Selection bias is the most powerful force in education • Hacker News Board

Re: Selection bias is the most powerful force in education

#181

Post by yorwba » Fri, Aug 18, 2017, 12:28 PM UTC

yorwba wrote: post #177

graycat wrote: post #172

Earlier quoted context omitted.

You are really super slow on the uptake, reading comprehension. Again, once again, over again, yet again, one more time, this time just for you, my writing is fine. Just fine. Nothing wrong with it. Instead of anything wrong, I presented a very well informed, well documented, well reasoned, well explained, serious, practical solution to a really big problem in the OP -- how to get good educational results for disadva…

The problem with your posts is not that they are hard to understand, it's that they are not nice to read. For one, you come off as arrogant, as if you were the only one who has any idea what they are talking about. You present a solution to help disadvantaged students learn better, and I agree that your solution is fine. But it will only work for students that have the will, time and ability to help themselves, and I…

Example: For positive integer n and the set R of real numbers, for any closed set C in R^n, there exists a function f: R^n --> R so that f(x) = 0 for all x in C, f(x) > 0 otherwise, and f is infinitely differentiable.

I have a hunch that this can be solved similarly to the construction of bump function on a given compact set [4], except the support is an open set and I'm not sure what the "appropriate scaling" should look like.

[4] https://en.wikipedia.org/wiki/Bump_function#Existence_of_bum...

Re: Selection bias is the most powerful force in education

#182

Post by yorwba » Fri, Aug 18, 2017, 12:29 PM UTC

yorwba wrote: post #177

graycat wrote: post #172

Earlier quoted context omitted.

You are really super slow on the uptake, reading comprehension. Again, once again, over again, yet again, one more time, this time just for you, my writing is fine. Just fine. Nothing wrong with it. Instead of anything wrong, I presented a very well informed, well documented, well reasoned, well explained, serious, practical solution to a really big problem in the OP -- how to get good educational results for disadva…

The problem with your posts is not that they are hard to understand, it's that they are not nice to read. For one, you come off as arrogant, as if you were the only one who has any idea what they are talking about. You present a solution to help disadvantaged students learn better, and I agree that your solution is fine. But it will only work for students that have the will, time and ability to help themselves, and I…

Examle: For positive integer n and the set of real numbers R, show that convex f: R^n --> R is continuous.

Choose an arbitrary point x in R^n and consider a hypercube centered in x. Each face of the hypercube together with the centerpoint x determines a hyperpyramid, and each point p within the hypercube is contained in at least one such hyperpyramid.

Since the hyperpyramid is convex, the point p can be expressed as a convex combination of its vertices, which is linear in the coordinates of p. Due to the convexity of f, there is an upper bound of f(p) that is a convex combination of the values of f on the vertices of the hyperpyramid, using the same coefficients. This means that the upper bound is linear in p as well.

Importantly, the bound is identical on the boundary of two hyperpyramids, since the coefficients will only involve those vertices that are shared between them. This means that f is bounded above by a piecewise linear function, which is tight in x (with the trivial convex combination).

There is a second hyperpyramid to consider, which is formed by p together with the opposite face of the hypercube, and which contains x. By the same convexity argument, there is an upper bound on f(x) that is a convex combination with coefficients linear in p.

The bound can be written as sum_v w_v f(v) + w_p f(p) >= f(x) and rewritten as f(p) >= 1/w_p (f(x) - sum_v w_v f(v)). This is possible because w_p = 0 would imply that x is a convex combination of the v alone and therefore in the hyperface. This bound is no longer linear in p, but still continuous.

Like the upper bound, this bound is identical on the boundary of two hyperpyramids containing p, because only the vertices shared by the opposite faces will be relevant. Additionally, the bound is tight in x as well, where the convex combination is w_p = 1, w_v = 0.

In summary, f is bounded above and below by continuous functions in a neighborhood of x, with the bounds coinciding at x itself. This implies that f must be continuous in x as well.

Re: Selection bias is the most powerful force in education

#183

Post by yorwba » Fri, Aug 18, 2017, 12:29 PM UTC

yorwba wrote: post #177

graycat wrote: post #172

Earlier quoted context omitted.

You are really super slow on the uptake, reading comprehension. Again, once again, over again, yet again, one more time, this time just for you, my writing is fine. Just fine. Nothing wrong with it. Instead of anything wrong, I presented a very well informed, well documented, well reasoned, well explained, serious, practical solution to a really big problem in the OP -- how to get good educational results for disadva…

The problem with your posts is not that they are hard to understand, it's that they are not nice to read. For one, you come off as arrogant, as if you were the only one who has any idea what they are talking about. You present a solution to help disadvantaged students learn better, and I agree that your solution is fine. But it will only work for students that have the will, time and ability to help themselves, and I…

Example: For triangle ABC, by Euclidean construction, find D on AB and E on BC so that the lengths AD = DE = EC.

Running out of time here. I guess you can do it algebraically: two variables for the placement of D and E, two quadratic equations, get the solutions in terms of square roots, multiplication, division etc., then implement the calculation using compass and straightedge.

Re: Selection bias is the most powerful force in education

#184

Post by gnaritas » Fri, Aug 18, 2017, 2:51 PM UTC

jstewartmobile wrote: post #175

gnaritas wrote: post #173

Earlier quoted context omitted.

> In the west, survival is a pretty low bar. You've never been poor I see, or really truly known anyone who was. Poverty is a real problem, here, in the good old USA still . Survival is all many people worry about. I'm relaying a reality to you that you clearly have no concept of. I didn't have indoor plumbing until I was a teenager. We lived off government handouts and what we could kill and bathed outdoors in rainw…

My family was on public assistance when I was younger, and I went to public schools where over half the students families were on some form of public assistance. None of us had to bathe in stagnant water...

Then count yourself lucky but don't presume to know what it is to be actually poor nor pretend it doesn't exist in the west; it does.

Re: Selection bias is the most powerful force in education

#185

Post by jstewartmobile » Fri, Aug 18, 2017, 3:27 PM UTC

gnaritas wrote: post #184

jstewartmobile wrote: post #175

Earlier quoted context omitted.

My family was on public assistance when I was younger, and I went to public schools where over half the students families were on some form of public assistance. None of us had to bathe in stagnant water...

Then count yourself lucky but don't presume to know what it is to be actually poor nor pretend it doesn't exist in the west; it does.

I presumed nothing about being "actually poor". I wrote that "survival is a pretty low bar" in the west.

Despite whatever hardships you have endured, here you are.