Contents
What is the meaning of the KL divergence?
In this context, the KL divergence, KL(P | | Q), is interpreted as the amount of information lost when you use the distribution Q to approximate the distribution P. Specifically, it is the error (in bits) of the observed distribution over the data points Q when you wanted the ideal cluster distribution P.
Can a cluster be defined by a delta distribution?
In the most extreme case, clusters could be defined by a delta distribution over a ball of a given radius around the cluster centroid (i.e. if the point is within the radius, it has probability 1 of being a member of the cluster). However, such a discontinuous definition is computationally impractical and makes the optimization problem difficult.
How is PIJ used to define a cluster?
The target distribution, pij represents ideal clusters. In the most extreme case, clusters could be defined by a delta distribution over a ball of a given radius around the cluster centroid (i.e. if the point is within the radius, it has probability 1 of being a member of the cluster).
The Kullback-Leibler (KL) divergence is often conceptualized as a measurement of how one probability distribution differs from a second probability distribution, i.e. as a measurement of the distance between two probability distributions.
Is the Kullback Leibler divergence a true metric?
Although it is often intuited as a way of measuring the distance between probability distributions, the Kullback–Leibler divergence is not a true metric. It does not obey the Triangle Inequality, and in general
What does it mean to have a correlation between two variables?
Generally speaking, when we talk of ‘correlation’ between two variables, we are referring to their ‘relatedness’ in some sense. Correlated variables are those which contain information about each other. The stronger the correlation, the more one variable tells us about the other.
When is a covariance is a negative number?
If they have a tendency to be on opposite sides of their means, the covariance will be a negative number. The stronger this tendency, the larger the absolute value of the covariance.
Why do we talk about negative log likelihood?
It’s because we typically minimize loss functions, so we talk about the “negative log likelihood” because we can minimize it. (Source: CrossValidated .) Thus, when you minimize the negative log likelihood, you are performing maximum likelihood estimation. Per the Wikipedia article on MLE,
Is the log likelihood the same as the cross entropy?
And here’s another summary from Jonathan Gordon on Quora: Maximizing the (log) likelihood is equivalent to minimizing the binary cross entropy. There is literally no difference between the two objective functions, so there can be no difference between the resulting model or its characteristics.
What is the log likelihood of no airplane?
This means we have a 1 – 0.01 = 0.99 probability of “NO airplane” – and so on, for all the output neurons. Thus, each neuron has its own “cross entropy loss” and we just sum together the cross entropies of each neuron to get our total sigmoid cross entropy loss.