# Questions tagged [map-estimation]

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### Discriminative Models with Class Priors

In discriminative models, we model $p(Y|X)$ directly while in generative models we model $p(X|Y)p(Y)$ where $X$ is the input and $Y$ is the output variable. I am confused when the parameters and ...
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### MAP estimate and Maximization step

I have a very simple question. My reference textbook is the Murphy, "machine learning, a probabilistic perspective". Let's imagine we are trying to fit a GMM $\gamma$ with MAP. We know that the ...
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### Multidimensional Bayes point estimates

Consider the posterior distribution $p(\theta|x)$. We aim to find a "good" estimate of the random variable $\theta$. The Bayes risk associated with the loss function $L(\hat{\theta}, \theta)$ is ...
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I have come across these slides (slide # 16 & #17) in one of the online courses. The instructor was trying to explain how Maximum Posterior Estimate(MAP) is actually the solution $L(\theta) = \... 1answer 378 views ### How can (L1 / L2) regularization be equivalent to using a prior when priors can't be changed? I understand the argument for how training with an L1/L2 regularizer is the same thing as finding the MAP estimate when the prior is Gaussian/Laplace. But there's a crucial difference. In Bayes' ... 1answer 262 views ### MAP estimation for multiple parameters Consider$N$observed data points$x_i$($i=1,..,N$), and a likelihood that depends on$p$parameters:$f(x_i|\theta_n)$($n=1,..p$). From Bayes' theorem$$p(\theta_n|x_i) = \frac{f(x_i|\theta_n)g(\... 2answers 433 views ### What is an example of a transformation on a posterior distribution such that the MAP estimate will be non-invariant? Suppose that we have a posterior distribution$p(\theta\mid y)$and we wish to define a transformation on$\theta$such that$\phi = f(\theta)$. I know that generally such transformations will not ... 1answer 93 views ### For a posterior$p(\theta |y)$, if I specify a one-to-one transformation$\phi = g(\theta)$, how can I apply the transformation? [duplicate] Suppose I have a posterior distribution,$p(\theta \mid y)$, where$y$was my data and$\theta$is a random variable with some prior distribution. If I specify a one-to-one transformation$\phi = g(\...
The most common usage of the variational inference looks like to be in computing the marginal distribution $P(X)$ in the denominator of the Bayes formula when computing the posterior probability of ...