# Questions tagged [laplace-distribution]

Use this tag when asking questions about the Laplace distribution. This probability distribution is sometimes called the double exponential distribution (not to be confused with the Gumbel distribution).

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### Relationship between laplace and l1 regularization

It is well known that an L1 regularized linear regression is equivalent to a regression with a Laplace prior on the distribution of the coefficients. This is explained here: https://bjlkeng.github.io/...
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### MLE of Laplacian with linear parameters

I'm stumped on this problem and was hoping someone could give me some guidance. I'm new to this sort of thing so it's possible that I'm leaving something out of this question or that my question isn't ...
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### Is a Laplace Prior the same thing or related to a Laplace Transformation?

Context: I was watching this video https://youtu.be/pOYAXv15r3A?t=796 about Facebook Prophet and the speaker mentioned they use a Laplace Prior $$\delta \sim Laplace(\lambda)$$. What I have gleaned so ...
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### Is there an any advantage to using Laplace transforms over Fourier transforms in Statistics?

Do you know the advantage of the Laplace transform over the Fourier transform in statistics? I say, it's more restrictive and I couldn't find any advantage I asked this because the professor used ...
1 vote
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### Output Distribution of ReLU given a Laplace Distribution as its Input

If input to a ReLU function (Max(X, 0)) is a Laplace Distribution, what would be the output distribution? will it have a density function? how would it look like? assuming that mean of the Laplace is ...
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### Linear Transformation of a Random Variable with a Laplace Distribution

I have read these two posts ( 1 and 2) about linear transformation of a random variable with a Gaussian distribution. I would like to find the first two moments of a linearly transformed Laplace ...
1 vote
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### Distribution of the dot product of a multivariate Laplace random variable and a fixed vector

This question is basically a follow-up: Distribution of the dot product of a multivariate gaussian random variable and a fixed vector But instead of a multivariate Gaussian random variable, what about ...
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### Laplace distribution as an Exponential Distribution and Minimizitaion of KL Divergence

In the context of Expectation Propagation [Minka's thesis-2001], I would like to approximate an unknown distribution with a Laplace distribution. This can be solved by minimizing KL-Divergence. In ...
345 views

### Logit Laplace Loss Function

In a recent OpenAi paper, the authors propose a novel loss function for the reconstruction term of a VAE coined Logit-Laplace loss. They detail the math on page 13 of the paper but I am having trouble ...
1 vote
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### Why does Chebyshev's inequality yield that the probability of Laplacian noise being bigger than x is bounded like this?

I am trying to understand this proof of the bounds of Laplacian noise used in a paper on differential privacy. Given a random variable $Lap\left ( \frac{\Delta f}{\varepsilon } \right )$, apparently ...
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### Can a folded LaPlace distribution (or other folded distributions) be used with Ɛ-differential privacy

I have a single value in (or over) our dataset, let's say a count of something, and we want to keep that value private within a certain range. This range is the sensitivity. The adversary can ask if a ...
1 vote
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### MLE of a Laplace density [closed]

How do you evaluate MLE of theta, considering a simple random sample of size n from a Laplace density?
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### Laplace Inequality

I am trying to prove that if $r_i \sim Lap(0,1/\varepsilon)$ where $\varepsilon >0$ then: $$Pr[r_i \geq 1+r^*] \geq e^{-\varepsilon}Pr[r_i \geq r^{*}]$$. I know that for $r*>0$ it satisfies ...
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### What is the difference between data perturbation and differential privacy?

I cannot distinguish the terms "data perturbation" and "differential privacy". If the data perturbation is the process that adds some small value sampled from specific distributions such as Laplacian ...
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### Global sensitivity of mean and variance in differential privacy?

Please explain me why global sensitivity of a mean or variance queries will be (b-a)/n and (b-a)^2/n where b is the upper ...
1 vote
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### Bonferroni confidence region for shifted Laplace parameters

Consider the shifted Laplace distribution with the density: $$f(y)=\frac{\theta}{2}e^{-\theta|y-\mu|}\quad, \quad y\in \mathbb R$$ Using the Bonferroni method, construct a $100(1-\alpha)\%$ ...
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### PDF for length of Laplace-distributed vectors

I am interested in finding an analytic expression for the length of a 3-vector whose components are distributed according to a Laplace distribution with zero mean and the same scale parameter. I ...
1 vote
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### Cumulative distribution function of a squared laplace random variable

I am trying to calculate $F_Y(x)$ (CDF) of $Y=X^2$ where $X$ is a random variable of Laplace Distribution $f_X(x) = \frac{1}{2}e^{-|x|}$ (let's take a simple case when parameters $\mu=0$ and $b=1$). ...
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### How can I get confidence interval from Laplace distribution in python?

I have a dataset and I checked that fits a Laplace distribution. I want to get different confidence intervals from it. I know that in a normal distribution, the confidence interval of 68% is mean + ...
1 vote
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### linear model with laplace-distributed residuals, where scale (not location) varies

I have a dataset where I suspect the residuals are approximately Laplace-distributed. There are three continuous predictors. When I split up the data into many bins, based on the values of these ...
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### Efficient random generation from truncated Laplace distribution

We have several ways of drawing random samples from Laplace distribution. Is there any efficient way of sampling from left truncated Laplace distribution? Inverse transform sampling is an obvious ...
1 vote
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### Is the CDF of a Laplace distribution well-defined?

So I'm asked to argue whether the CDF of a Laplace distribution is well-defined or not. Now I don't completely understand what well-defined actually means. CDF given by: Acording to wikipedia: "A ...
3k views

### Sufficiency of Sample Mean for Laplace Distribution

I recently started reading about sufficient statistics. I have the following questions: 1) Is sample mean a sufficient statistic for Laplace Distribution (aka Double Exponential) if we already know ...