Linked Questions

9 votes
2 answers
15k views

Why sum of squared errors for logistic regression not used and instead maximum likelihood estimation is used to fit the model? [duplicate]

I have a doubt on why sum of squared errors is not used for Logistic regression and instead maximum likelihood estimation is used and also why not the vice versa. Edited Many were asking me to ...
Sri Harsha Pinninti's user avatar
20 votes
2 answers
8k views

Least squares logistic regression [duplicate]

I have seen it claimed in Hosmer & Lemeshow (and elsewhere) that least squares parameter estimation in logistic regression is suboptimal (does not lead to a minimum variance unbiased estimator). ...
user9968's user avatar
  • 211
3 votes
1 answer
3k views

is cost function of logistic regression convex or not? [duplicate]

For logistic regression, the loss function is convex or not? Andrew Ng of Coursera said it is convex but in NPTEL it is said is said it is non convex because there is no unique solution. (many ...
Shubham Kumar's user avatar
5 votes
2 answers
2k views

Logistic regression cost surface not convex [duplicate]

I am building a simple logistic regression model on 2D data. Here is the input I use. I built a logistic regression model using this data and it successfully is able to find the discriminating line ...
Sait's user avatar
  • 153
1 vote
2 answers
408 views

Why can you not estimate Beta with least squares in logistic regression? [duplicate]

As the title says, why can you not estimate Beta (coefficients) in logistic regression with least-squares? I read in a book that it is not possible and that we use maximum likelihood instead, but I ...
Alexander's user avatar
3 votes
0 answers
935 views

Why using RMSE as loss function in logistic regression takes non convex form but doesn't in linear regression? [duplicate]

I am taking this deep learning course from Andrew NG. In the 3rd lecture of 2nd week of the first course, he mentions that we can use RMSE for logistic regression as well but it will take a nonconvex ...
ashish14's user avatar
  • 131
0 votes
1 answer
276 views

Why we do not use least squares in logit model? [duplicate]

I am very wondering why we do not use least squares instead of maximum likelihood? for example we have 3 choices k= 1, 2 ,3 $minimizing: (e^{\beta_{i} X}/(1+\sum e^{\beta_{i} X})- Y)^{2} $ for i=1,...
sherek_66's user avatar
  • 137
1 vote
0 answers
316 views

Fitting of logit using least squares [duplicate]

So I am asked to fit a logit model using the method of least squares in connection to logistic regression. Let $\pi(x)=\mathrm{P}(Y=1|X=x)$ be the probability of success of a binary response variable $...
StubbornAtom's user avatar
  • 11.4k
1 vote
0 answers
43 views

Logistic Regression For Classification [duplicate]

The origin of logistic regression is actually logistic curve which varies from the value 0 to the value 1. It looks like the letter S, and it specifies the growth of species. If our data distribution ...
Goktug's user avatar
  • 517
1 vote
0 answers
12 views

Difference between loss functions in neural networks [duplicate]

Supose I would like to build a neural network with a sigmoidal function in the output layer, why is there a preference in the use of cross-entropy as a loss function in regard square loss for example? ...
Marcus's user avatar
  • 71
72 votes
18 answers
91k views

Statistics interview questions

I am looking for some statistics (and probability, I guess) interview questions, from the most basic through the more advanced. Answers are not necessary (although links to specific questions on this ...
32 votes
3 answers
14k views

Is logistic regression a specific case of a neural network?

I ended up in a debate regarding logistic regression and neural networks (NNs). Is it wrong to say that logistic regression is a specific case of a neural network? I have seen a lot of explanation in ...
Nikaido's user avatar
  • 812
14 votes
4 answers
9k views

Importance of variables in logistic regression

I am probably dealing with a problem that has probably been solved a hundred times before, but I'm not sure where to find the answer. When using logistic regression, given many features $x_1,...,x_n$ ...
Guy Adini's user avatar
  • 348
11 votes
2 answers
12k views

How To Solve Logistic Regression Using Ordinary Least Squares?

I was self-learning machine learning. I came upon this section of the Wikipedia page on Logistic regression, where it claims Because the model can be expressed as a generalized linear model (see ...
kirakun's user avatar
  • 211
14 votes
2 answers
2k views

Disadvantages of using a regression loss function in multi-class classification

Given $k > 2$ classes, consider the following loss function $$ \sum_i||y^{(i)} - \hat y^{(i)}||^2 $$ Here $y^{(i)} \in \{0,1\}^k$ is the $i^{th}$ one-hot encoded true label and $\hat y^{(i)} \in [0,...
helperFunction's user avatar

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