用于公司收益预测的监督式自编码器

# Firm characteristics: dropping the factor structure and keeping the bottleneck


# Firm characteristics: dropping the factor structure and keeping the bottleneck

The three notebooks before this one all impose structure on how a prediction is formed.
[`08a_ipca`](08a_ipca.ipynb) and [`08b_conditional_autoencoder`](08b_conditional_autoencoder.ipynb)
require the prediction to be an exposure times a factor return;
[`08c_stochastic_discount_factor`](08c_stochastic_discount_factor.ipynb) requires it to fall out
of a no-arbitrage condition. The **supervised autoencoder** imposes neither. It maps the
characteristics to the forward return end to end, and the only thing left of the family is the
**bottleneck**: the network is forced to compress 57 characteristics through a small number of
units before predicting, and that width is the same `n_factors` the other three declare.

So the question this notebook puts is whether the compression is doing the work, or the factor
interpretation is. If a bottleneck alone gets you what the conditional-factor structure gets you,
then the structure was a constraint the data did not need; if it does not, the structure was
buying something.

**It is also the closest thing in this family to the earlier notebooks.** A network mapping
characteristics to returns is what [`07_tabular_dl`](07_tabular_dl.ipynb) fits, without a
bottleneck and with a different architecture, so those two are worth reading together as well.

**Learning objectives**

- Separate the two things a latent-factor model asserts: that a low-dimensional representation
  exists, and that it should be interpreted as factor exposures.
- Read a checkpoint path where the objective and the metric are the same kind of quantity, unlike
  the pricing model before it.
- See why the least-structured member of a family is worth publishing rather than assuming the
  structured ones dominate.

**Book reference**: Chapter 14, Section 14.7 (The stochastic discount factor and the supervised
autoencoder models). Chapter 6, Section 6.7 (Search accounting and run logging) introduces the
run log this notebook writes into.

**Prerequisites**: [`03_financial_features`](03_financial_features.ipynb),
[`04_evaluation`](04_evaluation.ipynb), [`08_latent_factors`](08_latent_factors.ipynb) and
[`08b_conditional_autoencoder`](08b_conditional_autoencoder.ipynb), whose bottleneck this one
keeps and whose factor structure it drops.

**What it writes**: one training run per label and one complete validation prediction set per
label and epoch checkpoint, 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
four notebooks, so each publishes its own population rather than one shared one.
[`11_backtest`](11_backtest.ipynb) reads them and selects on validation backtest Sharpe.
**Selection happens there, not here**, and the checkpoint is part of what is selected.

```python
"""Fit the declared firm-characteristics supervised-autoencoder population."""

import plotly.graph_objects as go
import polars as pl
import yaml

from case_studies.research import (
    declared_labels,
    load_model_configs,
    model_requests,
    open_study,
    plan_models,
    planned_model_plan,
    primary_label,
    run_model_population,
    supersedes_for_run,
)
from utils.paths import get_case_study_dir
from utils.style import COLORS, show_plotly_with_alt
```

```python
LABELS: list[str] = []
EXECUTION_TIER = "canonical"
WORKSPACE: str = ""
PREVIEW_REDUCTIONS: dict = {}
POPULATION_NAME = ""
SUPERSEDES_POPULATION: str = ""
# The device to fit on. Empty means the one declared in config/setup.yaml.
DEVICE: str = ""

MODEL_NAME = "sae"
```

```python
study = open_study(
    "us_firm_characteristics", execution_tier=EXECUTION_TIER, workspace=WORKSPACE or None
)
```

## 1. Which labels, and what the configuration says

Every label whose training menu declares `latent_factors:` is fitted, and all three do:
`fwd_ret_1m`, `fwd_ret_1m_win` - the same return with each month's cross-section clipped at its
own tails - and `fwd_class_1m`, which turns that return into a class. The target matters more
here than anywhere else in the family: this is the one member fitted directly against it, so a
change of label changes what the whole network is optimizing rather than only what the last stage
is scored on.

```python
declared_labels(study, "latent_factors")
```

`case_studies/config/sae/sae.yaml` declares the bottleneck width as `n_factors`, the training
budget and the checkpoint interval. The budget and the interval together decide the checkpoint
surface: a state is saved every `checkpoint_interval` epochs up to `n_epochs`, and each saved
state becomes a registered prediction set covering the whole validation period. The runtime comes
from `config/setup.yaml` under `modeling.latent_factors`.

```python
configs = load_model_configs(
    study,
    "latent_factors",
    labels=LABELS or None,
    config_names=[MODEL_NAME],
)
configs
```

`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 four notebooks and each publishes one model, so the complete
catalog is four times what this one publishes, and comparing against it would report every
canonical run as narrowed.

```python
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"
    )
```

The device is the second thing that can put a run outside the declared population, and it is
not a note beside the result: a network trained on a GPU and the same network trained on a CPU
accumulate their sums in different orders and reach different weights, so the two are different
computations and get different identities. `config/setup.yaml` declares the device this family
publishes on under `modeling.latent_factors`, and the runner refuses a device the machine does
not have rather than falling back to one it does. A reader without an NVIDIA card passes
`DEVICE="cpu"` with a `POPULATION_NAME` of their own.

```python
setup = yaml.safe_load(
    (get_case_study_dir("us_firm_characteristics") / "config" / "setup.yaml").read_text()
)
PUBLISHED_DEVICE = str(setup["modeling"]["latent_factors"]["device"])
device = DEVICE or PUBLISHED_DEVICE

if device != PUBLISHED_DEVICE and not POPULATION_NAME:
    raise ValueError(
        f"this run fits on device {device!r} rather than the declared {PUBLISHED_DEVICE!r}, so "
        "it cannot publish the canonical population; pass POPULATION_NAME to give it its own"
    )
```

## 2. Binding the declarations to the data

Planning reads the label and feature files, computes the fold boundaries from the walk-forward
parameters in `config/setup.yaml`, works out the exact rows each fit must predict, and derives
every training and prediction identity - without fitting anything. Four things to check:

- **`feature_count` and `eligible_rows` agree across the rows.** A row that differs is a label
  measured on a different sample from its neighbours.
- **`folds` is the same everywhere**, and equals the number of walk-forward splits
  [`04_evaluation`](04_evaluation.ipynb) established.
- **`validation_start` and `validation_end` bracket the development sample**, with none of the
  held-out 2016 tail visible.
- **`checkpoints` is how many training states each label will publish predictions for.**
  Multiply it by the number of rows to get the number of candidate models this notebook creates.

```python
requests = model_requests(
    study,
    configs,
    execution_tier=EXECUTION_TIER,
    overrides={"device": device},
    preview_reductions=PREVIEW_REDUCTIONS,
    notebook="08d_supervised_autoencoder",
)
plan = plan_models(study, requests=requests)

planned_model_plan(plan).select(
    "label",
    "config_name",
    "task",
    "feature_count",
    "eligible_rows",
    "folds",
    "checkpoints",
    "validation_start",
    "validation_end",
)
```

The plan is also where a short population is visible. A run that fitted fewer labels than the
menu declares, or published fewer checkpoints than the configuration does, would still print an
IC table and still register its rows; what it would not do is announce the gap.

```python
planned_pairs = {(member.label, member.config_name) for member in plan.members}
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 supervised-autoencoder menu; "
        f"missing {sorted(requested_pairs - planned_pairs)}, "
        f"unexpected {sorted(planned_pairs - requested_pairs)}"
    )
print(f"{len(requested_pairs)} label-configuration pairs")
print(f"{len(plan.expected_training_hashes)} training identities")
print(f"{len(plan.expected_prediction_hashes)} validation prediction sets")
```

## 3. Fitting the population

`run_model_population` runs every planned request. For one request it walks the folds, and on
each one:

1. takes the firm-months inside that fold's training window,
2. trains the network - characteristics in, through the bottleneck, forward return out - for the
   declared number of epochs, saving the fitted state at each checkpoint on the way,
3. applies each saved state to the validation months' characteristics to get a predicted return.

Step 3 is what makes one fit produce many results. 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. Nothing here chooses among them.

**This notebook passes the plan rather than resolved requests, and on this family that changes
what the plan table could show rather than how the fitting is ordered.** The linear, boosted and
TabM adapters each provide a batch runner that prepares one fold set for several configurations;
the latent-factor adapter provides none, so every request is fitted on its own whichever path is
taken. There is nothing here for a batch runner to share in any case: this notebook publishes one
model against three labels, and each label is a different set of rows. What passing the plan does
cost is `eligible_entities`, which needs the eligibility keys themselves; `eligible_rows` above
moves whenever the universe does, so the check that column existed for is still made.

**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.

```python
population_name = POPULATION_NAME or f"us_firm_characteristics-{MODEL_NAME}-validation-v1"
# The declared hash is only meaningful where a generation of this name already exists. A preview
# run, a reader's first canonical run against an empty `run_log/`, and a run under a caller-chosen
# `POPULATION_NAME` are all refused by `OfficialPopulation.create` if it is passed anyway. The
# resolution lives in shared code so no notebook branches on the tier.
supersedes = supersedes_for_run(
    study,
    population_name=population_name,
    declared=SUPERSEDES_POPULATION,
    execution_tier=EXECUTION_TIER,
)
execution, population = run_model_population(
    study, plan, population_name=population_name, supersedes=supersedes
)

print(f"{len(execution.runs)} configurations, fitted or served from the registry")
print(f"population {population.name}: {len(population.members)} prediction sets")
```

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.

**There are no fold counts above, and their absence is the honest reading rather than an
omission.** [`05_linear`](05_linear.ipynb) and [`06_gbm`](06_gbm.ipynb) print folds fitted
against folds served from the registry, because the linear and GBM runners record
`fitted_folds` and `reused_folds` on every path they take. The latent-factor runner records
neither - its result carries no diagnostics at all, so the only per-run keys are the status and
the training hash. Printing two zeros here would say every fold came from cache, which is the
opposite of what nothing-recorded means.

[`07_tabular_dl`](07_tabular_dl.ipynb) sits between the two and says so at run time. Its runner
records fold counts when it fits and none when it serves a whole configuration from the
registry, so on a re-run it reports how many of its runs recorded counts instead of printing a
split it was never given.

### 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("us_firm_characteristics", workspace="~/ml4t-experiments")
configs = load_model_configs(study, "latent_factors", labels=["fwd_ret_1m"], config_names=["sae"])
requests = model_requests(study, configs)
plan = plan_models(study, requests=requests)
execution, population = run_model_population(study, plan, population_name="my-sae-v1")
```

The bottleneck width, the training budget and the checkpoint interval live in
`case_studies/config/sae/sae.yaml`. Each changes this configuration's identity - the interval as
much as the budget, because it changes which states exist - so the 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.

## 4. What came out

One row per label and epoch checkpoint. `ic_mean` is the **information coefficient**: in each
validation month, rank the firms by the model's prediction, rank them by the return they went on
to earn, correlate the two rankings, and average that monthly correlation over the validation
period.

**Every count and aggregate below is keyed on `(label, checkpoint_value)`.** Grouping on the
checkpoint alone would average across targets; grouping on the label alone would collapse the
training path this notebook exists to show.

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.

```python
catalog = execution.catalog_rows.select(
    "config_name",
    "label",
    "task",
    "complete",
    "checkpoint_kind",
    "checkpoint_value",
    "ic_mean",
    "ic_std",
    "ic_t",
    "ic_n_days",
    "auc_mean_daily",
    pl.col("direction_label").alias("auc_scored_against"),
    "n_folds",
    "training_hash",
    "prediction_hash",
).sort(["label", "checkpoint_value"])

if set(catalog.get_column("prediction_hash")) != set(plan.expected_prediction_hashes):
    raise RuntimeError("the published catalog differs from the population planned before fitting")
if catalog.filter(~pl.col("complete")).height:
    raise RuntimeError("a partial supervised-autoencoder checkpoint cannot pass to backtesting")
if catalog.select("label", "config_name", "checkpoint_value").n_unique() != catalog.height:
    raise RuntimeError("each label and checkpoint must identify one prediction set")
if catalog.get_column("checkpoint_value").null_count():
    raise RuntimeError("every checkpoint must name the epoch it was taken at")

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 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
]
print(f"{catalog.height} candidate models across {len(panel_labels)} labels")
print(f"at {catalog.n_unique('checkpoint_value')} checkpoints each")
catalog.select(
    "label",
    "checkpoint_value",
    "ic_mean",
    "ic_std",
    "ic_t",
    "ic_n_days",
    "full_coverage",
).head(15)
```

### What more training does

Each line traces one label's out-of-sample IC as epochs are added, and the shape to read is where
it reaches its highest point.

This is the one member of the family where the objective and this axis measure the same kind of
thing - the network is fitted against the return and scored on how it ranks the return - so a
line that turns down is the ordinary story of a model beginning to fit its training window rather
than the objective-versus-metric gap that
[`08c_stochastic_discount_factor`](08c_stochastic_discount_factor.ipynb) has by construction.
That makes this the cleanest checkpoint path in the family to read, and the right one to compare
the others against.

```python
curves = catalog.filter("full_coverage").sort("label", "checkpoint_value")
fig = go.Figure()
for label in panel_labels:
    series = curves.filter(pl.col("label") == label).sort("checkpoint_value")
    fig.add_trace(
        go.Scatter(
            x=series.get_column("checkpoint_value").to_list(),
            y=series.get_column("ic_mean").to_list(),
            mode="lines+markers",
            name=f"{label} ({'primary' if label == primary else 'variant'})",
            line=dict(
                color=COLORS["blue"] if label == primary else COLORS["slate"],
                width=2 if label == primary else 1.5,
            ),
            marker=dict(size=6),
        )
    )
fig.add_hline(y=0, line_width=1, line_dash="dash", line_color=COLORS["neutral"])
fig.update_xaxes(title_text="Training epochs completed")
fig.update_yaxes(title_text="Mean IC (validation)")
fig.update_layout(
    title="Fitting the return directly makes the training path readable",
    height=460,
    width=900,
    margin=dict(t=90),
    legend=dict(title_text="Label"),
)
# Where each line peaks is a fact about the frame, so the alt text counts it rather than asserting
# a shape the next run may not reproduce.
peaks = (
    curves.group_by("label")
    .agg(
        peak_checkpoint=pl.col("checkpoint_value").sort_by("ic_mean", descending=True).first(),
        first_checkpoint=pl.col("checkpoint_value").min(),
        last_checkpoint=pl.col("checkpoint_value").max(),
    )
    .sort("label")
)
peak_text = "; ".join(
    f"{row['label']} peaks at epoch {row['peak_checkpoint']} of "
    f"{row['first_checkpoint']} to {row['last_checkpoint']}"
    for row in peaks.iter_rows(named=True)
)
show_plotly_with_alt(
    fig,
    "Line chart of mean validation information coefficient against training epochs completed, one "
    "line per label with a marker at each declared checkpoint: the primary target in dark navy and "
    f"the two variants in slate, over a dashed zero line. Counted from the frame: {peak_text}.",
)
```

### How much the stopping point is worth

The frame below puts the range a label's IC covers across its own checkpoints against the spread
across labels at a fixed amount of training. That is the quantity deciding whether the stopping
point is a decision worth making carefully or one being made by noise, and both sides are
computed within this model so the comparison is not smuggling in a difference between models.

```python
final_epoch = int(curves.get_column("checkpoint_value").max())
checkpoint_vs_label = (
    curves.group_by("label")
    .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_epoch).first(),
        scored_months=pl.col("ic_n_days").max(),
    )
    .with_columns(checkpoint_range=pl.col("ic_max") - pl.col("ic_min"))
    .sort("label")
)
across_labels = float(
    checkpoint_vs_label.get_column("ic_final").max()
    - checkpoint_vs_label.get_column("ic_final").min()
)
print(f"compared at {final_epoch} epochs; spread across labels there: {across_labels:.4f}")
checkpoint_vs_label
```

## 5. What to notice

**This model is the family's control, and that is why it is published rather than assumed to
lose.** It keeps the bottleneck and drops everything else - no conditional-factor structure, no
pricing condition. So reading it against
[`08b_conditional_autoencoder`](08b_conditional_autoencoder.ipynb), which has the same kind of
network and the same bottleneck width, isolates what the factor structure is worth on this data.
A structured model that does not beat its own unstructured control has not earned the structure.

**The four members are two pairs, not four points on a line.**
[`08a_ipca`](08a_ipca.ipynb) and `08b` are the two-stage models and differ in whether the loading
map is linear. `08c` and this one both break the two stages, from opposite ends - one because it
prices directly and one because it predicts directly. Ranking all four on one number would hide
that, which is part of why ranking happens in
[`10_model_analysis`](10_model_analysis.ipynb) with the whole population rather than here.

**The bottleneck is the only latent-factor assumption left, and it is a real one.** Forcing 57
characteristics through a small number of units asserts that the useful information in them is
low-dimensional. That is testable - widen the bottleneck and see - and it is not tested here,
because the width is declared and a search over validation IC is what this arrangement exists to
avoid.

**None of this selects anything.** IC measures whether predictions rank firms correctly, not
whether a strategy trading them makes money after costs and turnover. Selection is on validation
backtest Sharpe in [`11_backtest`](11_backtest.ipynb), where the checkpoint is part of what is
selected.

**Known limitations.** The bottleneck width, the training budget, the checkpoint interval and the
network's shape are declared rather than chosen. Fitting directly against the return means this
model inherits the target's shape problem that [`06_gbm`](06_gbm.ipynb) diagnosed - a monthly
cross-section of individual firms is heavy-tailed, and a squared-error objective is steered by
exactly the observations a rank correlation is indifferent to - which is one reason to read its
`fwd_ret_1m` and `fwd_ret_1m_win` rows against each other. The IC is an average of monthly rank
correlations with no adjustment for serial dependence, so `ic_t` is a diagnostic rather than a
test. And every number is measured on validation folds that have been read many times over by the
time a case study reaches this notebook.

**Next**: [`09_causal_dml`](09_causal_dml.ipynb) stops predicting altogether and asks a different
question of the same panel - what the effect of one characteristic on the forward return is once
the others are controlled for, which is not what any model in this family estimates.