Source file inference.ml

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open Costlang
open Maths
module NMap = Stats.Finbij.Make (Free_variable)

type constrnt = Full of Costlang.affine * measure

and measure = Measure of vector

type problem =
  | Non_degenerate of {
      lines : constrnt list;
      input : matrix;
      output : matrix;
      nmap : NMap.t;
    }
  | Degenerate of {predicted : matrix; measured : matrix}

type scores = {
  (* R2 score is uninformative when the input is constant. (e.g. constant model)
     We use `None` for the R2 score of such models. *)
  r2_score : float option;
  rmse_score : float;
  tvalues : (Free_variable.t * float) list;
}

let scores_encoding =
  let open Data_encoding in
  conv
    (fun {r2_score; rmse_score; tvalues} -> (r2_score, rmse_score, tvalues))
    (fun (r2_score, rmse_score, tvalues) -> {r2_score; rmse_score; tvalues})
  @@ obj3
       (req "r2_score" (option float))
       (req "rmse_score" float)
       (req "tvalues" (list (tup2 Free_variable.encoding float)))

let pp_scores ppf {r2_score; rmse_score; tvalues} =
  let scores =
    [
      ("R2: "
      ^ match r2_score with None -> "NA" | Some s -> Printf.sprintf "%f" s);
      "RMSE: " ^ Printf.sprintf "%f" rmse_score;
    ]
    @ List.map
        (fun (v, t) ->
          Printf.sprintf
            "T-%s: %f"
            (Free_variable.to_namespace v |> Namespace.basename)
            t)
        tvalues
  in
  Format.pp_print_list
    ~pp_sep:(fun ppf () -> Format.fprintf ppf " , ")
    (fun ppf s -> Format.fprintf ppf "%s" s)
    ppf
    scores

let scores_to_csv_column (local_model_name, bench_name) scores =
  let {r2_score; rmse_score; tvalues} = scores in
  let name = local_model_name ^ "-" ^ Namespace.to_string bench_name in
  let table =
    (match r2_score with
    | None -> []
    | Some f -> [("R2_score-" ^ name, Float.to_string f)])
    @ [("RMSE_score-" ^ name, Float.to_string rmse_score)]
    @ List.map
        (fun (v, f) ->
          ("T-value-" ^ Free_variable.to_string v, Float.to_string f))
        tvalues
  in
  [List.map fst table; List.map snd table]

type solution = {
  mapping : (Free_variable.t * float) list;
  weights : matrix;
  intercept_lift : float;
  scores : scores;
}

type solver =
  | Ridge of {alpha : float}
  | Lasso of {alpha : float; positive : bool}
  | NNLS

(* -------------------------------------------------------------------------- *)

(* Establish bijection between variable names and integer dimensions *)
let establish_bijection (lines : constrnt list) : NMap.t =
  let elements =
    List.fold_left
      (fun set line ->
        match line with
        | Full ({linear_comb; _}, _quantity) ->
            Free_variable.Sparse_vec.fold
              (fun elt _count set -> Free_variable.Set.add elt set)
              linear_comb
              set)
      Free_variable.Set.empty
      lines
  in
  NMap.of_list (Free_variable.Set.elements elements)

let line_list_to_ols (lines : constrnt list) =
  let nmap = establish_bijection lines in
  let lcount = List.length lines in
  let inputs = Array.make_matrix lcount (NMap.support nmap) 0.0 in
  let outputs = Array.make_matrix lcount 1 0.0 in
  (* initialize inputs *)
  List.iteri
    (fun i line ->
      match line with
      | Full (affine, Measure vec) ->
          Free_variable.Sparse_vec.iter
            (fun variable multiplicity ->
              let dim = NMap.idx_exn nmap variable in
              inputs.(i).(dim) <- multiplicity)
            affine.linear_comb ;
          let vec = Vector.map (fun qty -> qty -. affine.const) vec in
          outputs.(i) <- vector_to_array vec)
    lines ;
  Tezos_stdlib_unix.Utils.display_progress_end () ;
  (matrix_of_array_array inputs, matrix_of_array_array outputs, nmap)

(* -------------------------------------------------------------------------- *)
(* Computing prediction error *)

type error_statistics = {
  average : float;
  total_l1 : float;
  total_l2 : float;
  avg_l1 : float;
  avg_l2 : float;
  underestimated_measured : float;
}

let pp_error_statistics fmtr err_stat =
  Format.fprintf
    fmtr
    "@[<v 2>{ average = 1/N ∑_i tᵢ - pᵢ = %f;@,\
     total error (L1) = ∑_i |tᵢ - pᵢ| = %f;@,\
     total error (L2) = sqrt(∑_i (tᵢ - pᵢ)²) = %f;@,\
     average error (L1) = 1/N L1 error = %f;@,\
     average error (L2) = 1/N L2 error = %f;@,\
     underestimated = 1/N card{ tᵢ > pᵢ } = %f%% }@]"
    err_stat.average
    err_stat.total_l1
    err_stat.total_l2
    err_stat.avg_l1
    err_stat.avg_l2
    err_stat.underestimated_measured

let compute_error_statistics ~(predicted : matrix) ~(measured : matrix) =
  assert (Linalg.Tensor.Int.equal (Matrix.idim predicted) (Matrix.idim measured)) ;
  assert (Maths.col_dim predicted = 1) ;
  let predicted = vector_to_array (Matrix.col predicted 1) in
  let measured = vector_to_array (Matrix.col measured 1) in
  let error = Array.map2 ( -. ) measured predicted in
  let rows = Array.length error in
  let n = float_of_int rows in
  let arr = Array.init rows (fun i -> error.(i)) in
  let average = Array.fold_left ( +. ) 0.0 arr /. n in
  let total_l1 = Array.map abs_float arr |> Array.fold_left ( +. ) 0.0 in
  let total_l2 =
    let squared_sum =
      Array.map (fun x -> x *. x) arr |> Array.fold_left ( +. ) 0.0
    in
    sqrt squared_sum
  in
  let avg_l1 = total_l1 /. n in
  let avg_l2 = total_l2 /. n in
  let underestimated_measured =
    let indic_under = Array.map (fun x -> if x > 0.0 then 1.0 else 0.0) arr in
    Array.fold_left ( +. ) 0.0 indic_under /. n
  in
  {average; total_l1; total_l2; avg_l1; avg_l2; underestimated_measured}

(* -------------------------------------------------------------------------- *)
(* Making problems *)

let make_problem_from_workloads :
    type workload.
    data:(workload * vector) list ->
    overrides:(Free_variable.t -> float option) ->
    evaluate:(workload -> Eval_to_vector.size Eval_to_vector.repr) ->
    problem =
 fun ~data ~overrides ~evaluate ->
  (match data with
  | [] ->
      Stdlib.failwith
        "Inference.make_problem_from_workloads: empty workload data"
  | _ -> ()) ;
  let line_count = List.length data in
  let model_progress =
    Benchmark_helpers.make_progress_printer
      Format.err_formatter
      line_count
      "Applying model to workload data"
  in
  (* This function has to _preserve the order of workloads_. *)
  let lines =
    List.fold_left
      (fun lines (workload, measures) ->
        model_progress () ;
        let res = Eval_to_vector.prj (evaluate workload) in
        let res = Hash_cons_vector.prj res in
        let affine = Eval_linear_combination_impl.run overrides res in
        (* We hardcode determinization of the empirical timing distribution
           using the median statistic. *)
        let line = Full (affine, Measure measures) in
        line :: lines)
      []
      data
  in
  Format.eprintf "@." ;
  let lines = List.rev lines in
  if
    List.for_all
      (fun (Full (affine, _)) ->
        Free_variable.Sparse_vec.is_empty affine.linear_comb)
      lines
  then
    let predicted, measured =
      List.map (fun (Full (affine, Measure vec)) -> (affine.const, vec)) lines
      |> List.split
    in
    let measured =
      matrix_of_array_array (Array.of_list (List.map vector_to_array measured))
    in
    let predicted =
      matrix_of_array_array
        (Array.of_list predicted |> Array.map (fun x -> [|x|]))
    in
    Degenerate {predicted; measured}
  else
    let input, output, nmap = line_list_to_ols lines in
    Non_degenerate {lines; input; output; nmap}

let make_problem :
    data:'workload Measure.workload_data ->
    model:'workload Model.t ->
    overrides:(Free_variable.t -> float option) ->
    problem =
 fun ~data ~model ~overrides ->
  let data =
    List.map (fun {Measure.workload; measures; _} -> (workload, measures)) data
  in
  match model with
  | Model.Abstract {conv; model} ->
      let module M = (val model) in
      let module M = Model.Instantiate (Eval_to_vector) (M) in
      make_problem_from_workloads ~data ~overrides ~evaluate:(fun workload ->
          M.model (conv workload))
  | Model.Aggregate {model; _} ->
      make_problem_from_workloads ~data ~overrides ~evaluate:(fun workload ->
          let module A = (val model workload) in
          let module I = A (Eval_to_vector) in
          I.applied)

(* -------------------------------------------------------------------------- *)
(* Exporting/importing problems/solutions to CSV *)

let fv_to_string fv = Format.asprintf "%a" Free_variable.pp fv

let to_list_of_rows (m : matrix) : float list list =
  let cols = Maths.col_dim m in
  let rows = Maths.row_dim m in
  List.init ~when_negative_length:() rows (fun r ->
      List.init ~when_negative_length:() cols (fun c -> Matrix.get m (c, r))
      |> WithExceptions.Result.get_ok ~loc:__LOC__)
  |> WithExceptions.Result.get_ok ~loc:__LOC__

let model_matrix_to_csv (m : matrix) (nmap : NMap.t) : Csv.csv =
  let cols = Maths.col_dim m in
  let names =
    List.init ~when_negative_length:() cols (fun i ->
        fv_to_string (NMap.nth_exn nmap i))
    |> (* number of column cannot be negative *)
    WithExceptions.Result.get_ok ~loc:__LOC__
  in
  let rows = to_list_of_rows m in
  let rows = List.map (List.map string_of_float) rows in
  names :: rows

let timing_matrix_to_csv colname (m : matrix) : Csv.csv =
  let rows = to_list_of_rows m in
  let rows = List.map (List.map string_of_float) rows in
  [colname] :: rows

let problem_to_csv : problem -> Csv.csv = function
  | Non_degenerate {input; output; nmap; _} ->
      let model_csv = model_matrix_to_csv input nmap in
      let timings_csv = timing_matrix_to_csv "timings" output in
      Csv.concat model_csv timings_csv
  | Degenerate {predicted; measured} ->
      let predicted_csv = timing_matrix_to_csv "predicted" predicted in
      let measured_csv = timing_matrix_to_csv "timings" measured in
      Csv.concat predicted_csv measured_csv

let mapping_to_csv mapping =
  let headers = List.map (fun (fv, _) -> fv_to_string fv) mapping in
  let row = List.map (fun x -> Float.to_string (snd x)) mapping in
  [headers; row]

let solution_to_csv {mapping; _} =
  if mapping = [] then None else Some (mapping_to_csv mapping)

(* -------------------------------------------------------------------------- *)
(* Solving problems *)

(* Create a [matrix] overlay over a Python matrix.
   Note how we switch from row major to column major in
   order to comply to [Linalg]'s defaults. *)
let of_scipy m =
  let r = Scikit_matrix.dim1 m in
  let c = Scikit_matrix.dim2 m in
  Matrix.make (Linalg.Tensor.Int.rank_two c r) @@ fun (c, r) ->
  Scikit_matrix.get m r c

(* Convert a matrix overlay to a Python matrix. *)
let to_scipy m =
  let cols = Maths.col_dim m in
  let rows = Maths.row_dim m in
  Scikit_matrix.init ~lines:rows ~cols ~f:(fun l c -> Matrix.get m (c, l))

(* Convert a vector overlay to a Python vector. *)
let to_scipy_vector v =
  let open Bigarray in
  Array1.init Float64 C_layout (vec_dim v) (fun i -> Vector.get v i)

let median_of_output output =
  (* Scipy's functions expect a column vector on output. *)
  Matrix.of_col
  @@ map_rows
       (fun row -> Stats.Emp.quantile (module Float) (vector_to_array row) 0.5)
       output

let wrap_python_solver ~input ~output solver =
  let input = to_scipy input in
  let output = to_scipy output in
  solver input output |> of_scipy

let ridge ~alpha ~input ~output =
  wrap_python_solver ~input ~output (fun input output ->
      Pyinference.LinearModel.ridge ~alpha ~input ~output ())

let lasso ~alpha ~positive ~input ~output =
  wrap_python_solver ~input ~output (fun input output ->
      Pyinference.LinearModel.lasso ~alpha ~positive ~input ~output ())

let nnls ~input ~output =
  wrap_python_solver ~input ~output (fun input output ->
      Pyinference.LinearModel.nnls ~input ~output)

let predict_output ~input ~weights =
  let input = to_scipy input in
  let weights = to_scipy weights in
  Pyinference.predict_output ~input ~weights

let r2_score ~output ~prediction =
  let output = to_scipy output in
  Pyinference.r2_score ~output ~prediction

let rmse_score ~output ~prediction =
  let output = to_scipy output in
  Pyinference.rmse_score ~output ~prediction

let calculate_benchmark_scores ~input ~output =
  let output =
    let arrs =
      Array.init (row_dim output) (fun r ->
          let arr = Matrix.row output r |> vector_to_array in
          Array.sort Float.compare arr ;
          (* Eliminate the upper 10% to reduce influence of GC *)
          (* Don't eliminate when len <= 1 (e.g. allocation benchmark) *)
          let len = Array.length arr in
          let q = if len <= 1 then len else len * 9 / 10 in
          Array.init q (fun i -> arr.(i)))
    in
    Maths.matrix_of_array_array arrs
  in

  (* Duplicate input vector & Flatten output vector *)
  (* Input: (dim_of_workload,nsamples) matrix =>
            (dim_of_workload,bench_num * nsamples) matrix *)
  let input =
    let co = col_dim output in
    let r = row_dim input in
    let ci = col_dim input in
    Matrix.make (Linalg.Tensor.Int.rank_two ci (co * r)) @@ fun (c, r) ->
    Matrix.get input (c, r / co)
  in
  (* Output: (bench_num, nsamples) matrix =>
             (bench_num * nsamples) vector *)
  let output =
    let c = col_dim output in
    let shape = Linalg.Tensor.Int.rank_one (c * row_dim output) in
    Vector.make shape (fun i -> Matrix.get output (i mod c, i / c))
  in

  let input = to_scipy input in
  let output = to_scipy_vector output in
  let params, tvalues = Pyinference.benchmark_score ~input ~output in
  (params |> of_scipy, tvalues |> of_scipy)

let solve_problem : problem -> solver -> solution =
 fun problem solver ->
  let calculate_regression_scores ~output ~prediction =
    let r2_score =
      (* The R^2 score for a constant input problem is uninformative,
         and the score is usually negative, leading to a false positive alert.
         We skip calculating the R^2 score for such problems. *)
      let is_constant_input =
        match problem with
        | Degenerate _ -> false
        | Non_degenerate {lines; _} ->
            List.map (fun (Full (affine, _)) -> affine) lines
            |> List.all_equal (fun v1 v2 ->
                   Free_variable.Sparse_vec.equal v1.linear_comb v2.linear_comb
                   && Float.equal v1.const v2.const)
      in
      if is_constant_input then None else r2_score ~output ~prediction
    in
    let rmse_score = rmse_score ~output ~prediction in
    {r2_score; rmse_score; tvalues = []}
  in
  match problem with
  | Degenerate {predicted; measured} ->
      let prediction = to_scipy predicted |> Scikit_matrix.to_numpy in
      let output = median_of_output measured in
      let scores = calculate_regression_scores ~output ~prediction in
      {mapping = []; weights = empty_matrix; intercept_lift = 0.0; scores}
  | Non_degenerate {input; output; nmap; _} ->
      let params, tvalues = calculate_benchmark_scores ~input ~output in
      let output = median_of_output output in
      let weights =
        match solver with
        | Ridge {alpha} -> ridge ~alpha ~input ~output
        | Lasso {alpha; positive} -> lasso ~alpha ~positive ~input ~output
        | NNLS -> nnls ~input ~output
      in
      let prediction = predict_output ~input ~weights in

      (* The difference required to overestimate all measurements. *)
      let intercept_lift =
        let prediction = Scikit_matrix.of_numpy prediction |> of_scipy in
        let output = vector_to_array (Matrix.col output 0) in
        let prediction = vector_to_array (Matrix.col prediction 0) in
        Array.map2 (fun o p -> o -. p) output prediction
        |> Array.fold_left Float.max 0.0
      in

      let regression_scores = calculate_regression_scores ~output ~prediction in
      let lines = Maths.row_dim weights in
      if lines <> NMap.support nmap then
        let cols = Maths.col_dim weights in
        let dims = Format.asprintf "%d x %d" lines cols in
        let err =
          Format.asprintf
            "Inference.solve_problem: solution dimensions (%s) mismatch that \
             of given problem"
            dims
        in
        Stdlib.failwith err
      else
        let mapping =
          NMap.fold
            (fun variable dim acc ->
              let param = Matrix.get weights (0, dim) in
              (variable, param) :: acc)
            nmap
            []
        in
        let tvalues =
          NMap.fold
            (fun variable i acc ->
              (let w_true = Matrix.get weights (0, i) in
               let w_ols = Matrix.get params (0, i) in
               if
                 Float.(abs (w_true -. w_ols) /. min (abs w_true) (abs w_ols))
                 > 2.0
               then
                 Format.eprintf
                   "Warning: Estimation results for %s differ significantly; \
                    %f from statmodels.OLS, and %f from scikit. Problem might \
                    be underdetermined.@."
                   (Free_variable.to_string variable)
                   w_ols
                   w_true) ;
              let tvalue = Matrix.get tvalues (0, i) in
              (variable, tvalue) :: acc)
            nmap
            []
        in
        {
          mapping;
          weights;
          intercept_lift;
          scores = {regression_scores with tvalues};
        }