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From Jeremy Lewi <jer...@lewi.us>
Subject Re: Understanding log-likelihood
Date Mon, 09 May 2011 00:43:43 GMT
Thomas,

Are you asking a general question about log-likelihood or a specific
implementation usage in Mahout?

In general the likelihood is just a number, between 0 and 1 which
measures the probability of observing some data under some distribution.

So as a simple example, consider a coin toss. So the probability of
observing a heads is .5 and the probability of observing a tails is .5.

So now suppose you observe a toin coss, and the outcome is a heads. So
now we can ask how likely was this outcome under the assumption that
coin was fair. Well the likelihood in this case is just .5; because the
coin is fair.

So now suppose you observe two coin tosses, and the outcome is both
heads. How likely is this outcome? Since the tosses are independent, the
probability of getting two heads is simply the product of getting a
heads on both flips; so 
p(two heads| fair coin) = .5 *.5 = .25

We can also think of this as a counting problem and consider all
possible outcomes for flipping two coins. These are {HH,TH,HT,TT}.
Since the coin is fair all of these outcomes have equal probability of
1/4 or .25.

The probabilities we computed above are the likelihoods. The
log-likelihood is just the result of taking the log of them.

This is a pretty meager explanation so feel free to ask for
clarification.

J


On Mon, 2011-05-09 at 02:14 +0200, Thomas Söhngen wrote:
> Hello,
> 
> I struggle to understand the log-likelihood function. I would highly 
> welcome a simple example of how it is calculated, especially in Mahout.
> 
> Thanks in advance,
> Thomas


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