is a hyperparameter, and are common choices when doing dataset exploration, as they can be easily visualized on a planar plot.
The mapping is done by projecting all points to a dimensional hyperplane. PCA is an algorithm for choosing this hyperplane and the coordinate system within this hyperplane.
The hyperplane choice is done as follows:
- the hyperplane will have origin at the mean point
- the first axis is picked along the direction of greatest variance, i.e. where points are the most spread out.Intuitively, if we pick an axis of small variation, that would be bad, because all the points are very close to one another on that axis, so it doesn't contain as much information that helps us differentiate the points.
- then we pick a second axis, orthogonal to the first one, and on the direction of second largest variance
- and so on until orthogonal axes are taken
www.sartorius.com/en/knowledge/science-snippets/what-is-principal-component-analysis-pca-and-how-it-is-used-507186 provides an OK-ish example with a concrete context. In there, each point is a country, and the input data is the consumption of different kinds of foods per year, e.g.:so in this example, we would have input points in 4D.
- flour
- dry codfish
- olive oil
- sausage
Suppose that every country consumes the same amount of flour every year. Then, that number doesn't tell us much about which country each point represents (has the least variance), and the first PCA axes would basically never point anywhere near that direction.
Another cool thing is that PCA seems to automatically account for linear dependencies in the data, so it skips selecting highly correlated axes multiple times. For example, suppose that dry codfish and olive oil consumption are very high in Portugal and Spain, but very low in Germany and Poland. Therefore, the variation is very high in those two parameters, and contains a lot of information.
However, suppose that dry codfish consumption is also directly proportional to olive oil consumption. Because of this, it would be kind of wasteful if we selected:since the information about codfish already tells us the olive oil. PCA apparently recognizes this, and instead picks the first axis at a 45 degree angle to both dry codfish and olive oil, and then moves on to something else for the second axis.
In the case of machine learning in particular, it is not part of the training data set.
Hyperparameters can also be considered in domains outside of machine learning however, e.g. the step size in partial differential equation solver is entirely independent from the problem itself and could be considered a hyperparamter. One difference from machine learning however is that step size hyperparameters in numerical analysis are clearly better if smaller at a higher computational cost. In machine learning however, there is often an optimum somewhere, beyond which overfitting becomes excessive.
An impossible AI-complete dream!
It is impossible to understand speech, and take meaningful actions from it, if you don't understand what is being talked about.
- analyticsindiamag.com/5-open-source-recommender-systems-you-should-try-for-your-next-project/ 5 Open-Source Recommender Systems You Should Try For Your Next Project (2019)
It seems impossible to avoid the signaling server. With signaling server:
Tested on Ubuntu 23.10;
git clone https://github.com/google-deepmind/mujoco
cd mujoco
git checkout 5d46c39529819d1b31249e249ca399f306a108ac
mkdir -p build
cd build
cmake ..
make -jNow let's play. Minimal interactive UI simulation of a simple MJCF scene with one falling cube:Test soure code: github.com/google-deepmind/mujoco/blob/5d46c39529819d1b31249e249ca399f306a108ac/sample/basic.cc. The only thing you can do is rotate the scene with the computer mouse it seems. Mentioned at: mujoco.readthedocs.io/en/2.2.2/programming.html#sabasic
bin/basic ../doc/_static/hello.xmlSome more interesting models can be found under the
model/ directory: github.com/google-deepmind/mujoco/tree/5d46c39529819d1b31249e249ca399f306a108ac/model E.g. the imaginary humanoid robot DeepMind used in many demos can be seen with:bin/basic ../model/humanoid/humanoid.xmlA more advanced UI with a few controls:Test soure code: github.com/google-deepmind/mujoco/tree/5d46c39529819d1b31249e249ca399f306a108ac/simulate. Mentioned at: mujoco.readthedocs.io/en/2.2.2/programming.html#sasimulate
bin/simulate ../doc/_static/hello.xmlA very cool thing about that UI is that you can manually control joints. There are no joints in the hello.xml, but e.g. with the humanoid model:under "Control" you move each joint of the robot separately which is quite cool.
bin/simulate ../model/humanoid/humanoid.xmlThere's also a Mentioned at: mujoco.readthedocs.io/en/2.2.2/programming.html#sarecord but TODO that produced a broken video, related issues:
bin/record test executable that presumably renders the simulation directly to a file:bin/record ../doc/_static/hello.xml 5 60 rgb.out
ffmpeg -f rawvideo -pixel_format rgb24 -video_size 800x800 -framerate 60 -i rgb.out -vf "vflip" video.mp4 Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact