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?
create structure of package
set up automatic compiling and testing
Use packages:
## 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)
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)
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