# Vocabulary

MLE: maximum likelihood estimation, given a model, we find the parameter that make the observed data most probable.

Multivariate: multivariate data, datasets contains more than 1 observed variable.

Multivariate Gaussian Distribution: a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. The multivariate normal distribution in n-dimensions is parameterized with a mean vector and a covariance matrix. The mean vector is an n-dimensional vector where each value is the mean of one of the variables. The covariance matrix is an n x n matrix that shows the covariance between each pair of variables.

Covariance: Measures the joint variability of two variables. If the variables tend to show similar behavior (i.e., when one increases, the other also increases, and when one decreases, the other also decreases), the covariance is positive. Conversely, if one variable tends to increase when the other decreases, the covariance is negative.

Precision matrix: Inverse of the covariance matrix, gives about conditional independence and partial correlations.

<figure><img src="/files/f2Yqx6mjHTublrJzjyjJ" alt=""><figcaption><p>Precision matrix, source: fiveMinuteStats</p></figcaption></figure>

Bell numbers: possible partitions of a set

Lambert function: inverse of function f(w) = w \* e^w, where e is the base of the natural logarithm, and w is any complex number. The Lambert W function appears in the solutions to many kinds of mathematical problems.

Poisson distribution: The Poisson distribution is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

Degenerate distribution: distribution takes only a single point - where distribution of that point is 1 and 0 elsewhere.

<figure><img src="/files/dFolvtzq95z7M20LrUe6" alt=""><figcaption><p>Touchard Polynomials</p></figcaption></figure>

Moment: Measure describe the shape of points.


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