Ajuste de gradient boosting para sinais de ações baseados em opções

# 07_gbm.py


```py
# ---
# jupyter:
#   jupytext:
#     cell_metadata_filter: tags,-all
#     text_representation:
#       extension: .py
#       format_name: percent
#       format_version: '1.3'
#       jupytext_version: 1.19.3
#   kernelspec:
#     display_name: Python 3 (ipykernel)
#     language: python
#     name: python3
# ---

# %% [markdown]
# # Option analytics: conditioning one forecast on another
#
# [`06_linear`](06_linear.ipynb) made the point that separates this case study from every other one
# in the book. Its features are not a record of what happened to each stock - they are what the
# options market was willing to pay for a claim on what happens next. Implied volatility, the skew
# between puts and calls, the slope of the term structure, the gap between implied and realized
# variance: each is already a forecast, made by people with money at stake.
#
# A penalized linear model asks whether a weighted sum of those forecasts ranks the cross-section.
# Gradient boosting asks a different question, and on a volatility surface it is the more natural
# one. A tree splits on one feature inside a region defined by another, so it can express "read the
# skew one way when the term structure slopes upward, and another way when it is inverted" - a
# conditional statement, which is how practitioners actually read a surface. The linear model can
# only see that if someone multiplies the columns together first.
#
# Three dials control how far the model goes, and this notebook varies all three:
#
# - **Capacity**, set by `num_leaves`: how finely one tree may partition the feature space, and so
#   how many such conditions it can express at once.
# - **The loss function**, which decides what "got wrong" means. Squared error weights an
#   observation by the square of its error; absolute error and Huber do not. Five-day equity
#   returns have tails, and the metric here is a rank correlation, so the two do not want the same
#   thing from a fit.
# - **When to stop**, set by the number of trees. A boosted model has a meaningful state at every
#   iteration, so each configuration is scored at ten points along its own training run, and **a
#   checkpoint is part of a configuration rather than a detail of how it was fitted.** Each of the
#   three regression labels declares fifteen configurations, which is 150 candidates apiece; the
#   two classification labels declare five, which is 50 apiece.
#
# Two folds, one of which validates on 2020. The usable history of this option analytics dataset is
# short, so the walk-forward schedule `05_evaluation` set has few and wide windows, and a few
# hundred candidates judged on two of them is the arithmetic to keep in view while reading the
# table.
#
# **Learning objectives.** By the end of this notebook you will be able to:
#
# - Say what a tree ensemble can represent that a penalized linear model cannot, in terms of the
#   volatility surface rather than in the abstract.
# - Explain why a boosted model produces one result per checkpoint while a linear model produces
#   one result in total, and what that implies for counting candidates.
# - Read a learning curve of out-of-sample information coefficient against tree count, and say
#   whether an apparent peak is a turning point or the highest of ten noisy readings.
# - Say why the choice of loss function is a statement about the label's tails, and relate that to
#   what a rank-based metric rewards.
# - Judge whether a model built on features that are themselves forecasts adds anything to them.
#
# **Book reference**: Chapter 12, Section 12.2 (GBM libraries) and Section 12.3 (how to tune a
# boosted model). Chapter 6, Section 6.7 (Search accounting and run logging) introduces the run
# log this notebook writes to.
#
# **Prerequisites**: [`03_financial_features`](03_financial_features.ipynb) and
# [`04_model_based_features`](04_model_based_features.ipynb) have written the feature matrices,
# [`05_evaluation`](05_evaluation.ipynb) has established the walk-forward folds, and
# [`06_linear`](06_linear.ipynb) fitted the linear population this one is compared against.
#
# **What it writes**: one training run per configuration and one complete validation prediction
# set per configuration and checkpoint, in `run_log/registry.db` and under `run_log/training/` and
# `run_log/predictions/`, grouped under a named population.
# [`14_backtest`](14_backtest.ipynb) reads that population and selects on validation backtest
# Sharpe. **Selection happens there, not here.**

# %%
"""Fit the declared option-analytics gradient boosting population on the walk-forward folds."""

import plotly.graph_objects as go
import polars as pl
from plotly.subplots import make_subplots

from case_studies.research import (
    declared_labels,
    load_model_configs,
    model_requests,
    narrows_declared_catalog,
    open_study,
    primary_label,
    resolved_model_plan,
    run_model_population,
)
from utils.style import COLORS, show_plotly_with_alt

# %% tags=["parameters"]
LABELS: list[str] = []
EXECUTION_TIER = "canonical"
WORKSPACE: str = ""
PREVIEW_REDUCTIONS: dict = {}
CONFIG_NAMES: list[str] = []
POPULATION_NAME = ""
SUPERSEDES_POPULATION: str = ""

# %%
study = open_study(
    "sp500_equity_option_analytics",
    execution_tier=EXECUTION_TIER,
    workspace=WORKSPACE or None,
    entry_point="07_gbm",
)

# %% [markdown]
# ## 1. Which labels, and which models
#
# The labels are the ones the linear notebook used, and fitting the same set is what makes the two
# populations comparable: the families differ, the targets do not. `fwd_ret_5d` is the stock's
# total return over the five trading days after the decision date; `fwd_ret_10d` is the same over
# ten; `fwd_ret_risk_adj_5d` divides the five-day return by a measure of its own dispersion; and
# the two `fwd_dir_*` labels are the sign of the five- and ten-day returns.

# %%
declared_labels(study, "gbm")

# %% [markdown]
# The menu at `config/training/{label}.yaml` lists 15 named configurations under `gbm:`, and each
# resolves to a preset in `case_studies/config/lgb/`. The grid is a product of two axes:
#
# - **Five capacity profiles.** `default` uses the library's own leaf count; the rest fix it at 7,
#   15, 31 and 63. Leaf count is the direct control on how finely one tree may partition the
#   feature space. Here that decides whether a model can express a condition on the surface -
#   read the skew one way when the term structure slopes upward and another way when it does
#   not - which is the natural shape for an options-derived signal and one a linear model cannot
#   take unless someone builds the interaction column first.
# - **Three objectives.** `mse` minimizes squared error, `mae` absolute error, and `huber` behaves
#   like squared error for small residuals and like absolute error beyond a threshold derived from
#   each fold's own label spread.
#
# Every configuration runs the same number of boosting iterations with the same learning rate, so
# the grid isolates capacity and loss rather than confounding them with training length.

# %%
configs = load_model_configs(
    study,
    "gbm",
    labels=LABELS or None,
    config_names=CONFIG_NAMES or None,
)
configs

# %% [markdown]
# `LABELS` and `CONFIG_NAMES` both narrow what is fitted, and a narrowed run declares a different
# set of members than the canonical population does. A population is immutable once written, so
# such a run must publish under its own name: on a fresh workspace it would otherwise register an
# incomplete snapshot under the canonical one, and where the full population already exists the
# registry refuses it. Comparing the loaded rows against the complete declared catalog catches
# either knob, and says so here rather than several cells later in a message about hashes.

# %%
if narrows_declared_catalog(study, "gbm", configs) and not POPULATION_NAME:
    raise ValueError(
        f"this run declares {configs.height} label-configuration pairs, which is not the "
        "complete declared catalog, so it cannot publish the canonical population; pass "
        "POPULATION_NAME to give it its own"
    )


# %% [markdown]
# ## 2. Binding the declarations to the data
#
# Resolving reads the label and feature files, computes the fold boundaries, works out the exact
# rows each fit must predict, and turns any data-dependent parameter into the number it will use.
# Huber's threshold is one of those: it is a fraction of the training labels' standard deviation,
# so it is a different number on every fold and is resolved from that fold's own data.
#
# Nothing is fitted here, so the plan can be inspected first. Four things to check:
#
# - **`feature_count`, `eligible_entities` and `eligible_rows` agree across every row.** A row that
#   differs is a configuration measured on a different sample from its neighbours.
# - **`folds` is the same everywhere**, and equals the number of walk-forward splits.
# - **`validation_start` and `validation_end` bracket the development sample**, with none of the
#   held-out tail visible.
# - **`checkpoints` is where this differs from the linear plan.** It is the number of training
#   states each configuration will publish predictions for. Multiply it by the number of rows to
#   get the number of candidate models this notebook is about to create.

# %%
requests = model_requests(
    study,
    configs,
    execution_tier=EXECUTION_TIER,
    preview_reductions=PREVIEW_REDUCTIONS,
)
resolved = tuple(request.resolve() for request in requests)

plan = resolved_model_plan(resolved)
plan.select(
    "config_name",
    "feature_count",
    "eligible_entities",
    "eligible_rows",
    "folds",
    "checkpoints",
    "validation_start",
    "validation_end",
)

# %% [markdown]
# ## 3. Fitting the population
#
# `run_model_population` fits every resolved request. For one request it walks the folds, and on
# each one:
#
# 1. takes the rows inside that fold's training window,
# 2. casts the design matrix to the precision LightGBM works in and leaves missing values in
#    place - a tree routes a missing value down its own branch, so imputing a median here would
#    hand the model an observation nobody made,
# 3. fits the declared number of boosting iterations,
# 4. predicts the fold's validation rows at each checkpoint, using only the trees built up to that
#    iteration.
#
# Step 4 is what makes one fit produce many results. The fold predictions are concatenated into
# one series per checkpoint covering the whole validation period, and each becomes its own
# registered prediction set with its own identity.
#
# Preparing a fold - slicing the window, cleaning the rows - depends on the data and not on the
# model, so it does not differ between the configurations of one label. When it happens is decided
# by which path the run takes, and for gradient boosting **resolving is what prepares the folds**:
# `resolve_model_request` calls `prepare_gbm_folds_from_mds` and hands the prepared set to the
# fit, which only reads it. So the cell above, which resolves every request before the call so it
# can show the plan, gives each configuration its own prepared fold set and holds all of them at
# once. The path that prepares one fold set and walks the whole grid against it, holding one fold
# at a time, is the batch path in `case_studies/utils/gbm.py`, reached by handing
# `run_model_population` unresolved requests instead. Which to take is a question about the size of
# the panel, and on this one the plan is worth more than the memory it costs.
#
# **What the call publishes is a population**: a named, immutable list of the prediction sets it
# will produce, written down before the first fit. Afterwards every member must exist and be
# complete, which is what makes the downstream comparison well defined.

# %%
population_name = POPULATION_NAME or "sp500_equity_option_analytics-gbm-validation-v1"
execution, population = run_model_population(
    study, resolved, population_name=population_name, supersedes=SUPERSEDES_POPULATION or None
)

print(f"{len(execution.runs)} configurations fitted")
print(f"population {population.name}: {len(population.members)} prediction sets")

# %% [markdown]
# Re-running this notebook unchanged costs the time it takes to read the data. Every identity is
# re-derived from the inputs, the registry already holds the matching rows, and the runner returns
# the stored result rather than fitting again.
#
# ### Running configurations of your own
#
# The published run log is read-only. To add runs, open the study against a workspace, which holds
# its own registry and artifacts and reads the same labels and features:
#
# ```python
# study = open_study("sp500_equity_option_analytics", workspace="~/ml4t-experiments")
# configs = load_model_configs(
#     study, "gbm", labels=["fwd_ret_5d"], config_names=["leaves_15_huber", "leaves_31_huber"]
# )
# requests = model_requests(study, configs)
# resolved = tuple(request.resolve() for request in requests)
# execution, population = run_model_population(study, resolved, population_name="my-gbm-v1")
# ```
#
# `CONFIG_NAMES` fits a subset of what the menu declares. To fit something new, add a preset at
# `case_studies/config/lgb/leaves_127_huber.yaml` and list `leaves_127_huber` under `gbm:` in the
# label's menu. Editing an existing preset changes that configuration's identity, so its result
# registers as a new row beside the old one rather than replacing it.
# [`RUN_LOG.md`](../RUN_LOG.md#running-your-own-configurations) covers the rest.

# %% [markdown]
# ## 4. What came out
#
# One row per configuration, label and checkpoint. `ic_mean` is the **information coefficient**: on
# each validation date, rank the stocks by the model's prediction, rank them by the return they
# went on to earn, correlate the two rankings, and average that daily correlation over the
# validation period.
#
# The table is sorted by label and then by IC, and the top of each label's block is the trap this
# notebook exists to describe. The leading row for a label is the maximum over that label's whole
# grid at ten checkpoints each. Reading it as the result of one experiment would attribute to the
# model whatever the stopping point contributed, and the section below measures how large that
# contribution is before anything is concluded from the ranking.
#
# **Every count and every aggregate below is keyed on `(label, config_name)`, not on the
# configuration name alone.** A name is unique within one label's menu and not across them:
# `leaves_15_mae` is declared by all three regression labels here. Grouping on the name would
# average a configuration's result across the labels it appears in, and concatenate their learning
# curves into one line that runs from the last checkpoint of one label back to the first of the
# next.
#
# Coverage is judged against each label's own maximum number of scorable validation dates. The
# labels do not offer the same number to begin with - a ten-day forward window runs out earlier
# than a five-day one - so a single global maximum would mark a whole label incomplete for a
# reason that has nothing to do with any model.

# %% tags=["results"]
catalog = execution.catalog_rows.select(
    "config_name",
    "label",
    "task",
    "complete",
    "checkpoint_value",
    "ic_mean",
    "ic_std",
    "ic_n_days",
    "auc_mean_daily",
    "direction_label",
    "n_folds",
    "training_hash",
    "prediction_hash",
).sort(["label", "ic_mean"], descending=[False, True])

if catalog.filter(~pl.col("complete")).height:
    raise RuntimeError("gbm execution returned a partial prediction set")

catalog = catalog.with_columns(
    full_coverage=pl.col("ic_n_days") == pl.col("ic_n_days").max().over("label")
)

primary = primary_label(study)
present = sorted(set(catalog.get_column("label")))
# The primary label leads when it was fitted. A subset run that leaves it out orders the panels by
# whichever label it did fit rather than by one that is not there.
panel_labels = [label for label in [primary] if label in present] + [
    label for label in present if label != primary
]
order_label = panel_labels[0]
pairs = catalog.select("label", "config_name").unique().height
print(f"{catalog.height} candidate models: {pairs} label-configuration pairs")
print(f"at {catalog.n_unique('checkpoint_value')} checkpoints each, on {len(panel_labels)} labels")
catalog.select(
    "label",
    "config_name",
    "checkpoint_value",
    "ic_mean",
    "ic_std",
    "ic_n_days",
    "full_coverage",
).head(15)

# %% [markdown]
# ### What the grid does on each label
#
# The frame below is the comparison this notebook can make only because every declared label was
# fitted in one run. The features are the same and the folds are the same throughout. The grid is
# the same across the three regression labels, which share one menu of fifteen configurations, so
# down those three rows the only thing that changes is what is being predicted. The two
# `fwd_dir_*` labels declare their own menu of five, because a squared-error objective has
# nothing to say about a binary outcome; read those rows against each other and against their own
# regression sibling rather than as two more members of one sweep. `configurations` and
# `candidates` are what tell them apart.
#
# `ic_mean` is defined for every row, which is what puts every label on one axis. `auc_mean_daily`
# can be too, and `direction_label` says what it was scored against: a classification row scores
# its own label and leaves that column null, while a regression row has no classes of its own and
# is scored as a ranking signal against a declared direction sibling - `fwd_ret_5d` against
# `fwd_dir_5d`, `fwd_ret_10d` against `fwd_dir_10d`. A regression row and its sibling are
# therefore comparable on that one number. `fwd_ret_risk_adj_5d` declares no sibling and carries
# no AUC; null there means not computed, not zero.

# %% tags=["results"]
by_label = (
    catalog.filter("full_coverage")
    .group_by("label")
    .agg(
        task=pl.col("task").first(),
        configurations=pl.col("config_name").n_unique(),
        candidates=pl.len(),
        scored_dates=pl.col("ic_n_days").max(),
        best_ic=pl.col("ic_mean").max(),
        worst_ic=pl.col("ic_mean").min(),
        n_positive=(pl.col("ic_mean") > 0).sum(),
        best_auc_daily=pl.col("auc_mean_daily").max(),
        auc_scored_against=pl.col("direction_label").drop_nulls().first(),
    )
    .sort("best_ic", descending=True)
)
by_label

# %% [markdown]
# ### What more trees do
#
# Each line traces one configuration's out-of-sample IC as trees are added to it, in its own
# label's panel. This is the figure the checkpoint dimension exists to produce, and it separates
# two things a single end-of-training number cannot.
#
# A line that rises and then falls has an interior optimum: the model was still learning, then
# began fitting the training window at the expense of the validation folds. A line that wanders
# without trend around zero never had anything to learn in the first place, and its highest point
# is wherever the noise happened to peak. The difference matters, because both produce a
# respectable-looking maximum.

# %%
curves = catalog.filter("full_coverage").sort("label", "config_name", "checkpoint_value")
objectives = {
    "mse": COLORS["blue"],
    "mae": COLORS["amber"],
    "huber": COLORS["copper"],
    "binary": COLORS["slate"],
}


def objective_of(name: str) -> str:
    """Read the loss function out of a declared configuration name.

    Raising on an unrecognised name rather than defaulting is the point. The classification
    labels declare `*_binary` configurations, and a default of `mse` drew them in the
    squared-error colour under a legend that said the colour was the loss function.
    """
    match = next((key for key in objectives if name.endswith(key)), None)
    if match is None:
        raise ValueError(f"{name!r} does not end in a declared objective: {sorted(objectives)}")
    return match


fig_curves = make_subplots(
    rows=len(panel_labels),
    cols=1,
    shared_xaxes=True,
    vertical_spacing=0.04,
    subplot_titles=[
        f"{label} ({'primary' if label == primary else 'variant'})" for label in panel_labels
    ],
)
drawn_objectives: set[str] = set()
for row, label in enumerate(panel_labels, start=1):
    panel = curves.filter(pl.col("label") == label)
    for objective, color in objectives.items():
        members = [
            name
            for name in panel.get_column("config_name").unique(maintain_order=True)
            if objective_of(name) == objective
        ]
        for config_name in members:
            series = panel.filter(pl.col("config_name") == config_name)
            fig_curves.add_trace(
                go.Scatter(
                    x=series.get_column("checkpoint_value").to_list(),
                    y=series.get_column("ic_mean").to_list(),
                    mode="lines",
                    name=objective,
                    legendgroup=objective,
                    # One legend entry per loss function, not per configuration: the colour is
                    # the claim, and fifty-five named lines would bury it.
                    showlegend=objective not in drawn_objectives,
                    line=dict(color=color, width=1.5),
                    opacity=0.75,
                ),
                row=row,
                col=1,
            )
            drawn_objectives.add(objective)
    fig_curves.add_hline(
        y=0, line_width=1, line_dash="dash", line_color=COLORS["neutral"], row=row, col=1
    )
    fig_curves.update_yaxes(title_text="Mean IC (validation)", row=row, col=1)
fig_curves.update_xaxes(title_text="Boosting iterations (trees kept)", row=len(panel_labels), col=1)
fig_curves.update_layout(
    title="Validation IC against boosting iteration, by loss function and label",
    height=260 * len(panel_labels),
    width=1000,
    margin=dict(t=90),
    legend=dict(title_text="Loss function"),
)
# Which panels sit above zero is a fact about the frame, so the alt text reads it. Describing the
# whole chart as sitting below zero was true of the one label this notebook used to fit.
side_text = "; ".join(
    f"{row['label']} has {row['n_positive']} of {row['candidates']} above zero"
    for row in by_label.sort("label").iter_rows(named=True)
)
show_plotly_with_alt(
    fig_curves,
    "Line charts of mean validation information coefficient against boosting iteration, one line "
    "per configuration, coloured by loss function: dark navy for squared error, gold for absolute "
    "error, copper for Huber, slate for the binary objective the classification labels declare. "
    "One panel per label, sharing the iteration axis, each with a dashed zero line. Counted from "
    f"the frame: {side_text}. Within any one panel the lines wander up and down rather than "
    "rising to a common peak and falling away.",
)

# %% [markdown]
# ### Whether the loss function is what separates them
#
# The curves are coloured by objective because that is the axis with a mechanism behind it. If
# heavy tails are steering the squared-error fits, the three regression colours should separate,
# and they should separate more as trees are added, since each additional tree is fitted to the
# residuals the previous ones left.
#
# The chart below drops the checkpoint dimension by taking each configuration's final state, so
# every configuration is compared at the same amount of training. That is the comparison that does
# not require choosing anything after the fact. The configurations are held in one order across
# the panels - their ranking on the primary label - so a panel that does not descend is a label
# that orders the grid differently.

# %%
final = (
    catalog.filter(pl.col("checkpoint_value") == pl.col("checkpoint_value").max().over("label"))
    .filter("full_coverage")
    .sort(["label", "ic_mean"], descending=[False, True])
)
final_iteration = int(final.get_column("checkpoint_value").max())
config_order = (
    final.filter(pl.col("label") == order_label)
    .sort("ic_mean", descending=True)
    .get_column("config_name")
    .to_list()
)

# `shared_yaxes` matches axes across columns, so with one column it does nothing and each
# panel would be rescaled to fill itself. Matching every row to the first is what puts the
# labels on one vertical scale, which is what stacking them is for.
fig_obj = make_subplots(
    rows=len(panel_labels),
    cols=1,
    shared_xaxes=True,
    vertical_spacing=0.04,
    subplot_titles=[
        f"{label} ({'primary' if label == primary else 'variant'})" for label in panel_labels
    ],
)
for row, label in enumerate(panel_labels, start=1):
    panel = final.filter(pl.col("label") == label)
    # The classification labels declare their own configurations; they keep them and append them
    # after the shared order rather than being dropped from the figure.
    order = [name for name in config_order if name in set(panel.get_column("config_name"))]
    order += [name for name in panel.get_column("config_name").to_list() if name not in order]
    panel = panel.with_columns(
        rank=pl.col("config_name").replace_strict(
            {name: index for index, name in enumerate(order)}, return_dtype=pl.Int32
        )
    ).sort("rank")
    fig_obj.add_trace(
        go.Bar(
            x=panel.get_column("config_name").to_list(),
            y=panel.get_column("ic_mean").to_list(),
            marker_color=[
                objectives[objective_of(name)] for name in panel.get_column("config_name")
            ],
            showlegend=False,
        ),
        row=row,
        col=1,
    )
    fig_obj.add_hline(
        y=0, line_width=1, line_dash="dash", line_color=COLORS["neutral"], row=row, col=1
    )
    fig_obj.update_yaxes(title_text="Mean IC (validation)", row=row, col=1)
    if row > 1:
        fig_obj.update_yaxes(matches="y", row=row, col=1)
fig_obj.update_xaxes(
    title_text=f"Configuration, ordered by rank on {order_label}",
    tickangle=-45,
    row=len(panel_labels),
    col=1,
)
fig_obj.update_layout(
    title="The label sets which side of zero the grid sits on, not the loss function",
    height=260 * len(panel_labels),
    width=1000,
    margin=dict(t=90),
)
# `side_text` counts every checkpoint; this chart shows one, so it gets its own count rather
# than borrowing a number taken over a larger set.
final_side_text = "; ".join(
    f"{row['label']} has {row['n_positive']} of {row['configurations']} above zero"
    for row in (
        final.group_by("label")
        .agg(
            configurations=pl.len(),
            n_positive=(pl.col("ic_mean") > 0).sum(),
        )
        .sort("label")
        .iter_rows(named=True)
    )
)
show_plotly_with_alt(
    fig_obj,
    "Bar charts of mean validation information coefficient at the final boosting iteration, one "
    "panel per label on one shared vertical scale, bars coloured by loss function and held in "
    "the primary label's ranking order in every panel. Within a panel the colours are "
    "interleaved across the ranking rather than grouped, so the loss function does not order the "
    f"grid. Counted at this checkpoint: {final_side_text}. Each panel carries a dashed zero "
    "line.",
)

# %% [markdown]
# ### How much the checkpoint moves a configuration
#
# One number per label and configuration: the range its IC covers across its own ten checkpoints.
# This is the quantity that decides whether choosing a stopping point is a decision worth making
# carefully or one being made by noise. A configuration whose IC varies more across its own
# training run than the configurations vary among themselves is one where the checkpoint, not the
# model, is doing the ranking. Both quantities are computed inside a label, because comparing a
# within-run range against a spread taken across labels would compare two different things.

# %% tags=["results"]
spread = (
    curves.group_by("label", "config_name")
    .agg(
        ic_min=pl.col("ic_mean").min(),
        ic_max=pl.col("ic_mean").max(),
        ic_final=pl.col("ic_mean").filter(pl.col("checkpoint_value") == final_iteration).first(),
    )
    .with_columns(checkpoint_range=pl.col("ic_max") - pl.col("ic_min"))
    .sort("checkpoint_range", descending=True)
)
checkpoint_vs_grid = (
    spread.group_by("label")
    .agg(median_checkpoint_range=pl.col("checkpoint_range").median())
    .join(
        final.group_by("label").agg(
            across_configurations=pl.col("ic_mean").max() - pl.col("ic_mean").min()
        ),
        on="label",
    )
    .with_columns(
        checkpoint_dominates=pl.col("median_checkpoint_range") > pl.col("across_configurations")
    )
    .sort("label")
)
print(f"compared at {final_iteration} boosting iterations")
checkpoint_vs_grid

# %% [markdown]
# ## 5. What to notice
#
# **Read `checkpoint_dominates` before reading any ranking.** Where the median within-run IC range
# exceeds the spread across the whole grid, the leading configuration for that label was chosen by
# where its training run happened to be when it was measured, not by anything about the model. The
# ranking is still a real ordering of registered candidates - `14_backtest` selects over all of
# them - but it is not evidence that one configuration is better than another.
#
# **The label decides how much of the grid clears zero; the grid itself does not.** Read
# `n_positive` against `candidates` in `by_label`: the three regression labels share a menu, a
# feature set and a fold schedule, and the share of their candidates that clears zero is not
# the same. What moves is which target the ranking is asked about. This is not a claim that
# the labels are further apart than the grid is wide: read `best_ic` against `worst_ic` in the
# same frame and one regression label's own candidates span more than the leading candidates
# span across all five labels. Both readings come off the same frame and they say different
# things - the grid is where the magnitude lives, the label is where the sign lives. The linear notebook reaches the same place, which matters - two model families with very
# different representational power agree about which target these features rank, and that points
# at the target rather than at either model.
#
# **These features forecast dispersion rather than direction, and the label set tests it.** Implied
# volatility says how wide the market expects the distribution to be, skew how asymmetric, the term
# structure how that changes with horizon, the variance risk premium how much the market charges
# for bearing it. None is a claim about the *mean*, which is what a forward return is. A
# risk-adjusted return divides that mean by a measure of width, so a feature set that forecasts
# width well should rank it better than the raw return. The `by_label` frame is where that
# prediction meets the evidence.
#
# **The loss function does not separate the results, and that is worth stating.** In case studies
# whose labels have heavy tails the three regression objectives order themselves consistently -
# Huber, then absolute error, then squared error - because squared error spends the fit on extremes
# a rank metric does not reward. Here the colours interleave. That is the control working: these
# labels are equity returns over days, whose tails are mild next to a short straddle's or a
# perpetual's, and where the tails are mild the choice of objective stops mattering. A reader who
# took "always prefer Huber" from another notebook in this book should take this one as the
# boundary of that rule.
#
# **The sample is two folds, one of them 2020.** Every number above is an average over two
# validation windows of a short dataset, one covering a year in which the option surface behaved
# unlike any other in the sample. That is enough to say an effect is not large; it is not enough to
# characterise one, and it applies to whichever label leads as much as to the ones that do not.
#
# **None of this selects anything.** IC measures whether predictions rank stocks correctly, not
# whether a strategy trading them makes money after costs and turnover. Selection is on validation
# backtest Sharpe over the population just published, in [`14_backtest`](14_backtest.ipynb), where
# the checkpoint is part of what is selected.
#
# **Known limitations.** Two folds. The IC is an average of daily rank correlations with no
# adjustment for the serial dependence overlapping multi-day returns create, so it is a diagnostic
# rather than a test. The grid varies capacity and loss at a fixed learning rate. And every number
# is measured on validation folds already read many times by the time a case study reaches this
# notebook.
#
# **Next**: [`08_tabular_dl`](08_tabular_dl.ipynb) fits a neural network to the same rows, and
# [`11_latent_factors`](11_latent_factors.ipynb) asks whether the surface has structure that a
# supervised model is the wrong instrument for. Given that two supervised families have now agreed
# about which label they can rank, the latent-factor route is the more interesting of the two.

```