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283 comment karma

account created: Fri Jul 31 2020

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1 points

5 days ago

Hey, thanks for watching! Could you expand a bit more? Other than the fact that the target function is linear, why would it be called linear regression?

6 points

5 days ago

I started a channel VisuallyExplained where I try to make some important concepts in math, engineering, and machine learning as visual and intuitive as possible. I recently adopted a short and fast-paced style of 2 or 3 minute videos on any concept. Hope you like it.

5 points

19 days ago

OP here. Thanks for watching the video! I completely agree with your comment. I didn't realize how loud the music was until I posted the video on youtube (and used a different headphone). I will try not to make the same mistake again.

2 points

20 days ago

You asked very good questions. Explaining the whole theory behind Linear Programming would take a full semester of undergrad courses, but below is a brief answer to your questions. Just to make clear what we are trying to do here, we are trying to find the point x inside the pink set (sometimes called the *feasible set*) that makes the *objective function*

c^Tx

as large as possible. Here c is an arbitrary vector of R^n. Such an x is referred to as the optimal solution.

why must the solution be on a boundary?

The short answer is because the feasible set (i.e.e, the pink set) is convex, and the objective function (f(x) = c^Tx) is a linear function in x. The longer and more intuitive answer is that if you are at a point x strictly inside the feasible set (i.e., not in the boundary), you can move a little bit in the direction of the vector c and make c^Tx larger, hence x cannot be the optimal solution.

what functions are driving the particle toward the solution?

There are two algorithms presented in this animation, and they work in different manner.

- The simplex method starts on one of the vertices, and jumps to the neighboring vertex that has the largest objective value. It's a greedy algorithm.

- The interior point method is slightly more complicated, but essentially, the path that you see in the animation is parameterized in the following way:

`x(t) = argmax c^Tx + t * P(x)`

where P(x) is a penalty function that takes smaller and smaller values as you approach the boundary of the feasible set. On the boundary its value is -infty. I have a video about this fascinating algorithm if you're interested:

19 points

20 days ago

I made this animation for my video on the topic of linear programming (LP).

Most people in ML probably start directly with complicated models Neural Networks, but as is often the case, a simple model (e.g., a linear one) is much appropriate, and if not, then at least it gives a good baseline for all the future complications your want to try.

Linear Programming is arguably the most useful method is all of mathematical optimization, and there is a big ongoing effort to improve solve methods. This animation illustrate the two main methods for doing that: the Simplex method that jumps for one vertex to the next hoping to improve the solution, and the interior point method that goes through the feasible set towards the optimal solution.

1 points

21 days ago

This is a good place to start: https://try.manim.community/

(Look up some beginner's Python tutorial first, but there are tons of those on the net)

1 points

21 days ago

The (La)tex is manim, the 3D stuff is blender3d.

view more:

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## Impressive_Path2037

1 points

3 days ago

Impressive_Path2037

1 points

3 days ago

Fair enough, thank you for letting me know the reason.