# Obsidian Notes to Write 1. Note incorporating the ideas behind the actual translation and scaling of *space*, then applying a function on top of that. Circle example is great, we translate space "behind" the circle. The idea is to separate the circle from the specific space. How does scaling of a space factor in here? See your blog post on function composition. https://www.youtube.com/watch?v=CfW845LNObM, https://www.youtube.com/watch?v=mvmuCPvRoWQ&t=428s, https://en.wikipedia.org/wiki/Translation_(geometry)#:~:text=In%20Euclidean%20geometry%2C%20a%20translation,distance%20in%20a%20given%20direction. 1. [Scaling-Space-and-Function-Composition](Scaling-Space-and-Function-Composition.md) 2. [Relationship between Translating Space and Translating Objects](Relationship%20between%20Translating%20Space%20and%20Translating%20Objects.md) 3. Leaving off in concepts. Want to understand how translation doesn't need to be thought of as changing origin 4. In one case we are doing an implicit change of variables. This change of variables involves applying a change of variable function, which means we observed the “opposite” of what we expect. Hence, if look at f(x+3), we see that it is centered at x = -3, which may be the opposite of what we expect. This is because we are still evaluating wrt x, but we can say that u = x + 3. f(u) will look just like normal (a normal parabola). This is essentially the implicit c.o.v. I am talking about. f will always take in a number line and will always map 0 to 0, 1 to 1, 2 to 4, 3 to 9, and so on. So in a real sense, we are changing our variable from x to u, evaluating f as we always would, but - and this is the key idea - we still plot wrt to x. This is where the opposite behavior comes in! We know that, by the inverse c.o.v. formula, x = u - 3. We also know that f effectively saw u. If we plot f wrt x (instead of u) we will need to shift our number line TO THE LEFT 3 units (i.e. the subtraction in the inverse c.o.v. formula). It is in exactly this way that the subtle c.o.v. leads to needing to take the inverse of our addition, which is a subtraction, and this is what leads us to feeling that we are observing the opposite behavior of what we may expect. 2. Duality note (pg 61 eulers gem) 3. Simpsons paradox note ([see video here](https://www.youtube.com/watch?v=XVRfBhy5vGI)), book of why example 4. How do LSTMs solve the markovian problem? In other words, they allow us to capture state from many points in time instead of simply the previous time step. Resources to check out: my blog posts on lstms, UC Berkely DL course, colah blog lstms 5. Gamblers Fallacy vs. Regression to the mean (see [here](https://stats.stackexchange.com/questions/204397/regression-to-the-mean-vs-gamblers-fallacy)) 6. Linear regression data matrix as a linear transformation (transpose as well), see this [notion doc](https://www.notion.so/Matrix-Transpose-SVD-Linear-Reg-Col-Space-3419582af5884d9f89638b52403d10ae) --- Date: 20211109 Links to: Tags: References: * []()