See https://www.cs.princeton.edu/courses/archive/fall08/cos436/Duda/C/sk_means.htm

Would be nice to first do #23 and build it upon this

Extend the mean steamer to allow for multi-dimensional data

A generic particle filter with the ability to specify arbitrary noise, measurement, and control distributions.

As above

See here

Not sure if this is even possible, but it would be nice to have to obtain an algorithm for updating regression that has a lower time complexity than recomputing coefficients from scratch.

Implement approaches to the secretary problem.

Implement streaming median (with an optional window).

Implement common strategies for Bernoulli and normal bandits:

• Random
• Epsilon greedy
• Epsilon first
• Epsilon decreasing
• UCB
• Thompson sampling

Sort a list in an online fashion using insertion sort.

I think we should be aiming for test coverage in the 80%s at this point. An easy way to up it is to add unit tests for all mean and variance streamers, which can be based on those for SMA and CMA.

SGD with various batch sizes

Rather than $value() we can have $value using active fields.

https://adv-r.hadley.nz/r6.html#active-fields

Implement a method for the built-in summary() function which prints a summary of the streamer's internal state.

Implement the extended and unscented Kalman filters

Use Monte Carlo methods to extend Thompson sampling to any distribution.

E.g. random, e-greedy, e-decreasing, UCB

Implement streaming versions of the following statistics:

• Variance (biased and unbiased)
• Other streaming averages (see here)

You can base these off the Mean class. For the first, the goal is to solve for $\sigma^2_{n+1}$ in terms of $\sigma^2_n$ and $x_{n+1}$.

When the window size is greater than the initialisation vector length as in SMA$new(c(1, 2), window=3) the values vector is padded on the left with zeros so that SMA$value() is 1 rather than 1.5 initially. Is this intended behaviour? If so, it might be worth adding that to the docs.

Streamers for the minimum and maximum of numbers

This requires some looking into before going ahead. What algorithms exists for online collaborative filtering?

Thompson sampling for common distributions with conjugate priors. It might be cleanest to implement this as a general exponential family and then define special cases.

It would be helpful to add some benchmark vignettes or notebooks to demonstrate speed-ups/memory savings compared to offline methods using different implementations.