Probabilistic Modeling

Maximum Likelihood Estimation

Q1. Explain frequentist vs. Bayesian statistics.

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Maximum Likelihood Estimation

Q2. How can we estimate the parameters of a given probability distribution?

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Maximum Likelihood Estimation

Q3. What is the main assumption of MAP and MLE?

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Maximum Likelihood Estimation

Q4. How is likelihood different than probability?

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Maximum Likelihood Estimation

Q5. Write the mathematical expression of likelihood?

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Maximum Likelihood Estimation

Q6. What does Argmax mean?

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Maximum Likelihood Estimation

Q7. Describe how to analytically find the MLE of a likelihood function?

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Maximum Likelihood Estimation

Q8. What is the term used to describe the first derivative of the log-likelihood function?

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Maximum Likelihood Estimation

Q9. What is the relationship between the likelihood function and the log-likelihood function?

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Maximum Likelihood Estimation

Q10. What is likelihood function of the independent identically distributed (i.i.d) random variables:

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$X_1,··· ,X_n$ where $X_i ∼ binomial(n, p)$ , $∀i ∈ [1,n]$ , and where p is the parameter of interest?

Maximum Likelihood Estimation

Q11. How can we derive the maximum likelihood estimator (MLE) of the i.i.d samples $X_1, · · · , X_n$ introduced in above question?

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Maximum Likelihood Estimation

Q12. Derive the maximum likelihood estimator of an exponential distribution.

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Maximum Likelihood Estimation

Q13. A lot of machine learning models aim to approximate probability distributions. Let’s say P is the distribution of the data and Q is the distribution learned by our model. How do measure how close Q is to P?

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Q1. Explain frequentist vs. Bayesian statistics.

Q2. How can we estimate the parameters of a given probability distribution?

Q3. What is the main assumption of MAP and MLE?

Q4. How is likelihood different than probability?

Q5. Write the mathematical expression of likelihood?

Q6. What does *Argmax* mean?

Q7. Describe how to analytically find the MLE of a likelihood function?

Q8. What is the term used to describe the first derivative of the log-likelihood function?

Q9. What is the relationship between the likelihood function and the log-likelihood function?

Q10. What is likelihood function of the independent identically distributed (i.i.d) random variables:

Q11. How can we derive the maximum likelihood estimator (MLE) of the i.i.d samples $X_1, · · · , X_n$ introduced in above question?

Q12. Derive the maximum likelihood estimator of an exponential distribution.

Q13. A lot of machine learning models aim to approximate probability distributions. Let’s say P is the distribution of the data and Q is the distribution learned by our model. How do measure how close Q is to P?

Q6. What does Argmax mean?