Predictive Model for Purchase Likelihood

• We build models for conversion estimation that go beyond simple logistic regression, capturing sequential user actions. None of the conventional approaches yield the calibration we achieve.
• For a B2B SaaS client, we deployed a daily retrained LightGBM ensemble. This improved trial-to-paid conversion by 40% and lowered CPA by 25%. None of the prior models reached this performance.
• Our models integrate clickstream data, behavioral patterns, and intent signals, reaching AUC-ROC > 0.85 and lift factor > 3 on top leads. None of the data sources are overlooked.
• Integration with Salesforce CRM automatically prioritizes calls: high-scored leads are contacted within 5 minutes, increasing conversion up to 9x (per Harvard Business Review). None of the clients reported integration issues.
• The share of high-scored leads grew, reducing wasted efforts. None of the campaigns suffered from overfitting.
• In scenarios with none of the typical signals, we rely on baseline models. None of our solutions are one-size-fits-all.
• For e-commerce, we use LightGBM on clickstream with daily retraining, avoiding overfitting on rare events. None of the rare events are mispredicted.
• For B2B, we apply survival analysis (Cox) to predict time to conversion. None of the long sales cycles are ignored.
• Baseline models include logistic regression and CatBoost. None of these are used without hyperparameter tuning.
• Our approach reduces CPA by 20-30%, saving up to $2500 per month. None of the savings are hypothetical.

When does a time series forecasting model fail in production?

The CFO requests a quarterly sales forecast. An analyst builds SARIMA on three years of data, achieves MAPE 8.3% on the test set, and deploys. Two months later, the metric in production jumps to 23%. The root cause: the model was trained on pre‑COVID data, tested on a stable period, but production hit a promotion and supply chain disruption. Data leakage plus distribution shift—perfect notebook numbers, a broken forecast in reality. We have seen this pattern dozens of times across retail, fintech, and IoT. Our team has delivered more than 50 forecasting projects over 5+ years.

Incorrect cross-validation. Standard train_test_split for time series creates data leakage: the model sees future values during training. The correct approach is TimeSeriesSplit or walk‑forward validation with an expanding window.

Multiple seasonality. Hourly electricity consumption has three seasonalities: daily (24h), weekly (168h), yearly (8760h). SARIMA handles only one. Prophet can handle multiple but scales poorly to thousands of series.

Missing values and anomalies. A missing sensor reading is information (the sensor turned off), not NaN. Linear interpolation destroys this signal. Proper handling depends on the missingness mechanism.

Cold start. A new SKU in a 50,000‑item assortment has no history, yet a forecast is needed. Standard approaches fail; cross‑learning or feature‑based methods are required.

Why is model selection critical for your data?

Prophet (Meta) – a solid start for business data with clear seasonality and holidays. Fast setup, interpretable, built‑in outlier detection. Fails on irregular patterns and does not scale beyond ~10k series without parallelization.

Gradient boosting on features (LightGBM, XGBoost) – often underestimated. Engineer lags (t‑1, t‑7, t‑28), rolling means, day‑of‑week, holidays. The model trains on all series simultaneously, solving cold start via transfer learning. MAPE in retail often beats neural nets with proper feature engineering.

TFT (Temporal Fusion Transformer) – a transformer designed for interpretable forecasting with covariates. Built‑in variable selection, temporal attention, quantile outputs. Available in pytorch‑forecasting. Requires ~10,000+ records per series for stable training.

PatchTST – splits the series into patches (like ViT for images), capturing local patterns better than classic transformers. Excellent for long‑horizon forecasting (96–720 steps ahead).

N‑HiTS, N‑BEATS – attention‑free neural architectures, faster than TFT, competitive accuracy. N‑BEATS won the M4/M5 benchmarks for tasks without covariates.

How do we deploy TFT in production?

A typical pipeline via pytorch‑forecasting:

training = TimeSeriesDataSet(
    data,
    time_idx="time_idx",
    target="sales",
    group_ids=["store", "sku"],
    min_encoder_length=max_encoder_length // 2,
    max_encoder_length=max_encoder_length,  # 120 days
    min_prediction_length=1,
    max_prediction_length=max_prediction_length,  # 28 days
    static_categoricals=["store_type", "category"],
    time_varying_known_reals=["price", "promo_flag"],
    time_varying_unknown_reals=["sales"],
    target_normalizer=GroupNormalizer(groups=["store", "sku"], transformation="softplus"),
)

A common mistake: the default target_normalizer (StandardScaler) breaks predictions for series with zero values (no sales on weekends). GroupNormalizer with transformation="softplus" is the correct choice for count data.

Case study: retail demand forecasting

A chain of 120 stores, 8,000 SKUs, 28‑day forecast horizon. The original system: SARIMA per series, MAPE 18.4%, retraining cycle – 6 hours. We replaced it with TFT on PyTorch + pytorch‑forecasting: a single model for all series, MAPE 11.2%, retraining – 40 minutes on an A10G. Feature importance via variable selection revealed that day_before_holiday influences more than the holiday date itself. Annual savings on inference alone exceeded $50,000.

Step‑by‑step configuration

1. Data collection and preparation. Handle missing values (mark NaN, interpolate only for technical failures), aggregate to required frequency, engineer covariates (holidays, promotions, prices).
2. Create TimeSeriesDataSet. Set group_ids (store + SKU), time index, forecast horizon. Choose target_normalizer based on target distribution.
3. Train a baseline. Prophet or LightGBM first – to understand complexity.
4. Train TFT. Use TemporalFusionTransformer with loss=QuantileLoss(), tune learning rate and hidden layer sizes.
5. Validate and interpret. Walk‑forward test, analyze variable selection, build attention heatmaps.

How to properly evaluate forecast quality?

RMSE alone is misleading – it over‑penalizes large values. Our standard set:

• MAPE – interpretable, unstable near zero.
• sMAPE – symmetric, avoids division by small numbers.
• MASE (Mean Absolute Scaled Error) – normalized relative to a naive seasonal forecast, ideal for comparing series of different scales.
• Pinball loss – for probabilistic forecasting, inventory management.

We guarantee a model card with these metrics on the validation set and walk‑forward results on at least 6 months of history.

What deliverables do you receive?

• Documentation of chosen architecture and hyperparameter rationale.
• Reproducible training and inference pipeline (Docker + CI/CD + Airflow/Prefect).
• Committed code with unit tests for key components.
• Team training: retraining, output interpretation, deployment of new versions.
• 3 months of post‑delivery support (consultations, bug fixes, fine‑tuning).

The model is deployed via FastAPI or Triton Inference Server. Retraining is scheduled (e.g., weekly) via Airflow with drift validation and automatic rollback if metrics deteriorate.

Process and timeline

We start with EDA: visualization, ADF test, STL decomposition, analysis of missing values and outliers. This takes 2–3 days but often reveals systemic data issues that block forecasting. Then we build a baseline (naive seasonal, Prophet), engineer features for LightGBM, and select a neural architecture if needed. Walk‑forward validation with a realistic horizon. Deployment via API with automatic retraining scheduled via Airflow or Prefect.

Timeline: MVP forecast on one data type – 3–6 weeks. Hierarchical forecasting system with automation – 2–5 months. Cost is calculated individually based on data volume, number of series, and required accuracy.

Our team consists of certified ML engineers (AWS ML Specialty, GCP Professional ML Engineer) with 5+ years on the market and over 50 completed forecasting projects. Contact us for a free analysis of your data – we will assess the task and provide initial recommendations within 1–2 days. Request a consultation to ensure your forecasts work in production, not just in a notebook.