Questions tagged [logistic-regression]
For questions about logistic regressions, a regression model where the dependent variable is categorical.
276 questions
1
vote
1
answer
74
views
Reasoning behind logistic regression
For logistic regression the following holds:
$$ p = \frac{1}{1+\exp(-z)} \quad ; \quad z = b+\vec{w}\cdot\vec{x} $$
It turns out that we can get this expression if we fit $\operatorname{logit}(p)$ to $...
1
vote
1
answer
110
views
Finding a upper bound on $||\nabla^2 f(x)||_{p,q}$ for p,q $\neq 2$ that is faster to calculate than eigenvalues or smaller.
Beck (2017):
for a function $f:\mathbb{R}^n \rightarrow \mathbb{R}$ that is twice-differentiable, for a given $L>0$ $\beta$-smoothness with respect to the $L_p$ norm for $p \in [1,\infty)$ is ...
- 23
0
votes
1
answer
85
views
What is the shape of the $A^TA$ and $A$?
I am trying to find the shape of $A^TA$ and $A$
Either $A^TA$ has shape $\mathbb{R}^{dxd}$ or $A^TA$ has shape $\mathbb{R}^{nxn}$
$a_i$ is an observation in the data matrix. The data matrix has shape $...
- 23
1
vote
1
answer
117
views
Why is the Hessian of the negative log-likelihood in multinomial logistic regression positive definite?
I am studying the convexity properties of the negative log-likelihood in multinomial logistic regression.
Let me briefly set up the notation:
We have a dataset
$$
D = \{(x_n, y_n)\}_{n=1}^N, \quad ...
0
votes
1
answer
43
views
In logreg, why do we work with probabilities instead of just using a continous value?
In logistic regression, is there a FUNDAMENTAL reason why I map a continuous value to a probability? Couldn't I simply define a decision threshold from a continuous value? What is the mathematical ...
1
vote
1
answer
77
views
The Gradient of the Logistic Regression Objective Function
I’m learning logistic regression, and I’m just trying to derivative likelihood function by myself!
Here’s the likelihood function
$$LL(\theta) = \sum_{i = 0}^n y^{i} \log \sigma(AX + B) + (1-y^{(i)}) ...
- 83
0
votes
1
answer
62
views
Domain of the derivative of the logistic function $\sigma (x)$
I'm trying to prove that the derivative of the logistic function $\sigma (x) = \frac{1}{1+e^{-x}}$ verifies the inequality $0 \leq \sigma '(x) \leq \frac{1}{4}$.
I managed to find that $$ \sigma (x) = ...
- 49
0
votes
0
answers
71
views
MCMC and Bayesian Logistic Regression (simple)
Disclaimer: I am pretty rusty on Bayesian Analysis. I was trying to do a simple logistic regression example but was getting stuck. This is not the problem, but I wanted to do a reproducible example ...
- 591
0
votes
0
answers
84
views
Correct form of Richard's curve (generalized logistic function)
I'm studying logistic functions these days.
I came across generalized logistic function (Richard's curve) on Wikipedia here:[Generalised logistic function][1]
However, I cannot find any article that ...
- 9
0
votes
1
answer
61
views
Logistic Regression derivation of the MLE of the parameters
I am reading about the Logstic regression. I get confused when we take derivatives with respect to vectors. As an example we have the Loss function of the Logistic regression as the Log-odds function ...
- 2,712
1
vote
0
answers
90
views
Deriving the Logit Choice Probability from a Random Utility Model
Suppose we have a random utility model given by $u_{ij}=\delta_j + \varepsilon_{ij}$.
This model specifies the utility that consumer $i$ receives by choosing product $j$. We can interpret $\delta_j$ ...
1
vote
1
answer
63
views
Modelling Rate with Logistic regression
Current practice to model rate i.e. response variable ranging from 0 to 1 is model within the framework of Logistic regression. Both ...
- 225
3
votes
1
answer
114
views
How to map identity to a sigmoid?
Is there a way of smoothly defining a function that transforms the identity function to a sigmoid for a fixed range (say $[0,1]$)? What I want is to define a function $f(x,k)$ such that $f(0,k)=0,f(0....
- 3,585
1
vote
0
answers
21
views
Collaborative Planning, Forecasting, and Replenishment (CPFR) model
I'm trying to understand better the CPFR model but I can't find anywhere a numerical example of this.
I'm looking for a numerical example with solution for Collaborative Planning, Forecasting, and ...
- 85
1
vote
0
answers
76
views
Matrix Calculus, finding the weights of a 2 layered non-linear neural network, with sigmoid activation functions
I'm working on a method to calculate weights of a non-linear 2 layer neural network in 1 step, instead of working with the propagation algorithm.
I have chosen to make the non-linearity a sigmoid ...
