# Neural Processes

Standard neural processes treat inputs as noise-free observations, so sensor measurement error degrades both predictions and uncertainty estimates. DnNP makes the clean input a latent variable inside the neural-process framework and trains a denoiser jointly with meta-learning through variational inference, predicting directly from noisy inputs. On PM2.5 spatial interpolation from 34 air-quality sensors in Brookline, Massachusetts, DnNP reduces RMSE by up to 30% and NLL by up to 73% relative to standard neural processes.

Standard neural processes treat inputs as noise-free observations, so sensor measurement error degrades both predictions and uncertainty estimates. DnNP makes the clean input a latent variable inside the neural-process framework and trains a denoiser jointly with meta-learning through variational inference, predicting directly from noisy inputs. On PM2.5 spatial interpolation from 34 air-quality sensors in Brookline, Massachusetts, DnNP reduces RMSE by up to 30% and NLL by up to 73% relative to standard neural processes.

Counterfactual prediction can skip causal-graph estimation: CFGNP maps observational samples directly to a counterfactual distribution, achieves stronger predictive performance than existing approaches across synthetic and image-based benchmarks, and a model trained only on 10-node graphs transfers to graphs up to 30 nodes without retraining.

Counterfactual prediction can skip causal-graph estimation: CFGNP maps observational samples directly to a counterfactual distribution, achieves stronger predictive performance than existing approaches across synthetic and image-based benchmarks, and a model trained only on 10-node graphs transfers to graphs up to 30 nodes without retraining.