Summer of Math Exposition

The intuition about the MLE converging to a circle is something I haven’t seen before and made some things click for me! The animations are good and the explanation tol, although a small recap of what we are doing might be nice. The ending was slightly abrupt, I expected some take-home message.

While the motivation is sort of made clear at the start, a lot of the video feels like a part of a college lecture where you have to push through the terse information./////

The video was very confusing I think, a lot of different concepts were mixed together and I do not really understand why and how. I know quite a bit about maximum likelihood, and I also understand the principle behind neural networks. Most of the time we it is not maximum likelihood that is used by neural networks. We use empirical risk minimization and the loss may come from likelihood or for another thing entirely (for example the huber loss, cosine similarity… are a lot of losses that do not come initially from maximum likelihood). Moreover in the setting of neural networks, as soon as there is more than one layer, there is often not unicity of the parameter to which the neural network converges so the parameter would not converge as cleanly as what is depicted as the model is not regular and usual maximum likelihood convergence does not hold.

In my opinion the animation are quite nice by the content should be reworked in depth.

I really liked the video and especially the converging likelihood estimations! However, I found that they were kind of overlooked by either too much or too few explanations. Indeed, I would personally either remove the few equations you have and solely try to create an intuition on how the estimation works (for example by playing more the game of “where will it converge”), or go deeper into the mathematical aspects of the problem (for example by providing a quick intuitive proof on why the points converge as they do). In its current form, I personally do not really understand why this weird convergence occurs, but would have loved to do so, either fundamentally or intuitively :).

Overall, quite pleasant to watch, with cool converging animations!

PS: I understand that using keywords like “AI” and “Machine Learning” can appeal to some viewers, but I do not believe what you did in the end was more than standard statistics, and would thus either not mention these topics, or circle back to them at the end of the video to explain the link with what you did.

Maybe a clearer motivation on why one should care about interactive systems (Where are they used? What benefit over other systems/ when are they necessary to use). The conclusion feels a little abrupt; I feel the main takeaway of this video (how the structure of the self-coherent set can be used to infer better estimators) is not emphasized enough.

I thought the explanations were decently clear, but was confused by some of the equations not being fully explained. The mic quality was very poor, I would expect much better nowadays. It still managed to engage me enough to watch through the whole thing.

A nicely-animated video a topic I’ve never seen, with some cool surprising geometry.

I might have liked some more real-world-feeling applications/examples to tell a more compelling story.