# Update a Streaming GAM Incrementally

[StreamingGAM](../reference/StreamingGAM.md#whittaker.StreamingGAM) is designed for data that arrives in chunks, like sensor feeds, log streams, or any dataset too large to hold in memory at once. Each call to [partial_fit()](../reference/StreamingGAM.md#whittaker.StreamingGAM.partial_fit) accumulates sufficient statistics from one batch, and [solve()](../reference/StreamingGAM.md#whittaker.StreamingGAM.solve) computes the current best-fit model without revisiting earlier batches.


# Fit

Create the model once, then loop over incoming batches. Calling [solve()](../reference/StreamingGAM.md#whittaker.StreamingGAM.solve) after each [partial_fit()](../reference/StreamingGAM.md#whittaker.StreamingGAM.partial_fit) is optional but lets you inspect the model's state as data accumulates.


``` python
import numpy as np
import whittaker as wk

rng = np.random.default_rng(23)
n_per_batch = 200

# Initialize streaming model
model = wk.StreamingGAM("y ~ s(x, k=10)")

# Feed batches and solve incrementally
for i in range(5):
    x = rng.uniform(0, 2 * np.pi, n_per_batch)
    y = np.sin(x) + rng.normal(0, 0.3, n_per_batch)
    model.partial_fit({"x": x, "y": y})
    model.solve()
    print(f"Batch {i+1}: n_obs={model.n_obs}, edf={model.edf_total:.2f}")
```


    Batch 1: n_obs=200, edf=8.30
    Batch 2: n_obs=400, edf=8.92
    Batch 3: n_obs=600, edf=9.22
    Batch 4: n_obs=800, edf=9.38
    Batch 5: n_obs=1000, edf=9.48


# Summarize

After all batches have been processed, inspect the final model. The summary reflects the full accumulated dataset.


``` python
model.summary()
```


    'StreamingGAM summary\n============================================================\nFormula:     y ~ s(x, k=10)\nFamily:      Gaussian\nDecay:       1.0\nN obs:       1000\nN batches:   5\nEDF total:   9.5\nScale:       0.3639\nDeviance:    360.5\n\nSmooth terms:\n  s(x, k=10): edf=8.5\n\nSnapshots:   5'


# Predict

With the model solved, generate predictions on new inputs just as you would with a standard GAM.


``` python
new_data = {"x": np.linspace(0, 2 * np.pi, 100)}
preds = model.predict(new_data)
preds.values[:5]
```


    array([-0.12063   , -0.04200138,  0.03661861,  0.11504262,  0.19281312])


# Interpret

Incremental fitting is useful when data arrives in a stream or is too large to hold in memory. Because [StreamingGAM](../reference/StreamingGAM.md#whittaker.StreamingGAM) accumulates sufficient statistics rather than raw observations, memory usage stays constant regardless of how many batches have been processed. Setting `decay < 1.0` applies exponential downweighting to older batches, making the model responsive to distributional shifts over time.