Unlike in the traditional statistical modeling for which a user typically hand-specify a prior, Neural Processes (NPs) implicitly define a broad class of stochastic processes with neural networks. Given a data stream, NP learns a stochastic process that best describes the data. While this ``data-driven'' way of learning stochastic processes has proven to handle various types of data, NPs still relies on an assumption that uncertainty in stochastic processes is modeled by a single latent variable, which potentially limits the flexibility. To this end, we propose the Bootstrapping Neural Process (BNP), a novel extension of the NP family using the bootstrap. The bootstrap is a classical data-driven technique for estimating uncertainty, which allows BNP to learn the stochasticity in NPs without assuming a particular form. We demonstrate the efficacy of BNP on various types of data and its robustness in the presence of model-data mismatch.

Weaknesses: Given the paper's current state, I have following major comments: - The proposed method's motivation is to tackle the issue of model-data mismatch by modeling the context representation uncertainty. However the notion of the model-data mismatch is loosely defined. It would be more interesting if the paper's formulation would fomulate this problem in a principled way, e.g. the model-data mismatch problem can be framed in a more principled way, e.g. The combined objective of two models with/without bootstraps is somewhat questionable. The computation of residuals would influence a lot to the input hence the convergence of the full model.

This is an important paper on uncertainty quantification. However as the reviewers noted the main concerns are competitiveness with reespect to GPs and also an analysis (perrhaps with intuitions) of when the method underperforms would be useful. Overall, this paper might pave the way for really interesting follow-ups which will build on top of it.

Unlike in the traditional statistical modeling for which a user typically hand-specify a prior, Neural Processes (NPs) implicitly define a broad class of stochastic processes with neural networks. Given a data stream, NP learns a stochastic process that best describes the data. While this data-driven'' way of learning stochastic processes has proven to handle various types of data, NPs still relies on an assumption that uncertainty in stochastic processes is modeled by a single latent variable, which potentially limits the flexibility. To this end, we propose the Bootstrapping Neural Process (BNP), a novel extension of the NP family using the bootstrap. The bootstrap is a classical data-driven technique for estimating uncertainty, which allows BNP to learn the stochasticity in NPs without assuming a particular form.