DS | Statistics | Priority

Question 1

Sampling distribution?

Answer 1

tak “The sampling distribution of an estimator is the distribution of results we would see if we applied the estimator multiple times to different datasets sampled from some distribution;”

Probabilistic Machine Learning: An Introduction 4.7.1 Sampling distributions

Question 2

Sampling distribution?

Answer 2

tak “The sampling distribution of an estimator is the distribution of results we would see if we applied the estimator multiple times to different datasets sampled from some distribution;”

Probabilistic Machine Learning: An Introduction 4.7.1 Sampling distributions

Question 3

Treatment of data and parameter in frequentist vs. Bayesian approaches?

Answer 3

tak “In the frequentist approach, theta is treated as an unknown fixed constant, and the data is treated as random. In the Bayesian approach, we treat the data as fixed (since it is known) and the parameter as random (since it is unknown).“

Probabilistic Machine Learning: An Introduction 4.7.5 Caution: Confidence intervals are not credible

Question 4

Basic idea of a confidence interval.

Answer 4

tak “This means that, if we repeatedly sampled data, and compute I(~D) for each such dataset, then about 95% of such intervals will contain the true parameter” theta

Probabilistic Machine Learning: An Introduction 4.7.4 Confidence intervals

Question 5

Treatment of data and parameter in frequentist vs. Bayesian approaches?

Answer 5

tak “In the frequentist approach, theta is treated as an unknown fixed constant, and the data is treated as random. In the Bayesian approach, we treat the data as fixed (since it is known) and the parameter as random (since it is unknown).“

Probabilistic Machine Learning: An Introduction 4.7.5 Caution: Confidence intervals are not credible

Question 6

What is te equation for bias/variance for MSE?

Answer 6

MSE = variance + bias^2

Probabilistic Machine Learning: An Introduction 4.7.6.3 The bias-variance tradeoff

Question 7

How does regularization affect bias/variance?

Answer 7

tak “as we increase the strength of the regularizer, the variance decreases, but the bias increases.“

Probabilistic Machine Learning: An Introduction 4.7.6.5 Example: MAP estimator for linear regression

Question 8

Illustration of the bias variance tradeoff.

Answer 8

Figure 4.26: Cartoon illustration of the bias variance tradeoff.

Probabilistic Machine Learning: An Introduction 4.7.6.5 Example: MAP estimator for linear regression

Question 9

Bias-variance tradeoff for classification?

Answer 9

“If we use 0-1 loss … the bias and variance combine multiplicatively.“; “This little known fact illustrates that the bias-variance tradeoff is not very useful for classification. It is better to focus on expected loss … We can approximate the expected loss using cross validation“

Probabilistic Machine Learning: An Introduction 4.7.6.6 Bias-variance tradeoff for classification