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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27 views

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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1answer
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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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How can I control the firm size which affects my independent variable in the regression model?

I'm studying on the relationship between firm value and ESG disclosure. My regression model is like this: $$ P_{(i,t)} = ß_0+ß_1BV_{(i,t)}+ß_2AE_{(i,t)}+ß_3E_{(i,t-1)}+ß_4 S_{(i,t-1)}+ß_5 G_{(i,t-1)}+...
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66 views

Matlab hardlim (step) function does not have exact step

Hardlim matlab function should look like a step: But the code provided at the documentation page ...
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1answer
44 views

What is the domain and range of the PMF of the Bernoulli distribution with p = 0.1?

In probability theory and statistics, the Bernoulli distribution is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with ...
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Order of continuity of an ANN approximation dependent on the activation functions used?

If I have understood this correctly, a result from Hornik et al.'s Universal Approximation of an Unknown Mapping and Its Derivatives Using Multilayer Feedforward Networks essentially states that, if ...
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The function machine learning is trying to approximate

Consider a random experiment E with sample space S and the probability measure P. Assume that all events are measurable. Let X1, X2, X3,...., Xn are random variables over S. Now machine learning ...
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1answer
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Why use Regression in NN?

In a NN we first apply a Linear Function, ie. Multiplying the weights to the inputs/output of a layer and then apply a Non-Linear Activation function like ReLU to get the output of the layer. The ...
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Linear programming in R for Data Envelopment Analysis

Suppose I have this dataframe. ...
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1answer
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Binary Logistic Regression with the LASSO objective function

I am working on my MSc. Statistic which is on the Penalized Logistic Regression with the LASSO penalty. I am trying to understand the difference in two objective functions: argmin {$\frac{1}{n}$ $\...
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1answer
46 views

Function to fit acid reaction curve

Data in the image below shows a variable DME reacting to the increase in acid concentration. It looks like it has a very fast increase from when the concentration is raised from 0 to 0.5 and then a ...
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Finding the distribution of a piecewise function of a Gamma random variable

Let random variable $X \sim \text{Gamma}(\alpha,\beta)$. I want to derive the distribution of $Y$, where: $$ Y = \left\{ \begin{array}{ll} a X - k & \quad X \geq \frac{k}{a} \...
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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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417 views

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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1answer
38 views

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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51 views

Formulae for density function replacing probabilistic function

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^{(...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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 ...
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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} \...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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'...
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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 ...
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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(...
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1answer
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Estimating the mutual information in high dimension when all but one variable are iid

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 ...
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1answer
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Do optimization problems written in argmax form represent a function?

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 ...