at the very beginning!

Suppose that I have a coin that, when tossed, has a 1/2 probability of coming up heads and a 1/2 probability of coming up tails.

If I start tossing the coin and tracking the result, what is the probability of 𝑛𝑒𝑣𝑒𝑟 having heads?

To answer this, first, we calculate the probability of no heads in 𝑛 tosses. (That is, the probability of 𝑛 tails.)

Since tosses are independent of each other, we can just multiply the probabilities for each toss together.

Read 14 tweets

Tivadar Danka

@TivadarDanka

16 Sep

Data similarity has such a simple visual interpretation that it will light all the bulbs in your head.

The mathematical magic tells you that similarity is given by the inner product. Have you thought about why?

This is how elementary geometry explains it all.

↓ A thread. ↓

Let's start in the beginning!

In machine learning, data is represented by vectors. So, instead of observations and features, we talk about tuples of (real) numbers.

Vectors have two special functions defined on them: their norms and inner products. Norms simply describe their magnitude, while inner products describe
.
.
.
well, a 𝐥𝐨𝐭 of things.

Let's start with the fundamentals!

Read 11 tweets

Tivadar Danka

@TivadarDanka

14 Sep

You are (probably) wrong about probability.

If I toss a fair coin ten times and it all comes up heads, what is the chance that the 11th toss will also be heads? Many think that it'll be highly unlikely. However, this is incorrect.

Here is why!

↓ A thread. ↓

In probability theory and statistics, we often study events in the context of other events.

This is captured by conditional probabilities, answering a simple question: "what is the probability of A if we know that B has occurred?".

Without any additional information, the probability that eleven coin tosses result in eleven heads in a row is extremely small.

However, notice that it was not our case. The original question was to find the probability of the 11th toss, given the result of the previous ten.

Read 10 tweets

Tivadar Danka

@TivadarDanka

1 Sep

The early access of my Mathematics of Machine Learning book is launching today!

One chapter per week, we go from basics to the internals of neural networks. We are starting with vector spaces, the scene where machine learning happens.

Here is why they are so important!

🧵 👇🏽

As you probably know, data is represented by vectors.

Data points are just tuples of measurements. In their raw form, they are hardly useful for us. They are just blips in space.

Without operations and transformations, it is difficult to predict class labels or do anything else.

Vector spaces provide a mathematical structure where operations naturally arise.

Instead of a blip, just imagine an arrow pointing to the data point from a fixed origin.

Read 11 tweets

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