60 minReal data snapshotExecuted reading edition

Evaluate a chronological energy regression

Fit training-only weather/calendar regressions, compare a mean baseline and inspect held-out energy errors.

Engineering · Lesson 02🔋 Offline core analysis⏱ 60 minEmbedded real data📦 numpy · pandas · matplotlib · IPython

Goal and how to run

This lesson assumes basic Python knowledge. Read each method and caption before changing parameters. AI exercises are optional; no AI account is needed for the core workflow. Data lives in notebook metadata, so there is no companion data download. Keep the notebook saved in the active working folder.

Your goal is to understand the research question, execute transparent calculations, check the results, and state the limits of the conclusion.

Setup and parameters

In [1] · Python
from pathlib import Path
import base64, gzip, hashlib, json, platform
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from IPython.display import display, HTML
from datetime import datetime
from IPython.display import display as _display
def display(value):
    if isinstance(value,pd.DataFrame):
        table=value.to_html(max_rows=12,escape=True)
        style="<style>.vibeit-readable-table{max-width:100%;overflow-x:auto}.vibeit-readable-table table{width:max-content;max-width:none;border-collapse:collapse}.vibeit-readable-table td,.vibeit-readable-table th{white-space:nowrap!important;word-break:normal!important;overflow-wrap:normal!important}</style>"
        return _display(HTML(style+'<div class="vibeit-readable-table">'+table+'</div>'))
    return _display(value)
RECIPE_ID='en02-energy-regression'
OUTPUT_DIR=Path.cwd()/"results"/RECIPE_ID
plt.rcParams.update({"figure.dpi":120,"font.size":10,"axes.spines.top":False,"axes.spines.right":False,
                      "axes.prop_cycle":plt.cycler(color=["#18785f","#416aa6","#bc6541","#9974a5"])})
print("Python:",platform.python_version(),"; NumPy:",np.__version__,"; Pandas:",pd.__version__)
print("Working folder:",Path.cwd())
print("Core data mode: embedded snapshot; no network requests")
Python: 3.13.13 ; NumPy: 2.5.3 ; Pandas: 3.0.6
Working folder: /Users/zhiluo/Developer/vibeit-cookbook/cookbook/downloads
Core data mode: embedded snapshot; no network requests

Load the embedded snapshot

In [2] · Python
def load_snapshot(recipe_id, expected_sha256, snapshot_key):
    """Read embedded data from this notebook, including a renamed copy."""
    for path in sorted(Path.cwd().glob("*.ipynb")):
        try:
            notebook = json.loads(path.read_text(encoding="utf-8"))
            metadata = notebook.get("metadata", {}).get("vibeit_cookbook", {})
            blob = metadata.get("snapshots", {}).get(snapshot_key)
            if metadata.get("recipe_id") != recipe_id or not blob:
                continue
            if blob.get("sha256") != expected_sha256:
                continue
            raw = gzip.decompress(base64.b64decode(blob["gzip_base64"], validate=True))
            if hashlib.sha256(raw).hexdigest() != expected_sha256:
                raise ValueError("Embedded snapshot checksum mismatch: " + snapshot_key)
            return json.loads(raw)
        except (OSError, json.JSONDecodeError):
            continue
    raise FileNotFoundError(
        "Save/open the complete .ipynb in the active working folder. "
        "The embedded snapshot could not be located for " + recipe_id)

SNAPSHOT_HASHES={'energy': '81117ee0a0706bf416bedc50f23b455ee8dd771e588c91b6a420dc3b184f638f'}
def snapshot(key):
    return load_snapshot(RECIPE_ID,SNAPSHOT_HASHES[key],key)
print("Embedded snapshots:",list(SNAPSHOT_HASHES))
Embedded snapshots: ['energy']

Read the method functions

In [3] · Python
def audit_numeric_table(frame,columns):
    """Audit observed rows; never silently impute or remove them."""
    if frame.empty or frame.index.has_duplicates:
        raise ValueError('Expected a nonempty table with unique row IDs')
    missing=[name for name in columns if name not in frame.columns]
    if missing:raise ValueError('Missing required columns: '+str(missing))
    values=frame[columns].to_numpy(dtype=float)
    if not np.isfinite(values).all():raise ValueError('Non-finite measurements; inspect missing values explicitly')
    return {'rows':len(frame),'features':len(columns),'finite':True,'duplicate_measurement_rows':int(frame[columns].duplicated().sum())}

print("Method ready: audit_numeric_table")
Method ready: audit_numeric_table
In [4] · Python
def ridge_fit_predict(train_values,train_target,test_values,penalty=1.0):
    """Scale using training statistics and solve ridge by an augmented least-squares system."""
    train_values=np.asarray(train_values,dtype=float);test_values=np.asarray(test_values,dtype=float)
    target=np.asarray(train_target,dtype=float)
    if train_values.ndim!=2 or len(train_values)==0 or target.shape!=(len(train_values),) or penalty<0:raise ValueError('Invalid training data or penalty')
    if test_values.ndim!=2 or train_values.shape[1]!=test_values.shape[1]:raise ValueError('Training/test feature dimensions differ')
    if not np.isfinite(train_values).all() or not np.isfinite(test_values).all() or not np.isfinite(target).all():raise ValueError('Non-finite training data')
    mean=train_values.mean(axis=0);scale=train_values.std(axis=0);scale=np.where(scale==0,1,scale)
    design=np.column_stack([np.ones(len(train_values)),(train_values-mean)/scale])
    test_design=np.column_stack([np.ones(len(test_values)),(test_values-mean)/scale])
    regularizer=np.sqrt(penalty)*np.eye(design.shape[1]);regularizer[0,0]=0
    coefficients=np.linalg.lstsq(np.vstack([design,regularizer]),np.r_[target,np.zeros(design.shape[1])],rcond=None)[0]
    return dict(predictions=test_design@coefficients,coefficients=coefficients,mean=mean,scale=scale,train_predictions=design@coefficients)

print("Method ready: ridge_fit_predict")
Method ready: ridge_fit_predict
In [5] · Python
def regression_metrics(truth,predictions):
    truth=np.asarray(truth,dtype=float);predictions=np.asarray(predictions,dtype=float)
    if truth.shape!=predictions.shape or truth.size==0 or not np.isfinite(truth-predictions).all():raise ValueError('Invalid regression comparison')
    error=predictions-truth;denominator=np.sum((truth-truth.mean())**2)
    return dict(mae=float(np.mean(np.abs(error))),rmse=float(np.sqrt(np.mean(error**2))),r_squared=float(1-np.sum(error**2)/denominator) if denominator>0 else float('nan'))

print("Method ready: regression_metrics")
Method ready: regression_metrics
In [6] · Python
def iso_datetimes(values):
    """Parse source ISO dates with the standard library; keep tables as ISO strings."""
    return [datetime.fromisoformat(str(value)) for value in values]

print("Method ready: iso_datetimes")
Method ready: iso_datetimes

Data and model boundary

The building record contains real ten-minute energy and environmental observations from one source building. Airport weather fields include upstream interpolation and are not colocated calibration references. Beam, circuit and PID examples are declared numerical design models; computed responses do not establish hardware performance or commissioning acceptance.

Steps

1. Reserve a chronological test interval

Use the first 70% of timestamps for fitting and the final 30% for testing. A random row split would mix nearby and seasonally related observations. Target energy is Wh per interval, and this is conditional reconstruction using contemporaneous environmental variables.

In [7] · Python
energy=snapshot("energy");frame=pd.DataFrame(energy["rows"],columns=energy["columns"])
frame["timestamp"]=frame["date"].astype(str);frame=frame.sort_values("timestamp").reset_index(drop=True)
assert len(frame)==19735 and frame.timestamp.is_unique
dates=iso_datetimes(frame.timestamp)
assert all((b-a).total_seconds()==600 for a,b in zip(dates,dates[1:]))
audit=audit_numeric_table(frame,["Appliances","lights","T1","RH_1"])
assert frame.Appliances.ge(0).all() and frame.lights.ge(0).all()
frame["appliance_average_power_W"]=frame.Appliances/(600/3600)
print("Observed rows:",len(frame),"; energy: Wh/10 min; derived interval-average power: W; source timezone unspecified")
display(frame[["timestamp","Appliances","appliance_average_power_W","T1","RH_1"]].head(8))
split=int(.7*len(frame));train=np.arange(len(frame))<split;test=~train
frame["hour_sin"]=np.sin(2*np.pi*(np.array([value.hour+value.minute/60 for value in dates]))/24)
frame["hour_cos"]=np.cos(2*np.pi*(np.array([value.hour+value.minute/60 for value in dates]))/24)
features=["T1","RH_1","T_out","RH_out","hour_sin","hour_cos"]
assert frame.loc[train,"timestamp"].max()<frame.loc[test,"timestamp"].min()
print("Training/test rows:",int(train.sum()),int(test.sum()))
Observed rows: 19735 ; energy: Wh/10 min; derived interval-average power: W; source timezone unspecified
timestamp Appliances appliance_average_power_W T1 RH_1
0 2016-01-11 17:00:00 60 360.0 19.890000 47.596667
1 2016-01-11 17:10:00 60 360.0 19.890000 46.693333
2 2016-01-11 17:20:00 50 300.0 19.890000 46.300000
3 2016-01-11 17:30:00 50 300.0 19.890000 46.066667
4 2016-01-11 17:40:00 60 360.0 19.890000 46.333333
5 2016-01-11 17:50:00 50 300.0 19.890000 46.026667
6 2016-01-11 18:00:00 60 360.0 19.890000 45.766667
7 2016-01-11 18:10:00 60 360.0 19.856667 45.560000
Training/test rows: 13814 5921

2. Fit training-only scaling and compare a baseline

The random variables rv1/rv2 and other energy measurements are excluded. Ridge uses only training means/SDs. The mean baseline also uses the training target mean. Report held-out metrics even if the simple model performs poorly.

In [8] · Python
model=ridge_fit_predict(frame.loc[train,features].to_numpy(),frame.loc[train,"Appliances"].to_numpy(),frame.loc[test,features].to_numpy(),penalty=10)
truth=frame.loc[test,"Appliances"].to_numpy(float);prediction=model["predictions"]
baseline=np.full(len(truth),frame.loc[train,"Appliances"].mean())
metrics=pd.DataFrame({"ridge":regression_metrics(truth,prediction),"training-mean":regression_metrics(truth,baseline)}).T;display(metrics)
fig,ax=plt.subplots(figsize=(7,5));ax.scatter(truth,prediction,s=5,alpha=.25)
limit=[min(truth.min(),prediction.min()),max(truth.max(),prediction.max())];ax.plot(limit,limit,"k--")
ax.set(xlabel="Observed Wh/interval",ylabel="Predicted Wh/interval",title="Chronological held-out conditional predictions");plt.tight_layout();plt.show()
mae rmse r_squared
ridge 49.573429 87.729910 0.082222
training-mean 53.398043 91.646165 -0.001546
Computed figure from this code cell

3. Inspect time-dependent errors

Plot a bounded first-week test interval; errors and target values share Wh/interval units. A limited feature set may miss occupancy and appliance events. The residual trace is not an independent-series confidence calculation.

In [9] · Python
timestamp=frame.loc[test,"timestamp"].to_numpy();residual=prediction-truth;count=min(7*144,len(truth))
fig,ax=plt.subplots(figsize=(10,4));ax.plot(iso_datetimes(timestamp[:count]),residual[:count],lw=.8)
ax.axhline(0,color="black",linestyle="--");ax.set(xlabel="Source-local test timestamp",ylabel="Prediction − observation (Wh/interval)",title="First test-week conditional errors");plt.tight_layout();plt.show()
Computed figure from this code cell

4. Compare average errors by clock hour

Group test absolute errors by source-local hour on the same dates for model and baseline. Error patterns can motivate a new prospective design, but do not retrospectively tune this held-out result and still call it untouched.

In [10] · Python
hours=np.array([value.hour for value in iso_datetimes(frame.loc[test,"timestamp"])])
hourly=pd.DataFrame({"hour":hours,"ridge":abs(residual),"training-mean":abs(baseline-truth)}).groupby("hour").mean()
fig,ax=plt.subplots(figsize=(9,4));hourly.plot(ax=ax,marker="o")
ax.set(xlabel="Source-local clock hour",ylabel="Held-out MAE (Wh/interval)",title="Common-date error stratification");plt.tight_layout();plt.show()
Computed figure from this code cell

5. Reconcile predictors and export

Check training-only statistics and direct RMSE. Do not hide negative predictions by clipping. Export the time split, original target and both predictions, keeping the single-building observational limitation.

In [11] · Python
assert np.allclose(model["mean"],frame.loc[train,features].mean())
assert np.isclose(metrics.loc["ridge","rmse"],np.sqrt(np.mean(residual**2)))
assert not {"Appliances","lights","rv1","rv2"}&set(features)
OUTPUT_DIR.mkdir(parents=True,exist_ok=True)
pd.DataFrame({"timestamp":timestamp,"observed_Wh":truth,"ridge_Wh":prediction,"training_mean_Wh":baseline}).to_csv(OUTPUT_DIR/"held-out-energy.csv",index=False)
metrics.to_csv(OUTPUT_DIR/"metrics-Wh-per-interval.csv");hourly.to_csv(OUTPUT_DIR/"hourly-test-MAE.csv")
print("Prediction-boundary checks passed; negative model predictions:",int(np.sum(prediction<0)))
Prediction-boundary checks passed; negative model predictions: 0

Exercises and reference explanation

  1. Why prefer chronological over random-row holdout here?
  2. Why distinguish conditional regression from forecasting?

Reference explanation. Nearby seasonal observations can leak information across random splits. Contemporaneous environmental values are known for reconstruction, not necessarily for future predictions.

Keep a copy before changing parameters. Compare old and new figures and record which inputs, calculations and conclusions changed.

Optional AI coding exercises

Prompt 1

Using NumPy/Pandas/Matplotlib, add a training-only clock-hour mean baseline and evaluate on the same test timestamps.

Prompt 2

With the same packages, report error separately for high and low observed energy while keeping the original fitted model unchanged.

Human acceptance. No test values enter scaling or fitting; all methods share dates and Wh/interval units.

Review the edited source, then manually run affected cells and subsequent checks. Ask the assistant to explain the purpose, packages and data provenance of its changes, and reconcile that explanation with actual output.

Optional online extension

In [12] · Python
RUN_ONLINE_UPDATE=False
if RUN_ONLINE_UPDATE:
    import requests
    try:
        response=requests.get('https://archive.ics.uci.edu/dataset/374/appliances+energy+prediction',timeout=20)
        response.raise_for_status()
        print("Source:",response.url)
        print(response.text[:700])
    except requests.RequestException as error:
        print("Online extension unavailable:",type(error).__name__,str(error)[:160])
else:
    print("Online extension skipped; embedded core data unchanged")
Online extension skipped; embedded core data unchanged

Sources, snapshots and next steps

  • UCI energy — CC BY 4.0; credit UCI and original dataset authors; retrieved 2026-10-09. SHA-256 2fccf354445d886e7917620b0195db1f3e3e34d5a067a93b844694a4c561255a. Extract energydata_complete.csv from original download; preserve all rows and declared units; no imputation. Candanedo, L. (2017). Appliances Energy Prediction. UCI Machine Learning Repository. DOI: 10.24432/C5VC8G.

Next steps. Transfer these methods to your own public or authorized data while retaining input checks, recorded parameters and result validation. Document the new experimental design and method limits; this example does not validate a new experiment. Full data licenses and generation instructions accompany the cookbook.