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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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How to aggregate calibration curves which were created in cross validation?

When looking into Scikit's CalibratedClassifierCV I noticed that the object needs to keep multiple calibrated classifiers in memory to average the results in real time. I understand that these ...
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Can the vanishing gradient problem be solved by multiplying the input of tanh with a coefficient?

To my understanding, the vanishing gradient problem occurs when training neural networks when the gradient of each activation function is less than 1 such that when corrections are back-propagated ...
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Logistic function with a slope but no asymptotes?

The logistic function has an output range 0 to 1, and asymptotic slope is zero on both sides. What is an alternative to a logistic function that doesn't flatten out completely at its ends? Whose ...
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How can I even out the output of the sigmoid function?

I'm applying a sigmoid function to an array of values but the output is very concentrated near 1 (i.e. 25th percentile is 0.999). I think this is because the input array takes on values that are quite ...
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Is there a Gaussian Process Kernel that limits functions to sigmoids?

I am modeling a large number of Dose-response curves. I have strong reason to believe that the generating function will be sigmoidal against the concentration of the assay (Michaelis-Menten kinetics). ...
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Counting the number of neural network parameters [duplicate]

I am slightly confused by counting the number of NN parameters. Let's assume there is a NN with 4-dim vector as an input, then comes 5-dim hidden layers, and another one 6-dim hidden layer. There is a ...
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The link between logistic regression and logistic sigmoid

My professor once stated that the logistic sigmoid function is the inverse link function to logistic regression. I cannot find mathematical deductions showing this. Can anyone confirm his statement ...
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Difference between sigmoid and softmax [duplicate]

I know, that usually we use sigmoid in the hidden layer, and softmax as an output but what is the difference between neural network with one output and sigmoid activation layer and network with two ...
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93 views

How to convert IRT theta score to a percentage score

I am trying to implement an adaptive test using 3PL IRT model. We need to screen the candidates and label their expertise as ...
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2answers
124 views

When is logit function preferred over sigmoid?

I found out that logit and sigmoid functions are inverse of one another, and are used in binary classification, but is there a preference of one over another in any circumstances, or can they be used ...
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Does mixture of sigmoids make sense given the theories about mixture of bernoullis?

Mixture of bernoullis is the combination of bernoulli distributions, which can be illustrated by the sampling process of K bags of D coins, here is a quick tutorial about it https://cedar.buffalo.edu/~...
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557 views

Softmax weights initialization

I am a new to deep learning and neural networks, and I need to know if there is a good weights initialization method to use if the activation function is Softmax like Tanh, ReLU and Sigmoid. Related ...
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142 views

Compare two sigmoid shape curves

I have x and y-values for two sigmoid curves (probit). x-values are the same for both curves,...
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1answer
186 views

Does it make sense to use `logit` or `softplus` loss for binary classification problem?

With $z$ is the logit, $p \in \{1, 0\}$ is the class. Usually binary classification problem use sigmoid and cross-entropy to compute loss: $$\mathcal{L_1} = - \sum{p \log \sigma(z) + (1-p) \log \sigma(...
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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 ...
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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 $\theta$= ...
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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 ...
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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 ...
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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 $2^x$?
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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 $tanh$ ...
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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 ...
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1answer
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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+...
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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 $p$-...
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48 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?
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3k 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 ...
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1answer
176 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 ...
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2answers
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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 ...
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1answer
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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 ...
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3answers
449 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 ...
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1answer
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, ...
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612 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 ...
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1answer
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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 ...
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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, ...
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3answers
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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 ...
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7answers
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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 ...
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3answers
362 views

Predicting proportions from time with a discontinuity

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 ...