All Questions
Tagged with logarithm probability
23
questions
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92
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Carrying out statistics on -log(p)
I have an $n \times m$ matrix, where each row $\mathbf{v}_i$, for $i \in \{1, \ldots , n\}$, consists of some permutation of the set $\{1, \ldots, m\}$ (and so in particular, each $\mathbf{v}_{i, j} \...
- 1
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51
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Statistical comparison of two (log) probabilities
Using R, I built 2 logistic regression models (with outcome variable being depression status - present or absent) and used leave one out cross validation to obtain predicted values for the dataset. I ...
- 363
1
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0
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62
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Calculate difference in log odds between two logistic regression models
I would like to calculate the difference in log-odds between the error of two logistic regression models, given the correct answer aka ground truth (depression present${}= 1;$ depression absent${} = 0$...
- 363
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117
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Does Benford's Law Actually Work?
Recently, I have been reading about Benford's Law :https://en.wikipedia.org/wiki/Benford%27s_law
This law supposedly states that naturally occurring numbers are more likely to start with the number &...
2
votes
1
answer
532
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Is negative log likelihood calculated in log space or exponential space?
I have a question about calculating negative log likelihood in a machine learning model over a dataset which seems simple but I cannot find a solid answer/explanation online.
Is the NLL calculated as ...
- 942
2
votes
1
answer
298
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Log probabilities versus squared probabilities (entropy vs Gini)
The advantage of log probabilities over direct probabilities, as discussed here and here, is that they make numerical values close to $0$ more easy to work with. (my question, instead of the links, ...
- 4,025
44
votes
4
answers
21k
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Why are log probabilities useful?
Probabilities of a random variable's observations are in the range $[0,1]$, whereas log probabilities transform them to the log scale. What then is the corresponding range of log probabilities, i.e. ...
- 4,025
2
votes
1
answer
4k
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Summation of Log Probabilities
I am trying to implement the following:
where the right part returns a probability between 0 and 1. Regarding the product, the authors of the respective paper note:
Due to numerical precision ...
- 123
7
votes
1
answer
1k
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What is the expected value of x log(x) of the gamma distribution?
Let $w(x) = x \log{x}$
$x \sim Gamma(\alpha = 3.7, \lambda = 1)$
Find $E[w(x)]$
I have set up the following integral:
$\int_0^{\infty} x\log{x} \frac{\lambda^{\alpha}}{\Gamma(\alpha)} x^{\alpha -1}...
- 73
1
vote
0
answers
417
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Reporting the average log-probability the model assigns to some examples
I am currently studying Deep Learning by Goodfellow, Bengio, and Courville. In chapter 5.1.2 The Performance Measure, $P$, the authors say the following:
To evaluate the abilities of a machine ...
- 2,096
2
votes
0
answers
47
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Bound for type of correlation measure
Assume you have a finite, discrete probability distribution for a joint random variable and such that $P(X=i,Y=j) = p_{i,j}$ for $i \in \{1, \dots, |X|\},j \in \{1, \dots, |Y|\}$. The marginal ...
- 33
2
votes
1
answer
507
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Computation within log space
What is the conversion of the following equation into log space?
$bf2 = 1 + (p * (bf1 - 1))$
Given log.bf1 (log Bayes factor), how do I get to log.bf2 without having to compute bf1, but instead ...
- 23
6
votes
2
answers
5k
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Calculate binomial deviance (binomial log-likelihood) in the test dataset
I'm predicting probabilities $\mathbb{P}(Y=1)$ using a probability forest (ranger in R). I want to evaluate my predictions $\hat ...
- 81
1
vote
1
answer
6k
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linear probability model interpretation
I have a question regarding the interpretation of a log independent variable in a linear-probability model.
For example: I have $\log(GDP)$ as my independent variable and the coefficient is 0.35. Can ...
- 11
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1
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2k
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Logged control variable in linear probability model
I am wondering how a logged control variable is interpreted in a linear probability model. The interpretation in the following lin-log model is clear:
(1) y = b0 + b1*log(x1)
Here, a 1% increase in ...
