Sequential Indeterminate Probability Theory for Multivariate Time Series Forecasting

The manuscript proposes a model for multi-variate time series forecasting. However, the manuscript is not well self-contained. For instance, the background and the setup of the forecasting task is not well demonstrated; the theoretical contribution is highly dependent on [1], but I failed to figure out the key contribution of the manuscript upon [1].

The language could be improved.

The authors might want to distinguish the use of \citep{} and \citet{}, and update the references with their latest status, instead of the arXiv version.

LSTM is mentioned in the abstract and the experimental section but not discussed in related works.

Figure 4 is not discussed in the manuscript.

From my humble opinion, the manuscript needs a revision before publishing.

• Writing could benefit from further editing, including
  • sentences that are too short to understand them (especially in the introduction / notation, see below)
  • sentences that are grammatically not completely correct
  • typos
  • etc.
• Technically not sound (and so are the two references (Anonymous, 2023a,b) articles the paper is based on)
  • The described setup is unclear,
    • e.g., what exactly is $**z**$?
    • what is meant with $P(x_k)=1$? The experiments condition on $x_k$?
    • what is meant with the $k$th experiment?
    • what do you mean with "we can infer $Y = y_l, ...$"?
    • with respect to what measure is integrated in (1)?
    • what exactly is $P^Z$, because in (1) Z is integrated out and hence the posterior should not depend on Z
    • etc.
  • There are implicit assumptions made in the paper that are not discussed nor do they seem to be realistic:
    • $P(**z** | x_k)$ can be factorized (implicitly assumed in (2)) / $**z**$ are indepdent. Later $N$ is used for the number of time series, which would imply independence of time series -- and hence no need for an MTS approach
    • Eq. 5 and 6 implicitly assumes strong stationarity (if I understand their notation correctly -- not entirely clear though)
  • if the method does not require training, how do you obtain $\sigma^2$ in (14)?
  • etc.

Originality

The application domain is familiar to the community. Most of the novelty of this work rests on its use of "Indeterminate Probability Theory". Arguably, both of the application papers ought to be merged with the theory proposal, to provide demonstrations of its applicability. Such a work might become too long, and perhaps more appropriate to a journal submission.

Quality, Clarity

The quality of prose and exposition in this submission is poor. Indeterminate Proability Theory is inadequately explained in this submission, forcing the reader to the supplementary material for the concurrent submission. Even there, it is difficult to take at face value such broad claims such as "we only need sample two points (C = 2), even for a 1000-dimensional latent space". The authors attribute poor results on WTH dataset to an explanation in Section 3 without further comment, but I cannot find such an explanation.

Significance

A lack of parameters to optimize or even hyperparameters to tune seems likely to limit the applicability of the approach.

• The paper builds upon another work submitted at the same conference. The core ideas of indeterminate probability theory have not been presented in the paper, making this paper hard to read. The details about the implementation of the prediction function have also been omitted.
• The experimental performance of the proposed method is much worse than the baselines, as such there is a limited utility for this approach.
• Simple baselines such as linear models are missing from the results table.