approximations

The fact is, even for technical people, approximations and hand waving are great as starting points.

It can't be imagined, it can't be realized, it can't be used in mathematics - only finite approximations can.

Most introductions to statistics focus heavily on the mathematics needed to enable certain analytical approximations to difficult probabilistic calculations (e.g.

And really, I have no objection at all to approximations, but the lack of any acknowledgement that it even was an approximation is what bugged me.

There are probably quite a few album covers with that flag or approximations of it, let alone TV shows and movies.

Categories are useful for crude approximations but they are mere products of the mind.

Some adapt the algorithm to massively parallel setups with hundreds of GPUs, others use speculative execution, some use approximations, and so forth.

There are hacks [1] and approximations [2], but I'm not aware of anyone running them in production.

Now, a computer program has to do approximations such as confidence factors because _it_ is a digital entity (assuming a Von Neumann machine[1]).

Of course we cannot recover the exact values, but we can reproduce likely approximations of the data.

Edit: historical data is of course not available, but approximations must exist?

They were originally continuous approximations of binary threshold functions.

The idea is to have "library of various gradient shapes" to pick from, not full 8x8 DCT matrix capable of reconstituting 8x8 bitmap approximations.

In fact I think most Bayesians would consider Frequentist methods either plain "wrong" (like, at best works in special cases) or as approximations to the full Bayesian way.

Meaning: is there some class of functions which are "best" or "more efficiently represented" by network approximations, and what are the properties of the class that make this the case?

A point that has become more obvious over the years is this: there are "soft" instances of NP-complete problems where you can find good approximations in reasonable time, and there are "crunchy" instances of the same class of problem where you don't find a good approximation.

Approximations to this computation are even more fun: Asymptotically, this function tends to x/ln(x), or more accurately to the integral 1/ln(x) dx from x=2 to n, whose asymptotic expansion is x/ln(x) + 1!x/(ln(x))^2 + 2!x/(ln(x))^3 +...