MMiDS 6.2: Self-Assessment Quiz

Which of the following is NOT an example of an exponential family of distributions?

In the exponential family form pθ(x)=h(x)exp(θTϕ(x)A(θ)), what does A(θ) represent?

Given n independent samples X1,,Xn from a parametric family pθ with unknown θΘ, the maximum likelihood estimator θ^MLE is defined as:

What is the Kullback-Leibler divergence KL(pq) between two probability distributions p and q?

What is the relationship between the maximum likelihood estimator and the Kullback-Leibler divergence?

Under certain conditions, the maximum likelihood estimator is guaranteed to converge to the true parameter as the number of samples grows. This property is known as:

For exponential families, the maximum likelihood estimator (if it exists) solves which of the following equations?

What is the sufficient statistic for a multivariate Gaussian distribution in the context of exponential families?

In a generalized linear model, the maximum likelihood estimator w^MLE solves the equation:

In logistic regression, which distribution is used for the outcome variable?

In logistic regression, the log-likelihood is: