application-roadmap.md

Steps:

1. Read data (from simulation or file)
2. Add summary measures in wide form (lags, variance, mean, etc).
3. Wait / simulate the minimal number of measurements needed from a single time series
4. Using all these measurements, we estimate the density for q_w given w-, (g given g-), and q_y given y-. (If a dist is binary, we don't have to estimate its distribution, but we still can using Oleg's package, for consistency. The same goes for if a variable is discrete.)
5. SuperLearning will be done to estimate the densities. That is, we use several different estimators for estimating the densities (currently we only use logistic regression). We will also fit the number of bins that best resembles our data.
6. Now, using these densities, we generate a number of draws, using the scheme you sent earlier, in order to get the counterfactual distribution (j is time of intervention, tau is time of response) :

result <- 0
B <- seq(100000)
for b in B
  sample W(1) given C_w(1) from q_w
  sample A(1) given C_a(1) from g_a
  sample Y(1) given C_y(1)
  sample W(2) given C_w(2) from q_w
  sample A(2) given C_a(2) from g_a
  sample Y(2) given C_y(2)
  .
  .
  .
  sample W(j) given C_w(j) from q_w
  sample A(j) = a (= specified, deterministic intervention)
  sample Y(j) given C_y(j)
  .
  .
  .
  sample W(tau) given C_w(tau) from q_w
  sample A(tau) given C_a(tau) from g_a
  result += (sample Y(tau) given C_y(tau)) / B
endfor
result

which will give you the response for an intervention a on time j for an outcome at time tau.

1. Questions:
   • How do we deal with the initialization? Up to now I just expected that we'd skip the first Z measurements, where Z is the maximum number of observations needed for each of the summary measures we include.
   • In this scheme of drawing observations we are not including the change of probability $g_a^*(a(t) | c(a)) / g_a(a(t) | c(a))$, which is probably incorrect?
   • For the SuperLearning step, since we are not comparing a simple mean with an outcome, what would be our cross-validation step and loss function?

Initial roadmap

1. create structure of package

2. set up automatic compiling and testing

3. Use packages:

• 'R.oxygen'
• 'R.utils' ('Arguments$getNumeric' and the likes, 'throw', use of 'verbose')

  ## Example of verbose
  ## Argument 'verbose':
  verbose <- Arguments$getVerbose(verbose)
  verbose <- less(verbose, 10)
  verbose && print(verbose, table(U))
  verbose && enter(verbose, "Simulated  copy number and expression data
  for class 1")
  verbose && str(verbose, V)
  verbose && exit(verbose)

4. Keep in mind that we're interested in oos (online one-step) and otmle (online tmle) estimators

4a. new object S3 structure

4b. high-level description -- flow of the application

(i) learning step
(ii) targeting step

4c. encoding of a generic time series vocabulary:

- (W(t), A(t), Y(t)) is the t-th block
- W(t), A(t) and Y(t) are its nodes
- W(t) in WW and Y(t) in YY, WW and YY possibly multi-dim
- A(t) is discrete/binary?

4d. simulation (i) characterization of data-generating distribution (ii) simulation under the data-generating distribution (iii) characterization of the parameter of interest - => providing intervention nodes, and the corresponding intervention distributions (iv) evaluation of the parameter of interest

4e. encoding of summary measures of the past of each {W,A,Y}-node

4f. write functions implementing online (super-) learning - must rely on online "prediction" algorithms - think about H2O...

4g. Monte-Carlo procedures to derive - the estimates of the parameter from the estimated features - the efficient influence curve, used for targeting + CI (see draft)