A mapping between a set of inputs and a set of outputs.
Questions tagged [function]
208 questions
15
votes
2 answers
How can Logistic Regression produce curves that aren't traditional functions?
I think I have some fundamental confusion about how the functions in Logistic regression work (or maybe just functions as a whole).
How is it that the function h(x) produces the curve seen in the left of the image?
I see that this is a plot of two…
muZero
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15
votes
3 answers
How to find the mode of a probability density function?
Inspired by my other question, I would like to ask how does one find the mode of a probability density function (PDF) of a function $f(x)$?
Is there any "cook-book" procedure for this? Apparently, this task is much more difficult than it seems at…
mmh
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13
votes
3 answers
Can a neural network learn a functional, and its functional derivative?
I understand that neural networks (NNs) can be considered universal approximators to both functions and their derivatives, under certain assumptions (on both the network and the function to approximate). In fact, I have done a number of tests on…
Michael
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12
votes
1 answer
Proof that if higher moment exists then lower moment also exists
The $r$-th moment of a random variable $X$ is finite if
$$
\mathbb E(|X^r|)< \infty
$$
I am trying to show that for any positive integer $s
nona
- 121
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11
votes
3 answers
Is there a way to recover a temporal dependence structure in a time series from a regression against time?
Consider a time series:
$X_1,X_2,...X_{n-1},X_n$
This series can also be written as a function of time $X(t)$, so that:
$X_1,X_2,...X_{n-1},X_n = X(t_1),X(t_2),...X(t_{n-1}),X(t_n)$
Most forecasting methods, such as ARIMA or Exponential…
Skander H.
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11
votes
2 answers
How to estimate the accuracy of an integral?
An extremely common situation in computer graphics is that the colour of some pixel is equal to the integral of some real-valued function. Often the function is too complicated to solve analytically, so we're left with numerical approximation. But…
MathematicalOrchid
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10
votes
1 answer
Proving a sequence decreases (supported by plotting a large number of pts)
Many of the questions I've posted on SE in the last month have been in the goal of helping me solve this particular problem. The questions have all been answered, but I still can't come up with a solution. So, I figured that I should just ask the…
OctaviaQ
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9
votes
2 answers
Advantages of approaching a problem by formulating a cost function that is globally optimizable
This is a rather general question (i.e. not necessarily specific to statistics), but I have noticed a trend in the machine learning and statistical literature where authors prefer to follow the following approach:
Approach 1: Obtain a solution to a…
Amelio Vazquez-Reina
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8
votes
2 answers
How to properly handle Infs in a statistical function?
Suppose I have a function such like:
f <- function(x){
exp(x) / (1 + exp(x))
}
it's supposed to work for any real value of x, but actually it returns NaN when x is 710 or larger. I'm wondering what's a proper way to handle this issue. I realize…
David Z
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8
votes
2 answers
Function of random variables
I am not sure what the right keywords would be for this but I would like to know if it is possible to apply functions to random variables. I think it may make sense in terms of expected value but I would appreciate any information on a more formal…
Twiltie
- 357
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8
votes
2 answers
How to measure the shift between two cumulative distribution functions (CDFs)?
How to measure the shift between two cumulative distribution functions (CDFs)?
Specifically, in the image below, how meaningful is the shaded area?
It is supposed to measure the shift between the green and the red CDF.
On the x-axis, the value of…
thanks_in_advance
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8
votes
1 answer
How to understand the geometric intuition of the inner workings of neural networks?
I've been studying the theory behind ANNs lately and I wanted to understand the 'magic' behind their capability of non-linear multi-class classification. This led me to this website which does a good job of explaining geometrically how this…
PhD
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7
votes
1 answer
In spatial regression, what is a spherical autocorrelation structure?
I have a large gridded dataset for the globe (i.e a spherical, wraparound surface) that I'm applying spatial regression to (using a CAR model). I've been using the default autocorrelation function, however as my data is global (point 0,0 lies next…
alopex
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6
votes
1 answer
What is an induced probability function?
My textbook defined the probability function of a random variable as:
the function $P_X$ is an induced probability function on
$X(\Omega)$, defined in terms of the original function P.
In other words, the function $P_X$ induces a surjection by…
DataInTheStone
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6
votes
3 answers
Are dependent variables necessarily functions of one another?
The problem
Suppose you have two variables $X_1,X_2$ so that $X_1\not\perp\!\!\!\!\! \perp X_2$.
Do we necessarily have that a functional relationship exists between them?
I am assuming random variables are the usual real valued measurable…
ArnoV
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