# Questions tagged [logistic-regression]

For questions about logistic regressions, a regression model where the dependent variable is categorical.

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### Why in logistic regression for every threshold the decision boundary is a hyperplane?

I'm a beginner in machine learning study and I can't figure it out an exercise: The function h(x) = θ(w ̃x) is used to approximate ...
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### Normality assumption for predictors?

In data science, should we ensure that all variables are normally distributed? I do understand that the y-value would need to be normally distributed as a logistic regression assumption. For instance, ...
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### How do you transform a Derivative to a Recurrence Equation?

In the logistic equation, they say $\frac{dx}{dt} = rx(1-x)$ is equal to $x_{n+1} = rx_{n}(1-x_{n})$. How do they do that? And if you were to transform $\frac{dx}{dt} = 2$ to the recurrence equation, ...
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### Machine learning - Cost function for non linear functions [closed]

The cost function is some indication of the 'cost'/how the predicted value differs from the actual value. In linear regression, this can be measured using MSE. In the case of the logistic function, ...
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### Proof that the MLE of logistic regression doesn't have a closed-form solution

It is well known that the maximum likelihood estimator of logistic regression does not admit a closed form solution, at least in the general case where the predictors are not binary or categorical. ...
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### explanation for cross entropy for logistic regression

as far as I know, cross entropy of two distributions is: $$C(p,q) = -\sum_{s \in classes}p(s)\log(q(s))$$ however, the loss function for logistic regression (called "crossentropy loss") it'...
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### What is the best way to estimate the parameters of a logistic regresion model?

I recently read about logistic regression model. $$y=\frac{1}{1+e^{-(\beta_0+\beta_1x)}}$$ where y is a categorical variable with either 0 or 1 output. What seems to be perplexing to me is, I can see ...
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### How to determine labeled balls for logistic regression

I am studying this paper about logistic regression. In section 4.2 (Randomly Generated Problems) on page 1534, they say "Features of positive (negative) examples are independent and identically ...
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### Implementing multiclass logistic regression from scratch

This is a sequel to a previous question about implementing binary logistic regression from scratch. Background knowledge: To train a logistic regression model for a classification problem with $K$ ...
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### Interpretation of Proportion change in regression

I have two equations: expenditure = 10 + 20*income where income is measured as a proportion between 0 and 0.7 ln(expenditure) = 3.5 + 1.2 * income Assumption: expenditure measures in thousand ...
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I am a data scientist working for a company that takes user deposits. I wanted to answer the question of how likely an account that's dropped to $0 on deposit - or dies, in other words - would refund ... • 111 0 votes 0 answers 4 views ### Creating adversarial sample by projecting my data on the other side of the hyperplane I performed a binary classification using logistic regression. My goal is the following: I know the coefficient w of the hyperplane equation y = wTx + b. What I would like to do is create opposing ... 0 votes 0 answers 25 views ### Why is the sigmoid of a linear model equal to the probability of the target being$1$? From this resource, the writer starts with a linear model: $$y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + ... + \beta_m x_m$$ and then makes the RHS sigmoidal. This must then make the LHS sigmoidal to ... • 1,871 0 votes 1 answer 15 views ### Why does linear regression output numbers but logistic regression output probabilities? From reading this resource, the writer wrote: A linear model does not output probabilities, but it treats the classes as numbers (0 and 1) and fits the best hyperplane (for a single feature, it is a ... • 1,871 0 votes 0 answers 28 views ### Binary Logistic Regression with labels$\{-1, 1\}$I am reading about binary logistic regression and I have found an equivalent formulation given by $$\min_{w} \frac{1}{m}\sum_{i} \log \left(\exp(-y_iX_iw) + 1\right),$$ where$X \in \mathbb{R}^{m \...
In linear Regression we have the following loss function :- $$L(x)=\frac1{n}\left(\sum_{i=1}^n ((a+bx_i)-y_i)\right)^2$$ Hence, we can observe that L(x) is having a convex graph but when we use the ...