# Questions tagged [function]

A mapping between a set of inputs and a set of outputs.

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### TANH function going from 0 to 1 [migrated]

How to transform TANH sigmoid function so starts from f(0)=0 and goes asymptotically to 1 and has f(0.1)=a and f(0.9)=b? Is it possible with that function at all?
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### Convergence failure: initial par violates constraints

I am currently working with a self-starting function, I was able to determine the initial values of the parameters. However, when I try to fit the self-starting function on an nls, there is an error: ...
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### 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 ...
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### Perceptron results in WEKA. Which are the weights & how to graph sigmoid function?

i have this data set dataset.csv and these results ...
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### Sampling posterior distribution of a function

I have the following problem: let's say I have a function $y=f(x)$. Let $f$ be defined for all $x$ but it it might not be invertible. Further assume $x \sim p(x)$ with some probability density $p(x)$. ...
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### Correlation among variables-generating function

I have three independent variables and want to have a mathematical equation relating them and the dependent variable. I am assuming the (number of calls)/(total products sold) to be dependent variable ...
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### Modify fit or function to match certain values

I have following values: x = [0, 12.5, 25, 50, 75, 87.5, 100] y = [0.0, 0.2, 0.31, 0.5, 0.66, 0.76, 1.0] These values represent display values from a device that ...
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### Continuous mapping theorem and random vectors

My question is on whether or not continuous mapping theorem can be applied to elements of a random vector. Consider $[X_n,Y_n] \rightarrow [\mu, \sigma]$ Would it also be true that for any ...
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### Is it possible to approximate a function f(x), if I can observe the behavior of g(f(x))?

Say I have a hypothetical scenario with a 'cost function' f(x) over parameter space x. Typically, from an optimization point of view, minimizing this cost function is expected to result in an optimal ...
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### Dynamically updating posterior density in R

I want to redefine my function in a loop by calling the function from last iteration. However I know this is basically a recursive way which I don't want. To give an example, see the following ...
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### Maximum likelihood estimator in Uniform distribution [closed]

For Random sample with uniform distribution in Tetha< x< Tetha +1 What's the maximum likelihood function how can we maximize it?
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### How to make a custom activation function in keras with a learnable parameter?

The answer to this question is generally to implement it as a new layer and do layer = Dense(num_neurones)(previous_layer) out = TheActivationFunction()(layer) ...
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### Which trigonometric function I should use to generate the temperature with two peaks (i.e.one strong and one moderate peak)?

I want to generate seasonal temperature of Bay of Bengal. I want to do this with a trigonometric function. Seasonal temperature of Bay of Bengal has two peaks. One major peak during April and another ...
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### How to perform a regression for a multi-function?

How would one perform a regression analysis with a multi-function? That is, where a single X-value can correspond to a number of Y-values? Here is an example: Note that in this example, it is not ...
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### How to write diff() mathematically?

I am using R/Python diff() operation. e.g., https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.diff.html I would like to know if there is a ...
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### Expressing as a probability density function [closed]

The measuring error x is a normal random variable. Variance of the error = 4. If distribution of x can be shown by a probability density function f(x), how would you find the analytical expression of ...
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### How to find emprical PDF by using the normalized histogram?

first of all, thank you for your time, here is my question; Is it possible to find emprical PDF by using normalized histogram? I am trying to learn discrete event simulation and what I see is there ...
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### Mapping a range of values such that the resulting distribution is uniform [duplicate]

I have a set of values. Let's call the set X with values ... . Those values in [0, 1] have a non uniform distribution (empirically measured). I would like to re-map those values on [0, 1] such that ...
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### Little problem calculating hazard function

I'm starting to study maths again after a long time without having touch them and I'm currently with survival analysis. I want to get a hazard function h(x), and I know that it can be calculated as ...
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I am working with markov chains and in specific I am working with (Langrock, Roland MacDonald, Iain L. Zucchini, W (2016)). They define a forecast distribution given as: $$Pr(X_{T+h}=x|X^{(T)}=x^{(... 0answers 27 views ### Is Entropy conserved under invertible (but probabilistic) mappings? I know that under a one-to-one mapping, the entropy is conserved. This was answered very well here: Is entropy conserved under invertible mappings? I am having a doubt about this being applicable to ... 0answers 174 views ### How do I write a random walk with drift ARIMA? [closed] I modeled oil prices and got the following coeffecients for my arima model with drift. Is this the right way of writing the model? 1answer 679 views ### ReLu vs a linear activation function I read this great answer about how ReLu could approximate non-linear functions. However, if ReLu can approximate such functions, why cant linear activation function do the same? If they can, why ... 1answer 390 views ### Difference between function and distribution? I have constant function as$$y = exp(-x^2)$$This also represent gaussian distribution with mean zero and variance of 0.5 Now if we take sample from this function, which will always be from this ... 0answers 133 views ### Functional Forms of Independent Variables If our objective is to ascertain the relationship (specifically, sign and significance of Beta coefficient) between independent variables and dependent variable in an OLS regression (cross sectional ... 3answers 140 views ### Does \mathbb{P}(X < a) = \mathbb{P}(f(X) < f(a))? If f(x) is a monotonic increasing function, then does \mathbb{P}(X < a) = \mathbb{P}(f(X) < f(a))? My intuition says it's true but I cannot prove the case nor find the name of the theorem. 0answers 37 views ### Is there a function that combines correlation and convolution? I'm actually trying to find some correlations between functions, and i was wondering if there is a function that quantifies the amount of time we need to shift a curve to have a high correlation with ... 1answer 972 views ### Optimization using the optim function in R with a two parameter exponential distribution I'm having trouble trying to optimize a two-parameter exponential distribution, by finding the maximum likelihood function and then using the function optim() in R ... 0answers 31 views ### Limiting regression accuracy I am currently using a LSTM Network to solve a regressional problem. The goal is to predict the payload mass using various time series as input data. For our intents and purposes estimating the mass ... 0answers 255 views ### Mean and std of nonlinear function I have a gaussian random variable \xi \sim \mathcal{N} (\mu,\sigma^2), and the following function g(\xi): \begin{equation} g(\xi)=-( \xi +\textrm{b}^{\textrm{T}} x) + \left\lVert{\begin{matrix} \... 0answers 295 views ### Problems fitting a model to a variogram I am having problems fitting a variogram model. I tried to change some parameters to estimate or fix them but I am still not achieving any improvement. I remove trend of the data and use logarithms ... 1answer 64 views ### When a function of sufficient statistic is itself sufficient? I'm following notes at onlinecourses and I got confused on transformation of sufficient statistics. For example, if X is a sufficient statistic for \mu, why Y=X^2 is not a sufficient statistic ... 1answer 40 views ### Can a neural network have an activation function that is a transformation of the parent function? Neural networks can have activation functions like a tanh(x), a sigmoid function, ReLU, etc.. But can we have an activation function that is a transformation of any of these functions? For instance, ... 2answers 84 views ### Can a neural network learned function f be used for calculating its derivate f'? y is a scalar value, x is an m \times 1 vector. Function f is a map y = f(x). Say we have n examples {(y_1, x_1), (y_2, x_2), \cdots, (y_n, x_n)}, and we use these examples for fitting ... 2answers 347 views ### Function to Produce Periodic Spike and Decay I am seeking a function (or short algorithm, ideally implemented in R) that produces something similar to the following: See, I would like to be able to generate a vector of n items that follows ... 1answer 48 views ### How can I get a sample of a product of two independent random variables? I have three random variables: X_1, X_2 and Y such that X_1 and X_2 are independent and Y = X_1 \times X_2. I think that either this question is trivial or I'm making a rookie error, but I'... 0answers 25 views ### Minimize function curve 'length' Given a set of points (x_i, y_i), how can I find the serie of  C^\infty -functions for which the sum passes through all points and for which the length of the resulting curve is minimal; i.e. if ... 1answer 38 views ### What is f in this Neural Gas neighborhood width formula? I'm implementing the Online Visualization Neural Gas algorithm, as described in the Estévez, Figueroa 2006 paper. I am having trouble interpreting the formula below (Eq. (4) in the paper):$$\lambda(...
I have a function $f(x_{1},\dots,x_{n})$ where $n$ is large and I would like to estimate the mutual information between the random variable $f(X_{1},\dots,X_{n})$ and the independent and identically ...
If I write $$\hat{x} = \underset{x}{\text{argmax}}\ f(x,y)$$ can I assume that what is to the right hand side (RHS) of the equal sign is a function in the rigorous sense of the word? Under what ...