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arxiv: 2604.27814 · v2 · submitted 2026-04-30 · 💻 cs.LG

Recognition: unknown

Probabilistic Circuits for Irregular Multivariate Time Series Forecasting

Christian Kl\"otergens , Vijaya Krishna Yalavarthi , Lars Schmidt-Thieme
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Pith reviewed 2026-05-08 02:56 UTC · model grok-4.3

classification 💻 cs.LG
keywords probabilistic circuitsirregular multivariate time seriesforecastingjoint distributionsdensity estimationuncertainty quantificationmachine learning
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The pith

CircuITS adapts probabilistic circuits to forecast irregular multivariate time series while guaranteeing valid joint distributions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Irregular multivariate time series arrive at uneven intervals across multiple channels, making it hard to produce forecasts that quantify uncertainty without contradictions. Standard models often sacrifice either flexibility in modeling channel dependencies or the guarantee that all derived probabilities remain consistent. The paper introduces CircuITS, which restructures probabilistic circuits to accept irregular observation times. This yields a model that represents complex inter-channel relationships exactly while preserving tractable marginalization. On four real-world datasets the resulting forecasts improve both joint and marginal density estimates over existing methods.

Core claim

We propose CircuITS, a probabilistic-circuit architecture for irregular multivariate time series forecasting. The model is flexible in capturing intricate dependencies between time series channels while structurally guaranteeing valid joint distributions. Experiments on four real-world datasets demonstrate that CircuITS achieves superior joint and marginal density estimation compared to state-of-the-art baselines.

What carries the argument

Probabilistic circuits restructured to accept irregular sampling times, which encode the joint distribution so that any marginal can be obtained by exact summation without approximation.

If this is right

  • Forecasts include reliable uncertainty estimates because every marginal and joint remains a valid probability distribution.
  • Exact marginalization removes the need for post-hoc fixes or sampling approximations when querying single channels.
  • The same circuit structure can be queried for any subset of channels or time points without retraining.
  • Performance gains appear in both joint density and per-channel marginal accuracy on real data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same adaptation pattern may apply to other irregularly sampled data such as event streams or medical records.
  • Because marginals are exact, the model could serve as a drop-in component for downstream tasks like anomaly detection.
  • Hybrid extensions that replace some circuit nodes with neural networks might increase expressivity while retaining the validity guarantee.

Load-bearing premise

Probabilistic circuits can be adapted to irregular observation times while keeping both their expressivity for channel dependencies and their exact marginalization property intact.

What would settle it

A dataset of irregular multivariate series where CircuITS produces lower joint log-likelihood than a strong baseline or yields marginal probabilities that contradict the joint.

Figures

Figures reproduced from arXiv: 2604.27814 by Christian Kl\"otergens, Lars Schmidt-Thieme, Vijaya Krishna Yalavarthi.

Figure 1
Figure 1. Figure 1: Demonstrating MOSES inability to learn a multivariate bifurcation with 4 independent channels. MOSES-K, refers to MOSES with K-many mixture components. The plots of CircuITS are created by using 2 circuit components. allows it to capture intricate correlations and independent factors alike, while strictly guaranteeing marginalization consistency. As a result, CircuITS trivially resolves the independent bif… view at source ↗
Figure 2
Figure 2. Figure 2: Demonstration of Probabilistic circuit over three vari￾ables. 2.) Marginalization Consistency. A valid stochas￾tic process must satisfy the Kolmogorov extension the￾orem (Øksendal, 2003). This implies that the predicted marginal distribution of a query subset must match the inte￾grated joint distribution. Let yS denote a subset of variables that is dropped from y. Then the model fulfills Marginal￾ization C… view at source ↗
Figure 3
Figure 3. Figure 3: Detailed architecture of the CircuITS Encoder with tensor dimensions. The global context H˜ (dim C × D) branches to generate leaf contexts (dim D) and circuit weights. C. Sampling with CircuITS’ Sum Product Network Let zc ∈ {1, . . . , K} denote the index of the active sum node (latent component) for channel c. The sampling proceeds as follows: Root Initialization (c = C): We begin by sampling the final la… view at source ↗
Figure 4
Figure 4. Figure 4: Comparing samples from ProFITi and CircuITS for the four channel bifurcation task. 15 view at source ↗
Figure 5
Figure 5. Figure 5: Sensitivity Analysis on the 36-12 task for the number of circuit components K. J. Memory Consumption and Epoch Times We conduct an experiment to compare CircuITS’ memory consumption during training and epoch times with those of ProFITi and MOSES. To do this, we use toy datasets based on Brownian motion, in which we can vary the number of channels C and the number of time steps N. The models are tasked with… view at source ↗
Figure 6
Figure 6. Figure 6: Comparing memory consumption and epoch times during training on Toy datasets. For MOSES, we set the number of mixture components to 3, the hidden dimension to 128, and the number of attention heads to 4. ProFITi is applied using 7 flow layers and a latent dimension of 64. For CircuITS, we set the number of components K 20 view at source ↗
Figure 7
Figure 7. Figure 7: Query distribution for MIMIC-III 12–36 21 view at source ↗
read the original abstract

Joint probabilistic modeling is essential for forecasting irregular multivariate time series (IMTS) to accurately quantify uncertainty. Existing approaches often struggle to balance model expressivity with consistent marginalization, frequently leading to unreliable or contradictory forecasts. To address this, we propose CircuITS, a novel architecture for probabilistic IMTS forecasting based on probabilistic circuits. Our model is flexible in capturing intricate dependencies between time series channels while structurally guaranteeing valid joint distributions. Experiments on four real world datasets demonstrate that CircuITS achieves superior joint and marginal density estimation compared to state of the art baselines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes CircuITS, a probabilistic circuit architecture for joint probabilistic modeling and forecasting of irregular multivariate time series (IMTS). It claims flexibility in capturing intricate inter-channel dependencies while structurally guaranteeing valid joint distributions via the circuit properties, and reports superior joint and marginal density estimation performance against baselines on four real-world datasets.

Significance. If the adaptation to irregular sampling preserves the exact marginalization and validity guarantees of probabilistic circuits without post-hoc approximations, the work would offer a principled advance for uncertainty-aware IMTS forecasting. Probabilistic circuits' tractable exact inference is a notable strength here, as many neural density estimators sacrifice these properties; successful preservation could enable reliable joint forecasting in domains with asynchronous observations.

major comments (2)
  1. [Methods (circuit construction for irregularity)] The central claim of 'structurally guaranteeing valid joint distributions' for irregular data is load-bearing but insufficiently supported. The abstract and methods must explicitly show how variable observation counts and non-aligned timestamps are encoded (e.g., via time embeddings, dynamic node insertion, or masking) while preserving smoothness and decomposability of the DAG; without a formal argument or proof that exact marginalization holds by construction rather than empirically, the guarantee reduces to an unverified assertion.
  2. [Experiments section] Experiments report superior joint and marginal density estimation but supply no error bars, statistical significance tests, or ablation studies on the irregularity-handling components. Table or figure results (e.g., log-likelihood comparisons) should include variance across runs and controls that isolate whether performance gains stem from the structural guarantees or from increased model capacity.
minor comments (2)
  1. [Preliminaries] Notation for irregular time series (e.g., how timestamps and missing observations are represented as inputs to the circuit) should be introduced with a clear diagram or formal definition early in the paper.
  2. [Abstract and Experiments] The abstract mentions 'four real world datasets' but does not name them or provide summary statistics (e.g., average irregularity level); this information belongs in the experimental setup for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on our work. We have prepared point-by-point responses to the major comments and will make the necessary revisions to the manuscript.

read point-by-point responses

  1. Referee: [Methods (circuit construction for irregularity)] The central claim of 'structurally guaranteeing valid joint distributions' for irregular data is load-bearing but insufficiently supported. The abstract and methods must explicitly show how variable observation counts and non-aligned timestamps are encoded (e.g., via time embeddings, dynamic node insertion, or masking) while preserving smoothness and decomposability of the DAG; without a formal argument or proof that exact marginalization holds by construction rather than empirically, the guarantee reduces to an unverified assertion.

    Authors: We agree that the current presentation could be strengthened with more explicit details and a formal argument. In the revised manuscript, we will update the abstract and Methods section to clearly describe the encoding of irregular observations using time embeddings for timestamps and dynamic node insertion with masking to handle variable counts. We will also provide a formal proof sketch demonstrating that these modifications preserve the smoothness and decomposability of the DAG, ensuring the exact marginalization property holds by construction as a direct consequence of the probabilistic circuit framework. revision: yes

  2. Referee: [Experiments section] Experiments report superior joint and marginal density estimation but supply no error bars, statistical significance tests, or ablation studies on the irregularity-handling components. Table or figure results (e.g., log-likelihood comparisons) should include variance across runs and controls that isolate whether performance gains stem from the structural guarantees or from increased model capacity.

    Authors: We acknowledge these omissions in the experimental reporting. We will revise the Experiments section to include error bars (mean ± standard deviation) computed over multiple runs with different random seeds for all reported metrics. Statistical significance tests will be added to compare results against baselines. We will also incorporate ablation studies on the key irregularity-handling components and include comparisons with capacity-matched models to isolate the contribution of the structural guarantees. revision: yes

Circularity Check

0 steps flagged

No significant circularity; structural guarantees tied to circuit construction rather than fitted quantities.

full rationale

The abstract and context present the core claim as a direct consequence of adapting probabilistic circuits (known for exact marginalization and valid joints under decomposability) to IMTS via unspecified architectural modifications. No equations, self-citations, or fitted parameters are quoted that reduce the 'structurally guaranteeing' property to a post-hoc fit or self-definition. The reader's pre-assigned score of 2.0 is consistent with this assessment; the derivation chain remains self-contained and externally benchmarkable against standard PC properties without internal reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities. The central claim rests on the unstated assumption that probabilistic-circuit marginalization properties transfer to irregular time series without additional constraints.

pith-pipeline@v0.9.0 · 5385 in / 1075 out tokens · 50301 ms · 2026-05-08T02:56:35.876451+00:00 · methodology

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Works this paper leans on

2 extracted references · 2 canonical work pages

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    Proceedings of the IEEE 77, 257–286

    doi: 10.1109/5.18626. S¨arkk¨a, S. and Garc ´ıa-Fern´andez, ´A. F. Temporal Paral- lelization of Bayesian Smoothers.IEEE Transactions on Automatic Control, 66(1):299–306, January 2021. ISSN 1558-2523. doi: 10.1109/TAC.2020.2976316. Schirmer, M., Eltayeb, M., Lessmann, S., and Rudolph, M. Modeling Irregular Time Series with Continuous Recur- rent Units. In...

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    Yalavarthi, V

    doi: 10.1109/BigData59044.2023.10386325. Yalavarthi, V . K., Madhusudhanan, K., Scholz, R., Ahmed, N., Burchert, J., Jawed, S., Born, S., and Schmidt-Thieme, L. GraFITi: Graphs for Forecasting Irregularly Sampled Time Series.Proceedings of the AAAI Conference on Artificial Intelligence, 38(15):16255–16263, March 2024. ISSN 2374-3468. doi: 10.1609/aaai.v38...

    work page doi:10.1109/bigdata59044.2023.10386325 2023