تحلیل مؤلفه اصلی ابزارمند PCA برای مواجهه‌های عاملی ETF مشروط به ویژگی

# 11b_ipca.py


```py
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# %% [markdown]
# # ETFs: letting the features set the exposures
#
# [`11a_pca`](11a_pca.ipynb) gave each fund one loading per factor, fitted once on the training
# window's return matrix, and never looked at a feature. That is a strong assumption about these
# hundred funds: whatever a fund's momentum, volatility or yield-curve exposure was doing, its
# share of each common movement was a constant for the whole training window.
#
# **Instrumented PCA keeps the factor structure and drops that constant.** A fund's exposure on a
# given date is a linear function of its own feature row on that date - one map, shared by every
# fund and every date, from features to exposures - and the factor returns are then whatever best
# explains that date's cross-section given those exposures. The two are fitted together, by
# alternating between them until neither moves.
#
# What that buys is a constraint rather than more capacity. [`06_linear`](06_linear.ipynb) had one
# free coefficient per feature and one cross-section at a time to find them in. IPCA has one map
# from the features to `n_factors` exposures, estimated on every fund-date in the training window
# at once. That is fewer free parameters against more data, and it is the whole argument for the
# family. It is also its limitation: if the relationship between a feature and the exposure it
# implies is not linear, the constraint is wrong rather than merely tight, which is what
# [`11c_conditional_autoencoder`](11c_conditional_autoencoder.ipynb) relaxes.
#
# **The estimator can fail to fit, and this notebook refuses to publish when it does.** Alternating
# least squares is not guaranteed to converge, and it does not when the cross-section is too narrow
# to identify the number of factors asked for - a hundred funds against five factors is
# comfortable; a handful of funds against five is not. `_require_ipca_convergence` in
# [`case_studies/utils/latent_factors/cv.py`](../utils/latent_factors/cv.py) raises rather than
# registering predictions from a fit that never settled, so an unconverged run is a failure here
# and not a quiet row in the population.
#
# **Learning objectives.** By the end of this notebook you will be able to:
#
# - Say what changes between a factor model with fixed exposures and one whose exposures are a
#   function of observable features, and what each buys.
# - Read an alternating-least-squares configuration - iteration cap, tolerance, two ridge
#   penalties - and say what each controls.
# - Explain why a fit that has not converged must not be published, and where that is enforced.
# - Read a population published for every declared label rather than only the traded one.
#
# **Book reference**: Chapter 14, Section 14.5 (Bridging economics and statistics with advanced
# models). 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) for the feature matrix this one reads,
# [`05_evaluation`](05_evaluation.ipynb) for the walk-forward folds, and
# [`11a_pca`](11a_pca.ipynb), which is the same factor structure with the conditioning removed.
#
# **What it writes**: one training run per label and one complete validation prediction set per
# label, in `run_log/registry.db` and under `run_log/training/` and `run_log/predictions/`, grouped
# under a population named for this model. The family splits across five notebooks, so each
# publishes its own population rather than one shared one.
# [`13_model_analysis`](13_model_analysis.ipynb) compares them against the other families and
# [`14_backtest`](14_backtest.ipynb) backtests every member and selects on validation backtest
# Sharpe. **Selection happens there, not here.**

# %%
"""Fit the declared ETF instrumented-PCA population on the walk-forward folds."""

import json

import plotly.graph_objects as go
import polars as pl

from case_studies.research import (
    declared_labels,
    load_model_configs,
    model_requests,
    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 = {}
POPULATION_NAME = ""
SUPERSEDES_POPULATION: str = ""

MODEL_NAME = "ipca"

# %%
study = open_study("etfs", execution_tier=EXECUTION_TIER, workspace=WORKSPACE or None)

# %% [markdown]
# ## 1. Which labels, and what the configuration says
#
# Every label whose training menu declares `latent_factors:` is fitted, and both do: `fwd_ret_21d`,
# the total return over the 21 trading days after the decision date, and `fwd_ret_5d`, the same
# thing over five. Unlike [`11a_pca`](11a_pca.ipynb), the label is part of what is being estimated
# here - the factor returns are the ones that best explain the cross-section of *that* forward
# return - so the two rows below are two different fits and not one fit scored twice. `LABELS`
# restricts the run to a subset when you want one.

# %%
declared_labels(study, "latent_factors")

# %% [markdown]
# The configuration comes from two files, and they say different kinds of thing.
# `case_studies/config/ipca/ipca.yaml` declares `n_factors`, how many common factors to extract,
# and `checkpoint_interval: 0`, which says there is no intermediate training state to publish:
# alternating least squares runs to convergence rather than for a number of epochs, so a fold
# produces one fitted map and one set of predictions. There is no point at which a reader could
# have stopped it, and publishing a checkpoint schedule would invent a choice the estimator does
# not offer.
#
# `config/setup.yaml` declares the solver itself under `modeling.latent_factors.model_kwargs.ipca`:
# `max_iter`, the cap on alternations; `tol`, how small a step counts as settled; and
# `factor_ridge` and `gamma_ridge`, penalties on the two least-squares steps. Those four are inside
# the training identity rather than recorded beside it, because a fit stopped at a different
# tolerance is a different fitted model.

# %%
configs = load_model_configs(
    study,
    "latent_factors",
    labels=LABELS or None,
    config_names=[MODEL_NAME],
)
configs.select("label", "config_name", "params")

# %% [markdown]
# `LABELS` narrows 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.
#
# The comparison is against this model's own declared rows rather than the whole `latent_factors`
# catalog. The family is split across five notebooks and each publishes one model, so the complete
# catalog is five times what this one publishes, and comparing against it would report every
# canonical run as narrowed.

# %%
declared = load_model_configs(study, "latent_factors", config_names=[MODEL_NAME])
if set(configs.get_column("label")) != set(declared.get_column("label")) and not POPULATION_NAME:
    raise ValueError(
        f"this run fits {configs.height} of the {declared.height} declared labels, so it cannot "
        "publish the canonical population; pass POPULATION_NAME to give it its own"
    )

# %% [markdown]
# ### Where this one runs
#
# `config/setup.yaml` puts no device on the latent-factor family, which leaves it to whatever the
# machine offers - and a fit that lands on a GPU on one machine and a CPU on another is not the
# same computation, because the device is inside the hashed identity rather than recorded beside
# it. IPCA is alternating least squares over the panel and has no GPU implementation, so this
# notebook declares CPU explicitly, and a bounded number of fold workers with it: the folds are
# independent fits and this is the one member of the family the runner allows to run them in
# parallel.

# %%
overrides = {"device": "cpu", "fold_workers": 4}
overrides

# %% [markdown]
# ## 2. Binding the declarations to the data
#
# A menu entry says which estimator to fit. It does not say which fund-date pairs have both a
# feature row and a label, or where the walk-forward folds fall. **Resolving** a request goes and
# finds that: it reads the label and feature files, computes the fold boundaries from the
# walk-forward parameters in `config/setup.yaml`, and works out the exact set of rows each fit is
# expected to predict. It fits nothing, so the plan can be read before any training starts.
#
# Four things to check in it:
#
# - **`feature_count` is the width of the map being estimated.** It is the number of columns that
#   get turned into exposures, and unlike [`11a_pca`](11a_pca.ipynb) this member reads every one of
#   them. `eligible_entities` is the number of funds in the cross-section the factors are fitted
#   on, and it has to be comfortably larger than `n_factors` for the fit to be identified at all.
# - **`folds` is the same on both rows**, and equals the number of walk-forward splits
#   [`05_evaluation`](05_evaluation.ipynb) established.
# - **`validation_start` and `validation_end` bracket the development sample.** The held-out tail
#   is scored once, at the end of the case study; any of it visible here would mean it had been
#   used to choose something.
# - **`checkpoints` is 1**, for the reason the configuration gives above.
#
# Each row also carries a `training_hash`: the identity of that computation, derived from
# everything that can change its result. [`RUN_LOG.md`](../RUN_LOG.md#identity) sets out what goes
# into one and what follows from it.

# %%
requests = model_requests(
    study,
    configs,
    execution_tier=EXECUTION_TIER,
    overrides=overrides,
    preview_reductions=PREVIEW_REDUCTIONS,
    notebook="11b_ipca",
)
resolved = tuple(request.resolve() for request in requests)

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

# %% [markdown]
# The plan is also where a short population is visible. A run that fitted fewer labels than the
# menu declares would still print an IC table and still register its rows; what it would not do is
# announce the gap.

# %%
planned_pairs = set(zip(plan["label"], plan["config_name"], strict=True))
requested_pairs = set(zip(configs["label"], configs["config_name"], strict=True))
if planned_pairs != requested_pairs:
    raise RuntimeError(
        "the plan does not match the loaded IPCA menu; "
        f"missing {sorted(requested_pairs - planned_pairs)}, "
        f"unexpected {sorted(planned_pairs - requested_pairs)}"
    )
print(f"{len(requested_pairs)} label-configuration pairs")

# %% [markdown]
# ## 3. Fitting the population
#
# `run_model_population` runs every resolved request. For one request it walks the folds, and on
# each one:
#
# 1. takes the fund-dates inside that fold's training window,
# 2. alternates between two least-squares problems until they stop moving: given the current map
#    from features to exposures, solve for each date's factor returns; given those factor returns,
#    solve for the map. Both steps are ridge-penalised at the strengths `config/setup.yaml`
#    declares, and the alternation stops when the step falls below `tol` or the iteration cap is
#    reached,
# 3. applies the fitted map to the validation dates' feature rows to get each fund's exposure
#    there, and multiplies those exposures by the training-window average factor returns to get a
#    predicted return.
#
# Step 3 is what makes this a forecast rather than a decomposition: the map and the factor premia
# come from the training window only, and the validation dates contribute nothing to either. It is
# also where the difference from [`11a_pca`](11a_pca.ipynb) shows up in the output rather than in
# the description - the exposures are read off feature rows that change from day to day, so the
# prediction changes with them. Section 4 checks that against the published predictions.
#
# **A fold that did not converge stops the run.** The runner records whether each fold's
# alternation settled, and `_require_ipca_convergence` raises if any did not, before anything is
# registered. That is the check that turns a too-narrow cross-section into a failure instead of a
# population member fitted from wherever the iteration happened to stop.
#
# **How narrow is too narrow is a question with a measured answer, and it is the reason a reduced
# run of this notebook has to reduce the factor count as well as the universe.** A date's factor
# returns are solved from that date's cross-section, so the number of funds priced on a date is a
# hard ceiling on the number of factors: five funds cannot support five factors whatever the
# tolerance says. The practical ceiling is lower than the arithmetic one. Measured on the
# five-fund fixture the CI entry uses, at the `max_iter` declared above: five and three factors
# spend every alternation without settling, two factors settle on one fold and not the other, and
# one factor settles in under a second. `tests/overrides.yaml` carries the per-fold timings, which
# are what distinguish the two explanations - a fold that fails takes the full iteration cap and a
# fold that converges stops early, so the times read out the iterations. That is a system which is
# identified or is not, rather than one that needed a larger budget.
#
# **What the call publishes is a population**: a named, immutable list of the prediction sets it
# will produce, computed from the resolved specifications and written down before the first fit.
# Afterwards every member must exist and be complete, which is what makes the downstream comparison
# well defined - [`14_backtest`](14_backtest.ipynb) backtests this population, not whatever
# predictions happen to be in the registry.
#
# `SUPERSEDES_POPULATION` names the population hash this run replaces. A population is the set of
# prediction identities, so anything that moves a training identity - a changed tolerance as much
# as a changed label menu - produces a different set under the same name, and the registry refuses
# to write it without being told which snapshot it supersedes. It is empty here because this
# notebook, run as it stands, reproduces the members already published under that name rather than
# changing them, and reproducing a published list is not a replacement. Fill it in when you have
# changed something that moves an identity and want the new set to take the name; the error raised
# on the attempt tells you which hash to name. A reduced-scale run passes it empty whatever the
# default is: a population produced under a reduction is thrown away with the workspace it was
# written to, so it has no lineage to extend.

# %%
population_name = POPULATION_NAME or f"etfs-{MODEL_NAME}-validation-v1"
execution, population = run_model_population(
    study,
    resolved,
    population_name=population_name,
    supersedes=SUPERSEDES_POPULATION or None,
)

published_sets = sum(len(run.predictions) for run in execution.runs)
print(f"{len(execution.runs)} configurations, {published_sets} prediction sets")
print(f"population {population.name}: {len(population.members)} members")

# %% [markdown]
# A second run of this notebook fits nothing. 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 - so re-running it unchanged costs the time it takes to read the data. The
# latent-factor runner reports no per-fold fitted-or-reused breakdown, unlike the linear and
# boosted families, so the counts above are of what the population holds rather than of what this
# particular run computed.
#
# ### 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("etfs", workspace="~/ml4t-experiments")
# configs = load_model_configs(study, "latent_factors", labels=["fwd_ret_5d"], config_names=["ipca"])
# requests = model_requests(study, configs, overrides={"device": "cpu", "fold_workers": 4})
# resolved = tuple(request.resolve() for request in requests)
# execution, population = run_model_population(study, resolved, population_name="my-ipca-v1")
# ```
#
# To change the number of factors, edit `case_studies/config/ipca/ipca.yaml`; to change the solver,
# edit `model_kwargs.ipca` in `config/setup.yaml`. Either changes this configuration's identity, so
# its result registers as a new row beside the old one rather than replacing it. Give the run its
# own `population_name`: a name refers to one set of members permanently, and reusing it for a
# different set raises. [`RUN_LOG.md`](../RUN_LOG.md#running-your-own-configurations) covers the
# rest, including how to rehearse on a reduced universe first - and note that a reduced universe is
# exactly the setting where this estimator stops being identified, so a rehearsal has to reduce the
# factor count with it.
#
# **Choosing that reduced factor count has an obvious wrong answer, and it is worth naming because
# the reasoning for it sounds right.** The tempting choice is the largest count that can be made to
# finish - keep it close to the production five, and raise `max_iter` until the folds stop
# failing - because staying near the real configuration seems more faithful to it. What that
# actually buys is a rehearsal sitting on the identification boundary, where whether a fold settles
# depends on the order the floating-point operations happened to run in; the same fixture and the
# same parameters then converge on one machine and not another.
# `sp500_equity_option_analytics` runs its reduced IPCA at two factors and carries `reruns: 2`
# alongside it, which is that instability being absorbed by a retry rather than diagnosed. Pick a
# count below the boundary instead, and read where the boundary is off the per-fold iteration
# counts rather than off whether the run went green.

# %% [markdown]
# ## 4. What came out
#
# One row per label, read back from the registry. `ic_mean` is the **information coefficient**: on
# each validation date, rank the funds 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. It measures whether the model orders the cross-section correctly, on a scale where zero
# is no relationship.
#
# `ic_n_days` is how many validation dates produced a defined correlation, and a row measured on
# fewer of them is not comparable with one measured on all of them - which is why it is shown
# beside the mean rather than left implicit. The two labels have different numbers of scoreable
# dates before any model is fitted, because a 21-day forward return runs out of window earlier than
# a five-day one does.
#
# The published catalog is checked against the population planned before fitting rather than
# against its own row count, because a run that lost a member would otherwise report a shorter
# table and nothing else.

# %% tags=["results"]
catalog = execution.catalog_rows.select(
    "label",
    "config_name",
    "complete",
    "checkpoint_kind",
    "checkpoint_value",
    "ic_mean",
    "ic_std",
    "ic_n_days",
    "n_folds",
    "training_hash",
    "prediction_hash",
).sort("label")

if set(catalog.get_column("prediction_hash")) != set(population.members):
    raise RuntimeError("the published catalog differs from the population planned before fitting")
if catalog.filter(~pl.col("complete")).height:
    raise RuntimeError("a partial IPCA prediction set cannot pass to backtesting")

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 by whichever
# label it did fit rather than by one that is not there.
ordered_labels = [label for label in [primary] if label in present] + [
    label for label in present if label != primary
]
print(f"{catalog.height} candidate models across {len(ordered_labels)} labels")
catalog.select("label", "checkpoint_value", "ic_mean", "ic_std", "ic_n_days", "n_folds")

# %% [markdown]
# ### What the headline number averages, and what the fit had to do to produce it
#
# `ic_mean` is one number over the whole validation period, and the eight folds behind it are
# fitted on different training windows and scored on different years. The table below recomputes
# each fold's mean IC from the published predictions, which is where the dispersion behind a
# single figure becomes visible.
#
# Beside it, read back from the `fold_extras.json` the training run wrote, is how many alternations
# each fold's fit took before the step fell below `tol`. That count is the only evidence that the
# iteration cap in `config/setup.yaml` is a bound the estimator never meets rather than one it runs
# into, and it comes from the stored artifact rather than from the runner's log so it is here
# whether this execution fitted the folds or reused a fit already registered.

# %%
published = {result.hash: result for run in execution.runs for result in run.predictions}
training_by_label = {
    run.training.registry_record()["label"]: run.training for run in execution.runs
}


def _fold_ic(prediction_hash: str) -> pl.DataFrame:
    """Mean daily rank correlation of prediction against realised return, within each fold."""
    return (
        published[prediction_hash]
        .load()
        .group_by("fold", "timestamp")
        .agg(pl.corr("prediction", "actual", method="spearman").alias("ic"))
        .group_by("fold")
        .agg(pl.col("ic").mean().alias("fold_ic"))
        .sort("fold")
    )


def _fold_solver(label: str) -> pl.DataFrame:
    training = training_by_label[label]
    extras_path = training.root / "run_log" / "training" / training.hash / "fold_extras.json"
    return pl.DataFrame(
        [
            {
                "fold": int(extra["fold_id"]),
                "iterations": int(extra["iterations"]),
                "iteration_cap": int(extra["max_iter"]),
                "converged": bool(extra["converged"]),
            }
            for extra in json.loads(extras_path.read_text())
        ]
    ).sort("fold")


by_fold = {
    row["label"]: _fold_ic(row["prediction_hash"]).join(_fold_solver(row["label"]), on="fold")
    for row in catalog.iter_rows(named=True)
}
for label in ordered_labels:
    folds = by_fold[label]
    ic = folds.get_column("fold_ic")
    iterations = folds.get_column("iterations")
    # A narrowed population can leave a label with no scored fold, and polars returns None
    # for the mean of an empty column and for the standard deviation of a single row. Both
    # then raise on the format below, which turns an absent measurement into a crash in a
    # cell that only describes one. Say what is missing instead.
    if folds.height == 0:
        print(f"{label}: no fold scored, so there is no fold IC to summarise")
        continue
    spread = (
        f"standard deviation across folds {ic.std():.4f}"
        if folds.height > 1
        else "one fold only, so no spread across folds"
    )
    print(
        f"{label}: mean {ic.mean():+.4f}, {spread}, "
        f"{(ic < 0).sum()} of {folds.height} folds negative; "
        f"{iterations.min()}-{iterations.max()} alternations against a cap of "
        f"{folds.get_column('iteration_cap').max()}"
    )

by_fold[ordered_labels[0]]

# %% [markdown]
# ### The prediction moves within a fold, and that is the whole difference
#
# [`11a_pca`](11a_pca.ipynb) checked that each fund carried exactly one predicted value for the
# whole of a fold's validation window, because its loadings and factor premia were both fitted once
# and neither depended on the date. Here the premia are still fitted once per fold, but the
# exposures are read off feature rows that change daily, so the same check must come out the other
# way. The cell below counts the distinct predicted values each fund holds within each fold and
# raises if any fund holds only one: a constant would mean the feature rows were not reaching the
# exposures, which is the failure this conditioning exists to avoid and which no IC number would
# reveal.

# %%
# The label whose predictions the rest of this section reads, named rather than taken by position:
# `execution.runs` is ordered by how the requests were submitted, not by which label leads.
charted_label = ordered_labels[0]
charted_hash = catalog.filter(pl.col("label") == charted_label).get_column("prediction_hash")[0]
charted = published[charted_hash]
predictions = pl.read_parquet(
    charted.root / "run_log" / "predictions" / charted.hash / "predictions.parquet"
)
per_fund_values = predictions.group_by("fold", "symbol").agg(
    pl.col("prediction").n_unique().alias("distinct_predictions"),
    pl.len().alias("dates"),
)
frozen = per_fund_values.filter((pl.col("distinct_predictions") == 1) & (pl.col("dates") > 1))
if frozen.height:
    raise RuntimeError(
        f"{frozen.height} fund-fold pairs carry a single predicted value across several dates; "
        "the exposures are not moving with the features"
    )
print(
    f"{per_fund_values.height} fund-fold pairs over "
    f"{predictions.n_unique('timestamp')} validation dates"
)

# %% [markdown]
# ### How fast the ranking turns over
#
# Because the exposures move, the ordering of the funds moves with them, and how fast it does is a
# property of the fitted model worth reading on its own. The measure is the rank correlation
# between each validation date's predicted cross-section and the one that preceded it, averaged
# within a fold: near one means the conditioning is barely changing the ordering from day to day
# and the model is close to the static ranking [`11a_pca`](11a_pca.ipynb) publishes; well below one
# means the features are moving funds past each other, which a strategy trading this signal pays
# for in turnover.
#
# It says nothing about accuracy. A ranking that turns over quickly is not better or worse than one
# that does not; it is a different thing to hold, and [`17_costs`](17_costs.ipynb) is where the
# holding cost is priced.

# %%
ranked = predictions.with_columns(rank=pl.col("prediction").rank().over("timestamp"))
dates = ranked.select("fold", "timestamp").unique().sort("timestamp")
pairs = dates.with_columns(previous=pl.col("timestamp").shift(1).over("fold")).drop_nulls(
    "previous"
)
today = ranked.select("timestamp", "symbol", today_rank="rank")
yesterday = ranked.select(previous="timestamp", symbol="symbol", previous_rank="rank")
daily = (
    pairs.join(today, on="timestamp", how="inner")
    .join(yesterday, on=["previous", "symbol"], how="inner")
    .group_by("fold", "timestamp")
    .agg(pl.corr("today_rank", "previous_rank").alias("rank_correlation"))
)
persistence = (
    daily.group_by("fold")
    .agg(
        pl.col("rank_correlation").mean().alias("mean_day_over_day_rank_correlation"),
        pl.len().alias("date_pairs"),
    )
    .sort("fold")
)
persistence

# %%
fig = go.Figure(
    go.Bar(
        x=[str(fold) for fold in persistence.get_column("fold").to_list()],
        y=persistence.get_column("mean_day_over_day_rank_correlation").to_list(),
        marker_color=COLORS["blue"],
        showlegend=False,
    )
)
fig.add_hline(y=0, line_width=1, line_dash="dash", line_color=COLORS["neutral"])
fig.update_yaxes(title_text="Mean day-over-day rank correlation")
fig.update_xaxes(title_text="Fold")
fig.update_layout(
    title=f"How much the ordering carries from one day to the next ({charted_label})",
    height=420,
    width=800,
    margin=dict(t=90),
)
# The range is read off the frame rather than asserted, so the alt text stays true of the next run.
_values = persistence.get_column("mean_day_over_day_rank_correlation")
show_plotly_with_alt(
    fig,
    "Bar chart of the mean day-over-day rank correlation of the predicted cross-section, one bar "
    "per walk-forward fold, with a dashed zero line. Counted from the frame: "
    f"{persistence.height} folds, values from {_values.min():.2f} to {_values.max():.2f}.",
)

# %% [markdown]
# ## 5. What to notice
#
# **Letting the features set the exposures moves the average off zero, and not past the spread it
# would have to clear.** The mean validation IC is **+0.041** on the primary label and **+0.035**
# on the five-day variant, against **-0.033** and **+0.010** for the unconditioned decomposition in
# [`11a_pca`](11a_pca.ipynb). Behind the primary number the eight fold ICs run -0.008, -0.018,
# +0.118, +0.052, +0.150, +0.013, +0.157 and -0.133: three of the eight are negative, and their
# standard deviation across folds is 0.099, about two and a half times the mean they average to.
# Conditioning is worth something on both labels. It is not worth enough to make any one fold's
# ordering dependable.
#
# **The ordering moves every day, and by very little.** The check above found no fund holding a
# single predicted value through a fold, so the exposures are tracking the feature rows as
# intended. The day-over-day rank correlation says how far that gets: between **0.92 and 0.98** on
# every one of the eight folds. Two things follow, and they point in opposite directions for a
# reader deciding what to do with this model. A strategy trading it turns over slowly, which
# [`17_costs`](17_costs.ipynb) will price as an advantage. And the 1,995 daily correlations behind
# `ic_mean` are nowhere near 1,995 independent readings, because consecutive dates are scoring
# almost the same ordering against a different day of returns, so `ic_std / sqrt(ic_n_days)`
# understates the uncertainty on `ic_mean` here much as it did for the forecast that was frozen
# within a fold. It understates it by less; it does not stop understating it.
#
# **The iteration counts are a result, and this case study had never read them.** The primary
# label's eight folds settle at 85, 97, 110, 107, 69, 59, 53 and 77 alternations against
# `tol = 1e-05`; the five-day label settles between 28 and 61. `config/setup.yaml` declared a cap
# of 100 alternations, which sits inside the primary label's own distribution and above all of the
# five-day label's - two folds of one label needed more than the budget while the other label never
# came close to it. The cap is now 1000, set off these counts. No prediction was ever published
# from a truncated fit: `_require_ipca_convergence` refuses the whole run when any fold stops at
# the cap, which is why the wrong number surfaced as a failure rather than as eight plausible
# ICs. What made it survive being wrong is that nothing had fitted this estimator at production
# width in this case study before, so the declared cap had never been asked to hold.
#
# **What this establishes for the rest of the family.** PCA and IPCA differ in one thing: whether
# a fund's exposure is a fixed number or a function of that fund's 71 feature values on the day.
# Both fit the same panel over the same folds, both average their factor returns over the same
# training windows, and both publish one checkpoint. The gap between -0.033 and +0.041 on the
# primary label is what that one difference is worth with a **linear** map from features to
# exposures. [`11c_conditional_autoencoder`](11c_conditional_autoencoder.ipynb) keeps the two-stage
# structure and replaces that map with a network, so the comparison that follows isolates the map
# rather than the idea of conditioning.
#
# **Known limitations.** `n_factors` is declared at five rather than chosen, and nothing here tests
# whether a different count orders the cross-section better - that would be a search over
# validation IC, which this notebook is arranged to avoid. Five factors against roughly 96 funds is
# a comfortable ratio but not a large one, and the panel narrows as the folds roll forward: the
# last fold prices 90 funds where the first prices 96, so the eight fold ICs are not eight readings
# of one experiment. The ridge strengths are declared too, and a ridge that binds changes what
# converges. And every number here is measured on validation folds that have been read many times
# over by the time a case study reaches this notebook.

# %% [markdown]
# **Next**: [`11c_conditional_autoencoder`](11c_conditional_autoencoder.ipynb) keeps this exact
# structure - features to exposures, exposures times factor returns - and replaces the linear map
# with a network, so the difference between the two is the shape of one function and nothing else.

```