prediction interval of noise is not correct on T5 model

[nai-kon]

When predicting gaussian noise with the chronos_t5_base model, the 80% prediction interval is very narrower.
(also t5-large and t5-small was the same result)

I also tried the chronos_bolt_base model and it has 80% interval as wide as the noise as I expected.

The paper says the 80% interval of chronos_t5_base is as wide as the gaussian noise like below.

Why doesn't the chronos_t5 model output confidence intervals like in the paper?
How can I get correct 80% confidence intervals?
Here is my code. The version of chronos is chronos-forecasting 1.5.0.

import matplotlib as matplotlib
import matplotlib.pyplot as plt
import numpy as np
import torch
from chronos import BaseChronosPipeline

pipeline = BaseChronosPipeline.from_pretrained(
    # "amazon/chronos-bolt-base",
    "amazon/chronos-t5-base",
    device_map="cpu",
    cache_dir="./"
)

# generate gaussian noise
data = np.random.standard_normal(256+64)
train_data, test_data = data[:256], data[256:]

# predict
pred, _ = pipeline.predict_quantiles(
    context=torch.tensor(train_data), 
    quantile_levels=[0.1, 0.5, 0.9],
    prediction_length=len(test_data),
)
low, med, high = pred[0, :, 0], pred[0, :, 1], pred[0, :, 2]

# draw graph
plt.figure(figsize=(10, 5))
plt.plot(data, label="ground truth")
plt.plot(list(range(256, 256+64)), med, linestyle="--", label="median forecast")
plt.fill_between(list(range(256, 256+64)), low, high, color="tomato", alpha=0.2, label="80% prediction interval")

plt.grid()
plt.legend()
plt.savefig(f"gaussian_noise_test.png")

[lostella]

@nai-kon the figure was generated with larger values for top_k and num_sample in the call to predict (now predict_quantiles in your code). Adding

num_samples=100,
top_k=4096,  # this could even be smaller, I think

will make the distribution width wider as expected.

[nai-kon]

It worked fine. Thank you for your answer!