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# Questions tagged [sigmoid-curve]

A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve. Often, sigmoid function refers to a special case of the logistic function. It is closely related to the logistic regression.

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### Is there something like softmax but for top k values?

I have a dataset with binary labels of which exactly k outputs are 1, on which I want to train a neural network. If k=1, softmax can do the job of representing the output distribution. I am interested ...
17 views

### Why does the scaled probit function coincide with the logistic sigmoid function at lambda = pi/8?

I'm currently working through through "Pattern Recognition and Machine Learning" by Christopher Bishop, and chanced upon this question while working towards my finals: My two questions are: ...
61 views

### What is the interpretation of the “C” parameter in the five parameters logistic curve?

I'm using the following equation for the 5-parameters logistic curve: $$y = A + \frac{D-A}{\Bigl(1+\exp\bigl(B(C-x)\bigr)\Bigr)^S}$$ What is the interpretation of the $C$ parameter? I found some ...
46 views

### Generate odds ratios across deciles / quantiles of an indpendent variable

With reference to the following figure from Bellomo et al., 2011: How exactly are the odds ratios across the deciles 'referenced against the 4th decile' calculated? My initial impression is that a ...
21 views

185 views

### Has Arcsinh ever been considered as a neural network activation function?

The function $y = arcsinh(x)=ln(x+\sqrt{x^2+1})$ has some nice features that I could imagine being useful as an activation function in a neural network. It has sigmoid behaviour around zero, but far ...
323 views

### Question about Sigmoid Function in Logistic Regression

This is with reference with Andrew Ng's video on Logistic Regression, I just want to confirm a small doubt I have. I get the basic idea of Logistic Regression that $z=\theta^Tx$ Where $\theta$= ...
78 views

### How does Bayes' rule on two exponentials suggest a sigmoid?

In Platt's 1999 paper on turning support vector machine output into a probabilistic score, he says Bayes rule on two exponentials suggests using a parametric form of a sigmoid where he cites this ...
2k views

### Finding the slope at different points in a sigmoid curve

This is my data. x <- c(0.5,3.0,22.2,46.0,77.3,97.0,98.9,100.0) plot(x, pch = 19) I want to fit a curve through these points and then calculate the slope at ...
1k views

### Why do we use the natural exponential in logistic regression?

I would like to intuitively understand the benefit of using the natural exponential in the sigmoid function used in logistic regression. Why should it have to be $e^x$ instead of, for example $2^x$?
22k views

### Why is tanh almost always better than sigmoid as an activation function?

In Andrew Ng's Neural Networks and Deep Learning course on Coursera he says that using $tanh$ is almost always preferable to using $sigmoid$. The reason he gives is that the outputs using $tanh$ ...
104 views

### logistic regression - why we forget assumption on data?

I read logistic regression formula i.e. $\log\frac{P(C_1|X)}{P(C_2|X)}=w^Tx+w_o$ but this equation is true if we have $P(X|C_1)$ and $P(X|C_2)$ sampled from two Gaussian with the same covariance ...
62 views

### Difference between logistic regression models for classification problems

In various papers, I had often seen the logistic regression model for classification problems written in two forms. p(y =\pm1|\mathbf{x},\mathbf{w}) = \sigma(y\mathbf{w}^{T}\mathbf{x}) = \frac{1}{1+...
970 views

### Expected value of softmax transformation of Gaussian random vector

Let $\mathbf w_1,\mathbf w_2,\ldots,\mathbf w_n \in \mathbb R^p$ and $\mathbf v \in \mathbb R^n$ be fixed vectors, and $\mathbf x \sim \mathcal N_p(\boldsymbol{\mu}, \mathbf{\Sigma})$ be an $p$-...
53 views

### Finding the center of a logistic curve

Given a sigmoidal/logistic curve p what's the general procedure to finding at what value of x is the curve centered?
5k views

### How to model positive S-shaped-function? [closed]

I need to transform my data into a function shown below. My data should fit in the range from 0 to 1. The inflection point should be on 0.5. How I can do this mathematically? Is there any similar ...
249 views

### Modification of Sigmoid function

I need to model my data into a function like shown in the following picture. But how I can do this mathematically? Is there any similar function to model data that should increase on smaller values ...
268 views

### What is the difference between a logistic curve and something that overshoots?

In population dynamics, the growth of a population can have exponential growth, or a logistic curve growth up to its carrying capacity, or it can overshoot the carrying capacity and fluctuate before ...
56 views

### Approximation of Δoutput in context of Sigmoid function

I am currently learning the very basics of Machine Learning. This e-book looks quite helpful, but I am stuck at the first chapter already. There, the sigmoid function is defined like normal (equation ...
560 views

### How to do LASSO regression with a dependent variable that is continuous between 0 and 1

I am trying to do a LASSO regression on some data. However, my dependent variable is between 0 and 1. How do I go about this? Do I just apply a sigmoid function to the regression output? This will ...
2k views

### Sigmoid equals softmax in Bernoulli distribution (binary classification problem)? [duplicate]

Apparently, the sigmoid function $\sigma(x_i) = \frac{1}{1+e^{-x_i}}$ is generalization of the softmax function $\text{softmax}(x_i) = \frac{e^{x_i}}{\sum_{j=1}^{n}{e^{x_j}}}$. As far I've understood, ...
770 views

### Effect of e when using the Sigmoid Function as an activation function

I'm writing my own neural net from scratch (using Clojure). For the activation function for the nodes, I'm using the Sigmoid Function. I was messing around manually creating "trained" nets based on ...
2k views

### How do I calculate output of a Neural Network?

I just started learning about ANNs about a week ago with no classical training. Just by watching videos and reading blogs/white papers, I've gotten this far. I have a question about the final output ...
161 views

### How to analyse growth rate in R?

Within the framework of an experiment I followed to growth rate of bird nestlings. I measured them every day for weight and tarsus. I have a number of continuous and categorical explanatory variables, ...
21k views

### Relu vs Sigmoid vs Softmax as hidden layer neurons

I was playing with a simple Neural Network with only one hidden layer, by Tensorflow, and then I tried different activations for the hidden layer: Relu Sigmoid Softmax (well, usually softmax is used ...
13k views

### Looking for function to fit sigmoid-like curve

I'm looking for a function to fit sigmoid-like curves, from experimental data points. The model (the function) doesn't matter, it doesn't have to be physically relevant, I just want to be able to ...
Imagine having a dependent variable $Y$ that is a proportion (i.e., the proportion of observations made at the given time point that satisfy a condition, where each time point involves 50 to 250 ...