You have the option select what data to sample, you have ability to intervene. That is agency.

Baysean optimization

Get the optimal of function as quickly as possible

We deal with smooth functions

If you condtion on a gaussian it is still a gaussian

Conditioning means that you want the distribution for a particular value

Multivariate is defined by two parameters, the mean and the covariance.

Covariance: How much correlation their is between sample 1 and sample 2

The role of the covariance functino is how to encode the relationship

How do we determine the kernel parameters? : Hyper parameter tuning and maximum likelihood. Maximum lilelihood will look like a gaussian

The goal of a surrugate function is to approximate the function

The role of the aqusition function. It will tell you the value of how good it is to sample a point. 3 types: Probability of improvemenet, probabilty of improving the current best estimate. Estimate the area under the curve. Expected improvement: expectation, You weigh the probabilty by how much improvement there is. UCB: Takes the mean and add a constant time the variance. The larger the variance or the mean the better. Parameter kappa, increases importance of the variance

Active learning

We want to ask the right questions. We want to ask questions that we dont know the answer to. We want to know the uncertainy of samples. Three methods for uncertainty samplingg. Least confidence sampling you order by probabilty then take the least likely. You want to choose something that is half way in between for a two category problem. Margin sampling Considers the two most lileky samples. something. Entropy sampling: If its categorical then you weigh each of the options with log the put a minus in front. For a gaussian the entropy maps to the variance. The less you know about the higher the entropy.

Version space: All of the models that are curently compatible with the data you have. You want to reduce the version space. We want to choose data points that disagrees the most with the models we have. The best we can do is remove half the version space no matter the answer

Query by committee: A way to get uncertainties. Query labels we are uncertain about. The query is the approximation of the version space.

Ways to measure disagreecement. Vote entropy. We produce a probabilty by voting between comittee members. This doesnt require a problilty for the individual model