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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Why do fixed effects in a logistic regression model differ depending on the presence of a random slope?

If I have two linear regression models, one with a random slope and one without (but otherwise identical), the fixed effects in the two models are identical. My understanding is that this stems from ...
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Multinomial logistic regression decision border - unsure how to understand a scientific paper

I am reading a paper (https://ieeexplore.ieee.org/document/8442470) where the authors used multinomial logistic regression to fill the transition matrix of their markov chain and got nice results. ...
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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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Are log-odds a better explanatory variable than a percentage in logistic regression?

I am doing logistic regression with group percentages as a predictor and I'm wondering whether it is better to transform them into log-odds first. My logic is that if I were trying to predict ...
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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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Implementing logistic regression model in prediction model - use outcome or probability?

My question deals with the principles or way of thinking about implementing a logistic regression model in a larger scale forward prediction. Let's say I have a trained logistic model which can ...
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Using Sigmoid in Maximum Likelihood Estimates [duplicate]

I have two questions regarding the use of Sigmoid in MLE: Clearly, the Sigmoid Function is not a PDF. But in the MLE of Logistic Regression, we see Sigmoid being used as if it is a PDF. Is my ...
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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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Calculate future revenue based on a log growth formula similar to exponential growth formula?

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 ...
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When I normalize my X, it changes the curve

I am going between Excel and R for this understand the fitted lines of this experiment. I have X and I have Y. When plotted it give me a curve that looks slightly sigmoidal, but I realize the X goes ...
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Exponential growth curve similar to SSlogis?

I'm able to fit a logistic growth curve, e.g. like this. Example provided in that link: ...
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3 votes
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Decision boundary of logistic Regression and Hypothesis space in R

I am trying to generate a decision boundary of logistic regression. My Training set is 2/3 and the test set is 1/3, I have however tried producing the decision ...
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Sigmoid vs Softmax Accuracy Difference

I have trained a neural network on DNA sequences data and my training set has exactly the same number of data in both classes. When I select a softmax function at the end, my accuracy remains at 47% ...
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Fitting a sigmoid model to my data and comparing parameters for different factors

I acquired data from 20 subjects for 4 different conditions (2 factors) with 14 different intensity levels, created using a log-space distribution. I would like to model the response for each ...
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Logistic growth curve with R nls

I would like to fit a model 'logistic-growth' or 'sigmoid growth' per exercise 'Try It #3' over on this online textbook (almost halfway down the page): \begin{array}{|c|c|c|c|} \hline \text{Year}&...
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R fit a logistic regression of the form $y=\frac{c}{1+ae^{-bx}}$ [duplicate]

I'm working through some textbook exercises on fitting models to data, including exponential, logarithmic and now logistic regression. About a 3rd of the way down this page is the section on logistic ...
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3 votes
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Binary classification of each column in an image

I have a problem where I wish to classify each column in an image of a feature being present (1) or absent (0) in each column. The output of the model should be a vector of size of the width of an ...
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What is the extension(or generalisation) of the sigmoid function to non-binary classification? [duplicate]

I understand that one of the main points of using the sigmoid function on responses in binary classification is that we can interpret value outputted as the probability that an instance belongs to 1 ...
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Sigmoid confidence curves in logistic regression

I have a logistic regression model that predicts the probability of an outcome based on one input variable. I am able to plot the curve just fine and show my group how the probability is predicted to ...
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Logistic probabilities of state variable in a hidden Markov model always has variance of zero

Here is a simplified version of a more complicated problem that I have. Imagine a hidden Markov model where the state is $X_t\sim N(\mu,\sigma^2)$. The observed variable is $Y_t\sim Bin(N, p_t)$ ...
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Rounding output of sigmoid for binary linear classifier

I am working on a linear classifier with expected output to be 1 for class A belonging and 0 for class B belonging. The output, in some occasions is nearly 0 (...
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2 votes
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Adjustment factor in logistic growth model of facebook-prophet

In the paper it emphasizes: "When the rate k is adjusted, the offset parameter m must also be adjusted to connect the endpoints of the segments. The correct adjustment at changepoint j is easily ...
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Why SSgompertz does not work on similar data sets?

I have data that follows a sigmodial shape and the Gompertz function seem to make sense. I wanted to use SSgompertz in nls to find the parameters, but I get sometimes errors. So, I wanted to learn ...
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4 votes
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What is $\int_{c}^{\infty}\Phi(a+bx) \phi( x ) dx$ for $c\in\mathbb{R}$

It is straightforward to show $$\int_{-\infty}^{\infty}\Phi(a+bx) \phi( x ) dx = \Phi\left(\frac{a}{\sqrt{1+b^2}}\right)$$ but what value does $$\int_{c}^{\infty}\Phi(a+bx) \phi( x ) dx$$ have for $c&...
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Calculate probability of outcome of a medical procedure

I have data on medical procedures completed at hospitals in major U.S hospitals. Each medical procedure is assigned a code, for example: Kidney Transplant is X6571. I define the success criteria and ...
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How to model a sigmoid function? [closed]

I have a variable where Y ~ sigmoid(X). Y ranges between 0 and 1. Y, however, is not a probability, so I don't know if I can just get a logistic regression. What I do want is, for a change in X, ...
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How is an 'ogival function' defined?

Reading on a paper on factor analysis and measurement invariance I find the description of some functions as 'ogival' functions. In Google I find it referenced mostly in papers from the '70s and '80s....
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Conceptual explanation of taking derivative of sigmoid function in neural network

In a neural network, we have a bunch of inputs and corresponding weights + a bias which are represented by a multivariable equation. Now we squash this whole equation with a sigmoid function. How ...
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Why is learning slower for a sigmoid activation function in a neural network?

Andrew Ng in one of his deep learning course videos says that the sigmoid function acts as a slow learner in a neural network. My intuition is that the sigmoid as an activation function contributes ...
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Statistical comparison of numerous nonlinear model parameters

I have 84 data sets (n=3) corresponding to 28 conditions (sample composition and temperature) and have fit my data set to the following nonlinear model using MATLAB nonlinear curve fitting: $$y = \...
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