An introduction to one of the the most basic structures used in machine learning: a tensor.

🧵👇

Tensors are the data structure used by machine learning systems, and getting to know them is an essential skill you should build early on.

A tensor is a container for numerical data. It is the way we store the information that we'll use within our system.

(2 / 16)
Three primary attributes define a tensor:

▫️ Its rank
▫️ Its shape
▫️ Its data type

(3 / 16)
The rank of a tensor refers to the tensor's number of axes.

Examples:

▫️ The rank of a matrix is 2 because it has two axes.
▫️ The rank of a vector is 1 because it has a single axis.

(4 / 16)
The shape of a tensor describes the number of dimensions along each axis.

Example:

▫️ A square matrix may have (3, 3) dimensions.
▫️ A tensor of rank 3 may have (2, 5, 7) dimensions.

(5 / 16)
The data type of a tensor refers to the type of data contained in it.

For example, when thinking about Python 🐍's numpy library, here are some of the supported data types:

▫️ float32
▫️ float64
▫️ uint8
▫️ int32
▫️ int64

(6 / 16)
In the previous tweets I used the terms "vector" and "matrix," to referr to tensors with a specific rank (1 and 2 respectively.)

We can also use these mathematical concepts when describing tensors.

(7 / 16)
A scalar —or a 0D tensor— has rank 0 and contains a single number. These are also called "0-dimensional tensors."

The attached image shows how to construct a 0D tensor using numpy. Notice its shape and its rank (.ndim attribute.)

(8 / 16)
A vector —or a 1D tensor— has rank 1 and represents an array of numbers.

The attached image shows a vector with shape (4, ). Notice how its rank (.ndim attribute) is 1.

(9 / 16)
A matrix —or a 2D tensor— has rank 2 and represents an array of vectors. The two axes of a matrix are usually referred to as "rows" and "columns."

The attached image shows a matrix with shape (3, 4).

(10 / 16)
You can obtain higher-dimensional tensors (3D, 4D, etc.) by packing lower-dimensional tensors in an array.

For example, packing a 2D tensor in an array gives us a 3D tensor. Packing this one in another array gives us a 4D tensor, and so on.

(11 / 16)
Here are some common tensor representations:

▫️ Vectors: 1D - (features)
▫️ Sequences: 2D - (timesteps, features)
▫️ Images: 3D - (height, width, channels)
▫️ Videos: 4D - (frames, height, width, channels)

(12 / 16)
Commonly, machine learning algorithms deal with a subset of data at a time (called "batches.")

When using a batch of data, the tensor's first axis is reserved for the size of the batch (number of samples.)

(13 / 16)
For example, if your handling 2D tensors (matrices), a batch of them will have a total of 3 dimensions:

▫️ (samples, rows, columns)

Notice how the first axis is the number of matrices that we have in our batch.

(14 / 16)
Following the same logic, a batch of images can be represented as a 4D tensor:

▫️ (samples, height, width, channels)

And a batch of videos as a 5D tensor:

▫️ (samples, frames, height, width, channels)

(15 / 16)
If all of this makes sense, you are on your way! If something doesn't click, reply with your question, and I'll try to answer.

Either way, make sure to follow me for more machine learning content! 2021 is going to be great!

(16 / 16)

More from Santiago

You gotta think about this one carefully!

Imagine you go to the doctor and get tested for a rare disease (only 1 in 10,000 people get it.)

The test is 99% effective in detecting both sick and healthy people.

Your test comes back positive.

Are you really sick? Explain below 👇

The most complete answer from every reply so far is from Dr. Lena. Thanks for taking the time and going through


You can get the answer using Bayes' theorem, but let's try to come up with it in a different —maybe more intuitive— way.

👇


Here is what we know:

- Out of 10,000 people, 1 is sick
- Out of 100 sick people, 99 test positive
- Out of 100 healthy people, 99 test negative

Assuming 1 million people take the test (including you):

- 100 of them are sick
- 999,900 of them are healthy

👇

Let's now test both groups, starting with the 100 people sick:

▫️ 99 of them will be diagnosed (correctly) as sick (99%)

▫️ 1 of them is going to be diagnosed (incorrectly) as healthy (1%)

👇

More from Machine learning

With hard work and determination, anyone can learn to code.

Here’s a list of my favorites resources if you’re learning to code in 2021.

👇

1. freeCodeCamp.

I’d suggest picking one of the projects in the curriculum to tackle and then completing the lessons on syntax when you get stuck. This way you know *why* you’re learning what you’re learning, and you're building things

2.
https://t.co/7XC50GlIaa is a hidden gem. Things I love about it:

1) You can see the most upvoted solutions so you can read really good code

2) You can ask questions in the discussion section if you're stuck, and people often answer. Free

3. https://t.co/V9gcXqqLN6 and https://t.co/KbEYGL21iE

On stackoverflow you can find answers to almost every problem you encounter. On GitHub you can read so much great code. You can build so much just from using these two resources and a blank text editor.

4. https://t.co/xX2J00fSrT @eggheadio specifically for frontend dev.

Their tutorials are designed to maximize your time, so you never feel overwhelmed by a 14-hour course. Also, the amount of prep they put into making great courses is unlike any other online course I've seen.
Happy 2⃣0⃣2⃣1⃣ to all.🎇

For any Learning machines out there, here are a list of my fav online investing resources. Feel free to add yours.

Let's dive in.
⬇️⬇️⬇️

Investing Services

✔️ @themotleyfool - @TMFStockAdvisor & @TMFRuleBreakers services

✔️ @7investing

✔️ @investing_city
https://t.co/9aUK1Tclw4

✔️ @MorningstarInc Premium

✔️ @SeekingAlpha Marketplaces (Check your area of interest, Free trials, Quality, track record...)

General Finance/Investing

✔️ @morganhousel
https://t.co/f1joTRaG55

✔️ @dollarsanddata
https://t.co/Mj1owkzRc8

✔️ @awealthofcs
https://t.co/y81KHfh8cn

✔️ @iancassel
https://t.co/KEMTBHa8Qk

✔️ @InvestorAmnesia
https://t.co/zFL3H2dk6s

✔️

Tech focused

✔️ @stratechery
https://t.co/VsNwRStY9C

✔️ @bgurley
https://t.co/NKXGtaB6HQ

✔️ @CBinsights
https://t.co/H77hNp2X5R

✔️ @benedictevans
https://t.co/nyOlasCY1o

✔️

Tech Deep dives

✔️ @StackInvesting
https://t.co/WQ1yBYzT2m

✔️ @hhhypergrowth
https://t.co/kcLKITRLz1

✔️ @Beth_Kindig
https://t.co/CjhLRdP7Rh

✔️ @SeifelCapital
https://t.co/CXXG5PY0xX

✔️ @borrowed_ideas

You May Also Like

@franciscodeasis https://t.co/OuQaBRFPu7
Unfortunately the "This work includes the identification of viral sequences in bat samples, and has resulted in the isolation of three bat SARS-related coronaviruses that are now used as reagents to test therapeutics and vaccines." were BEFORE the


chimeric infectious clone grants were there.https://t.co/DAArwFkz6v is in 2017, Rs4231.
https://t.co/UgXygDjYbW is in 2016, RsSHC014 and RsWIV16.
https://t.co/krO69CsJ94 is in 2013, RsWIV1. notice that this is before the beginning of the project

starting in 2016. Also remember that they told about only 3 isolates/live viruses. RsSHC014 is a live infectious clone that is just as alive as those other "Isolates".

P.D. somehow is able to use funds that he have yet recieved yet, and send results and sequences from late 2019 back in time into 2015,2013 and 2016!

https://t.co/4wC7k1Lh54 Ref 3: Why ALL your pangolin samples were PCR negative? to avoid deep sequencing and accidentally reveal Paguma Larvata and Oryctolagus Cuniculus?