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Conformal Distributed Remote Inference in Sensor Networks Under Reliability and Communication Constraints

Meiyi Zhu, Matteo Zecchin, Sangwoo Park, Caili Guo, Chunyan Feng, Petar Popovski, Osvaldo Simeone

TL;DR

This work tackles reliable, multi-label inference in distributed sensor networks under strict communication constraints. It extends distributed conformal risk control (D-CRC) to a constrained setting by introducing CD-CRC, which jointly optimizes local thresholds, global thresholds, and sensor combining weights via online optimization, incorporating a capacity-aware allocation and a CRC-based global update to enforce a target false negative rate (FNR). Theoretical results establish deterministic long-term guarantees on FNR and communication overhead, together with a bound on the long-term FPR, showing sublinear regret relative to the best sensor in hindsight. Empirical evaluation on a binary segmentation task demonstrates that CD-CRC can closely match the performance of unconstrained methods while satisfying capacity constraints, by adaptively concentrating communication on the most informative sensors. The framework provides a principled, assumption-free approach to robust distributed decision-making in IoT and sensor networks with limited bandwidth, with potential extensions to online model updates and privacy-preserving variants.

Abstract

This paper presents communication-constrained distributed conformal risk control (CD-CRC) framework, a novel decision-making framework for sensor networks under communication constraints. Targeting multi-label classification problems, such as segmentation, CD-CRC dynamically adjusts local and global thresholds used to identify significant labels with the goal of ensuring a target false negative rate (FNR), while adhering to communication capacity limits. CD-CRC builds on online exponentiated gradient descent to estimate the relative quality of the observations of different sensors, and on online conformal risk control (CRC) as a mechanism to control local and global thresholds. CD-CRC is proved to offer deterministic worst-case performance guarantees in terms of FNR and communication overhead, while the regret performance in terms of false positive rate (FPR) is characterized as a function of the key hyperparameters. Simulation results highlight the effectiveness of CD-CRC, particularly in communication resource-constrained environments, making it a valuable tool for enhancing the performance and reliability of distributed sensor networks.

Conformal Distributed Remote Inference in Sensor Networks Under Reliability and Communication Constraints

TL;DR

This work tackles reliable, multi-label inference in distributed sensor networks under strict communication constraints. It extends distributed conformal risk control (D-CRC) to a constrained setting by introducing CD-CRC, which jointly optimizes local thresholds, global thresholds, and sensor combining weights via online optimization, incorporating a capacity-aware allocation and a CRC-based global update to enforce a target false negative rate (FNR). Theoretical results establish deterministic long-term guarantees on FNR and communication overhead, together with a bound on the long-term FPR, showing sublinear regret relative to the best sensor in hindsight. Empirical evaluation on a binary segmentation task demonstrates that CD-CRC can closely match the performance of unconstrained methods while satisfying capacity constraints, by adaptively concentrating communication on the most informative sensors. The framework provides a principled, assumption-free approach to robust distributed decision-making in IoT and sensor networks with limited bandwidth, with potential extensions to online model updates and privacy-preserving variants.

Abstract

This paper presents communication-constrained distributed conformal risk control (CD-CRC) framework, a novel decision-making framework for sensor networks under communication constraints. Targeting multi-label classification problems, such as segmentation, CD-CRC dynamically adjusts local and global thresholds used to identify significant labels with the goal of ensuring a target false negative rate (FNR), while adhering to communication capacity limits. CD-CRC builds on online exponentiated gradient descent to estimate the relative quality of the observations of different sensors, and on online conformal risk control (CRC) as a mechanism to control local and global thresholds. CD-CRC is proved to offer deterministic worst-case performance guarantees in terms of FNR and communication overhead, while the regret performance in terms of false positive rate (FPR) is characterized as a function of the key hyperparameters. Simulation results highlight the effectiveness of CD-CRC, particularly in communication resource-constrained environments, making it a valuable tool for enhancing the performance and reliability of distributed sensor networks.
Paper Structure (35 sections, 6 theorems, 49 equations, 8 figures, 2 algorithms)

This paper contains 35 sections, 6 theorems, 49 equations, 8 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Distributed Remote Inference
  3. Distributed Conformal Risk Control
  4. Related Work
  5. Contributions and Organization
  6. System Model and Problem Definition
  7. Setting
  8. Design Problem
  9. False negative rate and false positive rate
  10. Communication constraint
  11. Design problem
  12. Online optimization
  13. Distributed Conformal Risk Control
  14. Local Threshold Update
  15. Combining Weights Update
  16. ...and 20 more sections

Key Result

Theorem 1

For any $T\geq 1$, given an FNR target $\alpha\in[0,1]$, the time-averaged global FNR achieved by D-CRC is upper bounded by where $\lambda^1$ is the initial local threshold and $\rho$ is the learning rate in eq_loc_thre_up_DCRC. Furthermore, the time-averaged global FPR achieved by D-CRC is upper bounded by where $\mathcal{P}^*$ is the long-term local FPR of the best sensor in hindsight, i.e., t

Figures (8)

  • Figure 1: Illustration of the system model and design problem: Each sensor generates a local prediction for a general multi-label problem, e.g., segmentation, based on a partial and noisy observation of the underlying input. The local predictions are transmitted through a shared channel to a central server, which combines them to obtain a global prediction. After the decision is made, feedback on the correct decision makes it possible to compute FNR and FPR at the central server. The system is optimized online to minimize long-term FPR, while meeting long-term constraints on FNR and channel capacity.
  • Figure 2: Illustration of the overall workflow of the studied distributed multi-label classification system.
  • Figure 3: Time-averaged FNR (left), time-averaged communication load (center), and time-averaged FPR (right) for CD-CRC, U-CD-CRC and D-CRC gasparin2024conformal over time $t$ with FNR constraint $\alpha=0.15$ and capacity constraint $C=1$.
  • Figure 4: Evolution of the weights (top-left corner), global thresholds (top-right corner), local thresholds for the optimal sensor (bottom-left corner), local thresholds for other non-optimal sensors (bottom-right corner) for CD-CRC, U-CD-CRC and D-CRC gasparin2024conformal over time $t$ with FNR constraint $\alpha=0.15$ and capacity constraint $C=1$.
  • Figure 5: Time-averaged FNR (left), time-averaged communication load (middle), and time-averaged FPR (right) for CD-CRC, U-CD-CRC, and D-CRC gasparin2024conformal versus the FNR constraint $\alpha$ with capacity constraint $C = 1.5$.
  • ...and 3 more figures

Theorems & Definitions (6)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Lemma 1
  • Theorem 4
  • Lemma 2