複数ケースの特徴量選別と戦略予測における限界

# 02_feature_evaluation.py


```py
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# %% [markdown]
# # Feature Evaluation Across Case Studies
#
# **Docker image**: `ml4t`
#
# Each case study runs an FDR-controlled triage pass on its candidate
# feature menu (Ch7 §7.3 sets the triage gates, §7.4 the FDR control),
# classifying every feature as PROCEED, REVISE,
# or STOP. This notebook reads those nine ledgers side by side and asks
# whether feature-level survival predicts strategy-level survival once
# the rest of the pipeline runs.
#
# The forward link is the point. §03 (signal quality) and §04
# (signal-to-strategy) build on whatever this notebook surfaces.
#
# **Book Reference**: Chapter 20, Section 20.2.
#
# **Prerequisites**: Run [`01_aggregate_synthesis`](01_aggregate_synthesis.ipynb)
# first. Each case study's `case_studies/{cs}/evaluation/triage_ledger.parquet`
# must exist (regenerated by the per-case-study `05_evaluation` notebooks).

# %%
"""Ch20 Feature Evaluation — cross-case-study triage ledger comparison."""

import matplotlib.pyplot as plt
import numpy as np
import polars as pl
from IPython.display import Markdown, display

from case_studies.utils.analytics import CASE_STUDY_IDS, SHORT_NAMES, load_triage_ledger
from case_studies.utils.strategy_analysis import rank_one
from utils.paths import REPO_ROOT, get_chapter_dir
from utils.style import COLORS, show_with_alt

# %% tags=["parameters"]
MAX_CASE_STUDIES = 0  # 0 = all available
# Benjamini-Hochberg level the ledger's `fdr_p` is compared against. The ledgers
# store the adjusted p-value rather than a significance flag, so the threshold
# lives here and is applied once.
FDR_ALPHA = 0.05

# %%
OUTPUT_DIR = get_chapter_dir(20) / "output"

CS_LIST = CASE_STUDY_IDS[:MAX_CASE_STUDIES] if MAX_CASE_STUDIES else CASE_STUDY_IDS

# %% [markdown]
# ## 1. Load Triage Ledgers
#
# Each per-case-study ledger has the same schema: one row per candidate feature,
# with IC moment estimates, a HAC-adjusted t-statistic, a Benjamini-Hochberg
# adjusted p-value (`fdr_p`), fold sign consistency, monotonicity, coverage, a
# categorical decision in {PROCEED, REVISE, STOP}, and a `note` giving the reason
# for that decision.
#
# The ledgers are generated artifacts, not repository content. Without them this
# notebook has nothing to compare, so a missing ledger stops the run rather than
# producing an empty table under a heading that promises nine case studies.


# %%
ledgers = {cs: load_triage_ledger(cs) for cs in CS_LIST}
available = [cs for cs, df in ledgers.items() if df is not None]
missing = [cs for cs in CS_LIST if cs not in available]
print(f"Loaded {len(available)}/{len(CS_LIST)} ledgers")
if missing:
    raise FileNotFoundError(
        f"No triage ledger for {missing}. Each is written by that case study's "
        "`05_evaluation` notebook to case_studies/{cs}/evaluation/"
        "triage_ledger.parquet; run those first."
    )

# `fdr_sig` is derived here rather than read: the ledger stores the adjusted
# p-value, and a stored boolean would freeze one alpha into the artifact.
panel = pl.concat(
    [
        df.select(
            "feature",
            "decision",
            "note",
            "case_study",
            fdr_sig=pl.col("fdr_p") < FDR_ALPHA,
        )
        for df in ledgers.values()
        if df is not None
    ],
    how="vertical_relaxed",
)

# %% [markdown]
# ## 2. Two Routes to PROCEED
#
# A feature earns PROCEED by either of two independent routes, recorded in the
# ledger's `note`: it clears Benjamini-Hochberg at the level above
# (`fdr_significant`), or its IC clears that case study's own effect-size floor
# and holds its sign across enough folds (`stable_and_above_threshold`) without
# clearing BH. The floor is set per case study, from 0.003 to 0.01 in absolute
# mean IC, so the second route is calibrated to each market rather than shared
# across them. The second
# route exists because BH over a menu of dozens of correlated features is a
# blunt instrument at these sample sizes, and a feature can be worth carrying
# forward on effect size and stability alone.
#
# PROCEED is therefore a union of the two routes, not a narrowing of the first.
# A case study can show more PROCEED features than FDR-significant ones, so the
# three counts below are drawn side by side rather than stacked -
# stacking them would assert a nesting that does not hold.

# %%
funnel = (
    panel.group_by("case_study")
    .agg(
        n_candidate=pl.len(),
        n_fdr_sig=pl.col("fdr_sig").sum(),
        n_proceed=(pl.col("decision") == "PROCEED").sum(),
        n_proceed_by_fdr=((pl.col("decision") == "PROCEED") & pl.col("fdr_sig")).sum(),
    )
    .with_columns(
        n_proceed_by_stability=pl.col("n_proceed") - pl.col("n_proceed_by_fdr"),
        pct_fdr_sig=(pl.col("n_fdr_sig") / pl.col("n_candidate") * 100).round(1),
        pct_proceed=(pl.col("n_proceed") / pl.col("n_candidate") * 100).round(1),
        cs_short=pl.col("case_study").replace(SHORT_NAMES),
    )
    .sort("pct_proceed", descending=True)
)
funnel.select(
    "cs_short",
    "n_candidate",
    "n_fdr_sig",
    "n_proceed",
    "n_proceed_by_fdr",
    "n_proceed_by_stability",
    "pct_fdr_sig",
    "pct_proceed",
)

# %%
fig, ax = plt.subplots(figsize=(9, 5))
y = np.arange(funnel.height)
height = 0.26
series = [
    ("n_candidate", "candidates", COLORS["silver_muted"]),
    ("n_fdr_sig", f"clears BH-FDR at {FDR_ALPHA:.2f}", COLORS["blue_light"]),
    ("n_proceed", "PROCEED", COLORS["blue"]),
]
for offset, (col, label, color) in zip((-height, 0.0, height), series):
    ax.barh(
        y + offset,
        funnel[col].to_numpy(),
        height=height,
        color=color,
        label=label,
        edgecolor=COLORS["neutral"],
        linewidth=0.4,
    )
ax.set_yticks(y)
ax.set_yticklabels(funnel["cs_short"].to_numpy())
ax.invert_yaxis()
ax.set_xlabel("Number of features")
ax.set_title("Candidate features, FDR-significant, and PROCEED, by case study")
ax.legend(loc="lower right", frameon=False)
show_with_alt(
    fig,
    "Grouped horizontal bars per case study giving the candidate feature count, "
    "the number clearing Benjamini-Hochberg, and the number reaching PROCEED. "
    "The PROCEED bar exceeds the FDR-significant bar in most case studies, "
    "because the stability route to PROCEED does not require BH significance.",
)

# %% [markdown]
# The nine case studies share the triage structure, and the two columns are
# comparable to different degrees. The BH-FDR share is recomputed here from each
# ledger's stored p-values at one `FDR_ALPHA`, so it is on a common scale. The
# PROCEED share is read from each ledger's own decision, taken at that case
# study's own effect-size floor and sign-consistency minimum, so it is not. The
# summary below is computed from the table above rather than typed, so it cannot
# drift from the ledgers as they are regenerated.

# %% tags=["results"]
_f = funnel.sort("pct_fdr_sig", descending=True)
_none = _f.filter(pl.col("n_fdr_sig") == 0)["cs_short"].to_list()
_top = _f.row(0, named=True)
_pr = funnel.sort("pct_proceed", descending=True)
_hi, _lo = _pr.row(0, named=True), _pr.row(-1, named=True)
_stab = funnel["n_proceed_by_stability"].sum()
_total_proceed = funnel["n_proceed"].sum()
display(
    Markdown(
        f"Across {funnel.height} case studies, the share of candidate features "
        f"clearing BH-FDR at {FDR_ALPHA:.2f} runs from "
        f"{_f['pct_fdr_sig'].min():.1f} to {_top['pct_fdr_sig']:.1f} percent "
        f"({_top['cs_short']} highest). "
        + (
            f"{len(_none)} clear it for none of their candidates: {', '.join(_none)}. "
            if _none
            else ""
        )
        + f"PROCEED rates run from {_lo['pct_proceed']:.1f} percent "
        f"({_lo['cs_short']}, {_lo['n_proceed']} of {_lo['n_candidate']}) to "
        f"{_hi['pct_proceed']:.1f} percent ({_hi['cs_short']}, "
        f"{_hi['n_proceed']} of {_hi['n_candidate']}). "
        f"Of {_total_proceed} PROCEED decisions in total, {_stab} "
        "were reached on effect size and fold stability without clearing BH, "
        "which is why the PROCEED bars are not contained inside the FDR bars."
    )
)

# %% [markdown]
# A case study can reach zero surviving features and still support a trained
# model. Univariate IC asks whether one feature predicts on its own; the model
# is fitted on all of them jointly and can use combinations that no single
# column carries. The two measurements disagree by construction, so a zero here
# does not by itself establish that the market is unpredictable.

# %% [markdown]
# ## 3. Forward Link: Feature Survival vs Strategy Survival
#
# Pair each case study's PROCEED rate against the selected configuration's
# validation Sharpe and holdout Sharpe from §01. The triage ledger sits upstream
# of every model and backtest, so this is the most direct available test of
# whether a richer surviving feature menu produces a stronger strategy.
#
# It is a weak test. Sharpe figures exist only for case studies with registered
# backtests, and §01 reports that several registries are empty while their
# rebuild is in progress. The pairing below therefore rests on a handful of
# points, which is too few to support a claim about the relationship in either
# direction. It is shown because the absence of a relationship at this sample
# size is itself worth seeing, not because it settles the question.

# %%
mq = pl.read_parquet(OUTPUT_DIR / "measurement_quality.parquet")
forward = (
    funnel.select(["case_study", "cs_short", "pct_proceed"])
    .join(
        mq.select(
            pl.col("cs_id").alias("case_study"),
            "rank1_val_sharpe",
            "holdout_sharpe",
        ),
        on="case_study",
        how="left",
    )
    .sort("pct_proceed", descending=True)
)
forward

# %%
fig, axes = plt.subplots(1, 2, figsize=(11, 4.2), sharey=False)
for ax, ycol, ylabel in zip(
    axes,
    ["rank1_val_sharpe", "holdout_sharpe"],
    ["Carrier validation Sharpe", "Carrier holdout Sharpe"],
):
    pts = forward.filter(pl.col(ycol).is_not_null()).to_pandas()
    ax.scatter(
        pts["pct_proceed"],
        pts[ycol],
        color=COLORS["blue"],
        s=40,
        edgecolor=COLORS["neutral"],
        linewidth=0.5,
    )
    for _, row in pts.iterrows():
        ax.annotate(
            row["cs_short"],
            (row["pct_proceed"], row[ycol]),
            fontsize=8,
            xytext=(4, 3),
            textcoords="offset points",
        )
    ax.axhline(0, color=COLORS["neutral"], linestyle="--", linewidth=0.7)
    ax.set_xlabel("% candidate features in PROCEED")
    ax.set_ylabel(ylabel)
fig.suptitle("Feature survival against strategy Sharpe, by case study")
show_with_alt(
    fig,
    "Two scatter panels plotting each case study's percentage of PROCEED "
    "features against its validation Sharpe on the left and its holdout Sharpe "
    "on the right, points labelled by case study. Only case studies with "
    "registered backtests appear, and they are too few to show a trend.",
)

# %% tags=["results"]
_paired = forward.filter(pl.col("holdout_sharpe").is_not_null())
_absent = forward.filter(pl.col("holdout_sharpe").is_null())["cs_short"].to_list()
# rank_one, not a one-key sort: the case study this picks is named in the sentence below,
# so a tie on holdout Sharpe would publish whichever row the join happened to emit first.
_best = (
    rank_one(_paired, by="holdout_sharpe", name="cs_short").row(0, named=True)
    if _paired.height
    else None
)
display(
    Markdown(
        f"{_paired.height} of {forward.height} case studies carry a holdout "
        "Sharpe; the rest have no registered backtests"
        + (f" ({', '.join(_absent)})" if _absent else "")
        + ". "
        + (
            f"Among those that do, the highest holdout Sharpe is "
            f"{_best['holdout_sharpe']:+.2f} ({_best['cs_short']}, "
            f"{_best['pct_proceed']:.1f} percent PROCEED). "
            if _best
            else ""
        )
        + "With this many points, no ordering of PROCEED rate against holdout "
        "Sharpe is distinguishable from chance, and none is claimed here."
    )
)

# %% [markdown]
# What the count of surviving features cannot tell you is how large those
# features are relative to the frictions of the market they trade in, or how
# they are turned into positions. Those two questions are what §03 and §04
# measure, and they are where the differences between these case studies
# actually appear.

# %% [markdown]
# ## Takeaways
#
# - The nine case studies share the triage structure but not all of its
#   parameters. The BH-FDR column is re-thresholded here at one alpha and can be
#   compared across markets; the PROCEED column carries each case study's own
#   effect-size floor, which spans a factor of three, so a difference in PROCEED
#   rate is a difference in market and in floor together and cannot be assigned
#   to either alone.
# - PROCEED is a union of two routes, BH significance and effect-size-plus-fold-
#   stability. Reading it as a stricter version of BH significance inverts the
#   relationship and inflates how selective the screen appears.
# - Univariate IC and joint prediction answer different questions. A case study
#   where no single feature clears BH can still train a usable model, and that
#   is a property of the two tests rather than evidence about the market.
# - Whether feature survival predicts strategy survival is not settled here. Too
#   few case studies currently carry holdout backtests for the comparison to
#   discriminate, and this notebook says so rather than reading a trend into
#   five points.
#
# ## Known Limitations
#
# - The ledgers are regenerated by each case study's `05_evaluation` notebook and
#   are not versioned with this repository. Numbers here move when those are
#   re-run; nothing in this notebook is pinned to a particular generation.
# - BH-FDR treats the candidate menu as one family of tests, but the candidates
#   are heavily correlated - overlapping return windows, related volatility
#   measures - so the effective number of independent tests is smaller than the
#   row count and the adjustment is conservative. This is part of why the
#   stability route to PROCEED exists.
# - The forward link compares one selected configuration per case study, not a
#   distribution over configurations, so it carries the selection uncertainty
#   §01 documents in `measurement_quality.parquet`.

```