# 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 linearize logistics function? [closed]

The function is $y=L/(1+e^{(-kx)} )$. After research I found this equation to linearize it, replace y values by this: $\ln(1/(y/(L-1)))$ , then keep x values the same and plot it. But with further ...
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### Logistic function with different asymptotic slopes

The asymptotic slope of both sides of a logistic/sigmoid function is zero. What would be the equation of a logistic function with a different asymptotic slope on each side? I'm trying to model data ...
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### Example where the initial random state of a logistic regression matters?

I am looking into how random initialisation of a model would impact final results after tuning. This is a well known problem for deep learning (NN or gbdt), notably with random initialisation and ...
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### What is a visual representation of an ordinal logistic fitted model

Naturally, the above image is a graphical representation of a sigmoid function fit for a logistic regression I'm trying to understand the equivalent of an ordered logit. Below is an image that, to the ...
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### Does linear separability with gamma margin guarantee convergence of perceptron algorithm?

I am studying perceptron for the first time. I came across the assumption from online resources that if the data is linearly separable with gamma margin then the perceptron algorithm will converge. Is ...
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### Is there a way to stretch sigmoid function output

I have an array of values and a value that lies outside of array's max value: arr = [10, 15, 20, 30] value = 150 and I want to make that value less of an outlier, ...
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### Statistic for assessing quality of dose response curve (fit with logistic regression)

I want to assess the quality of a 4-parameter logistic regression fit on dose response data. I am in the process of assessing the quality of some compound screening data. This is characterising the ...
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### Influence of big values in hidden layers on the output value of the output layer

In the lab on Tensorflow classification, we are trying to predict wether a coffe is well roasted or badly. A 1 is good roasted and 0 is bad. The architecture is: Now we try to visualize the trained ...
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### Test of good fitting on a sigmoid [closed]

as you can see on the figure i linked i am currently fitting my data (which looks like a sigmoid) using a function i defined with 5 parameters. ...
1 vote
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### Do the # of weights (non-intercept coefficients) in logistic regression = # of features

A simple question that I just want to clarify for understanding: In logistic regression, if we have $n$ input features, will there therefore be $n$ weights used for classification, one for each ...
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### logistic regression graph - understanding data

I am trying to understand why my data is not showing a full S-curve? Is it because the predictor does not do a good job of predicting fellow = 1, or simply because there are few fellow = 1 that score ...
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### GLM: Sigmoid link with MSE for linear regression?

I have a relatively simple regression problem where I wanted to model y given x. X is continuous and is bounded [0,inf); y is bounded (0,1). My question is, is it appropriate for me to insert a ...
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### Decision boundary in Logistic regression?

According to me in logistic regression, we just try to get a line (polynomial) and then based on which side the point is from that line the sigmoid gives ans>=0.5 or <0.5, which we then ...
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### Simulate binary response ground-truth from real causes [duplicate]

In an attempt trying to understand logistic regression throughout, I want to generate simulated data in a way that corresponds the way the logistic regression finds out the classes. The idea is that I ...
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### Sigmoid function with parameter that controls length of approximate linearity [closed]

It is well known that many sigmoid functions are approximately linear around x=0. I am looking for a sigmoid function that has a parameter that controls the length of this segment. I want to measure ...
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### Continuous variable (1-100 scale) logistic function fitting

I've been working with a dataset where there are judgments of brightness from 1-100 (1= less bright) for 5 different brightness categories. patient Brightness level Judgment 1 1 10 1 4 80 1 5 99 ...
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### Is this simple, univariate logistic regression valid?

I am working on a research project. We have roughly 300 study participants that have been categorised into 4 groups. Some of these participants had a recurrence of a disease, and the rest did not. I'm ...
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### Why does SKLearn's Logistic Regression model have the same coefficients as my own model for 1 class but have different coefficients for other classes

I am currently implementing logistic regression from scratch and I'm comparing my model with SKLearn's logistic regression. Since this is just an exercise, I decided to use toy data, specifically ...
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### Mean of $t$ in the logistic regression model

The question comes from a sentence of page 208 of Christopher M. Bishop's "Pattern Recognition and Machine Learning". The sentence is excerpted as follows: My questions are mainly two: Why ...
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### Define plateau of sigmoid function

I have a sigmoid function ...
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### Multiclass (OVR) Logistical Regression on "Surrounded" Classes

I'm trying to understand/visualize how multiclass logistic regression works but most of the examples I've seen concern 3 classes with all of them on the outside. How does logistic regression work when ...
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### Where does the Logistic Distribution get its name?

Having read around on the topic I understand its application as a close approximation of the normal distribution with a nicer mathematical form, but where does its name come from? Is it associated ...
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### Reference for Logistic and Sigmoid Kernels

I've been close reading a paper and was mystified when the author mentioned two kernels: The logistic kernel $\frac{1}{e^x + 2 + e^{-x}}$ and the sigmoid kernel $\frac{2}{\pi}\frac{1}{e^x + e^{-x}}$. ...
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### confusion about logistic regression and its weights [duplicate]

I have studied Logistic regression and I am still confused about certain things: does logistic regression use linear regression to predict a continuous output, but since linear regression can output ...
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### How does the TI-84 calculate the best fit for a logistic model?

Back in High School I remember the TI-84 calculator allowing the user to enter a few data points and then select from a list of options to find an equation that best fit the data points. One of these ...
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### Impact of change in independent variable on probability in logistic regression

Take the following logistic regression: $$\log(o) = \beta_0 + \beta_1 x + \epsilon$$ We know that increasing $x$ by 1 increases the log-odds of the event by $\beta_1$, and multiply the odds of the ...
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### Why do fixed effects in a logistic regression model differ depending on the presence of a random intercept?

If I have two linear regression models, one with a random intercept and one without (but otherwise identical), the fixed effects in the two models are identical. My understanding is that this stems ...
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### How do I find probabilities in logistic regression?

let's assume we have continuous independent variable and obviously binary dependent one. How can we calculate probabilities which is displayed on y-axis? With scale like in the image below, it's clear ...
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### What is a sigmoid function and what does it give as output?

I know the equation of the sigmoid function and use it in logistic regression, SVM, etc. $$S(x) = \frac{1}{1 + e^{-x}}$$ In the case of the sigmoid function, What is the exact input and output of ...
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### Binary classification neural network - equivalent implementations with sigmoid and softmax

in order to solidify my understanding, I am doing some simple calculations with pen and paper for some very simple NN for binary classification (input vector with two entries, 1 hidden layer and just ...
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### Sigmoid equivalent to Softmax exercise 2 [duplicate]

This question is not the same as this one I asked previously. In the previous question I asked to prove that the sigmoid and softmax are equivalent. I found a solution here, but I think it's not ...
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### Sigmoid equivalent to Softmax exercise

I am currently studying the Sutton and Barto Intro To RL Book, and I'm trying to do exercise 2.9 (at the bottom of the following picture): So the exercise wants me to show that the softmax is ...
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### Determine the optimal threshold for sigmoid layer in neural network for binary classification [duplicate]

I have a neural network that gives out a continuous value as output and I need to classify it as class 0 or 1. I am currently using a sigmoid on this continuous output value but after sigmoid the ...
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### Using logistic regression to classify data set (asking about the steps)

I have a training data set of predictors being classified into 2 classes. For now, I have already created a logistic regression model, that is, having solved the coefficients $\beta_0, \beta_1,\cdots$....
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### How does logistic growth rate coincide with the slope of the line in the exponential phase of the growth?

For a logistic function $$f(x) = \frac{L}{1 + e^{-k(x - x_0)}},$$ people call $k$ the logistic growth rate. Now, I have encountered this statement: In the log scale the logistic growth rate coincides ...
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### What is the best practice for logistic regression data perspective?

I'm running into an interesting problem (for me at least) right now where I'm worried that my data setup is negatively influencing the accuracy of my model. Lets use historical chess matches as our ...
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### Can I use a logistic regression as a calibration curve?

Lets use basketball as our example. The use case: There is a model that predicts the probability that the favored team will win. The probability range then is necessarily constrained between 0.5 and ...
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### Logistic regression : incoherent coefficient values from z tests?

I am working on a customer purchase problem. I have 150 campaigns sent by email, that I denote C0, C1 ... ...
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### Is Wikipedia's page on the sigmoid function incorrect?

Is Wikipedia's page on the sigmoid function incorrect? It states that: A common example of a sigmoid function is the logistic function From my knowledge of machine learning, I thought that "the ...
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### Is there any difference between a Logistic Regression for inference and for prediction?

When studying Linear Regression, I remember that Multicollinearity is something that impacts inference and not prediction, at least not always. Also, I noted that the assumptions tends to be neglected ...
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### Re-parameterization to resolve non-identifiability in this squiggly model (linear combination of logistic functions)?

So my desire here is to be able to capture a variety of temporal dynamics governing the change in value of some feature of interest. I want the model to be able to represent, for example, bounded: ...
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### For prediction problems, why cant we simply use softmax as activation for hidden layers and no activation function for output layer

I am a beginner who is learning how to use neural networks for prediction problems, and almost all tutorials I have found use relu for hidden layer and sigmoid function for output later. My question ...
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### Likelihood values from Sigmoid [duplicate]

Repost of Mathemetics StackExchange question. There are multiple doubts of mine associated around this theme: In MLE, we try to find the PDF parameters ($\theta$) which maximise the likelihood of the ...
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### Why $1/(1+e^{-x}) = e^x/(1+e^x)$

I am currently learning the sigmoid/logistic function and have completely forgotten how the maths behind this equivalence works: $$\dfrac{1}{1+ e^{-x}} = \dfrac{e^{x}}{1+e^{x}}$$ By this I mean how ...
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### sklearn logistic regression converging to unexpected coefficient for a simple case

The case is as follows: Suppose that import numpy as np X = np.array([1, 1, 1]) y = np.array([1, 0, 1]) Then I perform a logistic regression with no intercept to ...
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### What value of predictions minimizes the binary cross entropy loss function? Is it 0.5?

I saw some examples of Autoencoders (on images) which use sigmoid as output layer and ...
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### Do you do linear regression in logistic regression?

I just studied single & multiple linear regression 2 days ago now I'm reading about logistics regression and I want to implement it from scratch, I just want to know If my understanding about ...
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### Binary logistic regression coefficients

Consider the following MWE example. A dataset with only one feature (categorical feature with 4 different categories ['cat', 'dog', 'hamster', 'frog']) + target (overall 10% positive class). After ohe ...
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The exponential (not continuous) growth formula from high school is: $$A(t)=A^{kt}$$ Where $A$ is the initial amount, $t$ is the number of time periods and $k$ is the shape or growth rate. Looking ...