Question: Express each of the following tasks in the framework of learning from data by specifying the input space X, output space Y, target function f:X->Y and the specifics of the data set that we will learn from.

a)Medical diagnosis: A patient walks in with a medical history and some symptoms , and you want to identify the problem.

*My answer: Input space: Medical history. Output space:Symptoms. target function: Identify problem: Medical history -> Symptoms *

b)Handwritten digit recognition(for example postal zip code recognition for mail sorting)

My answer: Input space: postal zip code. Output space: Handwritten digit recognition. Target function: Mail sorting

c) Determining if an email is spam or not.

My answer Input space: email, Output space: spam or not. Target function determining

d)Predicting how an electric load varies with price,temperature,and day of the week.

My answer: Input space:Price,temperature and day of the week. Output space: Electric load. Target function: prediction.

e)A problem of interest to you for which there is no analytic solution, but you have data from which to construct an empirical solution.

No answer

This is my question and I provide answer of those question except the last one.

My question is that my answers are correct or not?


I think all your answers are wrong or I miss a crucial part of information. For example with the digit recognition, I would say the input is a pixel image, the output is one of ten digits and the dataset could be MNIST. To be more specific:

$X=R^{28 \times 28}$, $Y=\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$

e)A problem of interest to you for which there is no analytic solution, but you have data from which to construct an empirical solution.

Polynomials of degree 5 have no analytical closed-form solution. For example $$x^5 + x^4 + x^3 + x^2 + x + 1 = 0$$ But they can be solved using Newton's method.

What also comes to my mind here are some differential equations.

The three-body problem in physics might also be interesting: While you can observe the position of 3 bodies at different timesteps and interpolate the positions in between easily, there is no analytic solution for it.

  • $\begingroup$ The three body problem never was solved. It is only possible to predict the next step in the simulation. That means, if the position of the bodies is known, we can calculate the position in the next timestep with the help of a physics engine. But it's not possible to view into the future and calculate the body's position for 100 steps in advance. Instead we can only iterate step by step through the simulation. This is important, because most interesting problems have the same characteristics: they are non-linear and unsolvable. $\endgroup$ – Manuel Rodriguez Nov 15 '18 at 7:18
  • 1
    $\begingroup$ @ManuelRodriguez Right. I clarified what I meant. I'm not a physicist and I didn't look at the equations, but in most cases if you make the interval small enough you can assume that things behave linearly. This assumption is wrong, of course, but as the intervall is small the error is in an acceptable range. Hence interpolating positions from observed data is easy, but only given some start configuration it is (currently?) not possible analytically get there. $\endgroup$ – Martin Thoma Nov 15 '18 at 7:35
  • $\begingroup$ @MartinThoma If all my answer was wrong then what will be the solution of those question. Your explanation is not clear to me. Can you take the 1st problem a) and explain it so that I can find out my flaws. $\endgroup$ – Encipher Nov 15 '18 at 18:30

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