[Feature request] windowed wrls

[m00ngoose]

I propose some additional functionality; consider a dataframe with multiple observations per day, and suppose I wish to regress with daily state updates (generalizing: update based on some suitable class of windowing function, rather than update once / row). This could apply to all of rolling/expanding/rls. The output shape would be according to the window groups (eg. one row per day containing coefficients for that window). Additionally, I would like to be able to provide per-row sample weights.

[azmyrajab]

Hi @m00ngoose , I thought a bit about this - and my proposal for the flexible spec you are after is:

(
    df
    .with_row_index()  # <-- in general can be any intraday timestamp, daily date, or index
    .rolling(index_column="index", period="252i", min_periods=1) # <--- period can be temporal e.g. "7d" if index is time
    .agg(pl.col("y").least_squares.ols(cs.starts_with("x"), mode="coefficients")) # <-- can pass weights, ridge penalty, etc. here
)

• Pros:
  • can support literally any windowing (e.g. rolling/expanding) scheme you like, can do in a group by dynamic context, benefit from polars core windowing parameters
  • And you can do this without restrictions on model choice (e.g. elastic net works).
  • every window is independent, and both the windowing logic and polars ols are operating in rust, so everything will be parallel
• cons:
  • computationally less efficient (given finite resource) than doing rank 1 updates which I implemented for the existing dynamic models. i.e. inv(xtx) @ xty, or equivalent, will need to be recomputed repeatedly. This may be offset by more parallelism in some cases though

Could you have a go at trying this and letting me know if this works for you?