Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Overpredictive Signal Analytics in Federated Learning: Algorithms and Analysis

Vijay Anavangot

TL;DR

This work addresses privacy and communication constraints in federated learning by introducing overpredictive signal analytics that compute envelope approximations $\widehat{f}_{i,\mathrm{env}}(t)$ at edge devices using a convex optimization framework based on a Fourier-basis representation. The server aggregates these envelopes to produce analytics such as the aggregate signal $\widehat{s}(t)$ and the empirical CDF $\widehat{F}_N(x)$ via Glivenko–Cantelli theory, without accessing raw data. The authors derive bounds on the envelope approximation error and the resulting CDF estimation error, revealing tradeoffs between the bandwidth parameter $L$ and accuracy, including order-optimality results for ${\cal L}_1$ and ${\cal L}_2$ envelopes and subsampling effects. Experiments on a publicly available residential energy dataset validate the theoretical bounds and demonstrate practical applicability for energy-demand analytics in smart-city contexts.

Abstract

Edge signal processing facilitates distributed learning and inference in the client-server model proposed in federated learning. In traditional machine learning, clients (IoT devices) that acquire raw signal samples can aid a data center (server) learn a global signal model by pooling these distributed samples at a third-party location. Despite the promising capabilities of IoTs, these distributed deployments often face the challenge of sensitive private data and communication rate constraints. This necessitates a learning approach that communicates a processed approximation of the distributed samples instead of the raw signals. Such a decentralized learning approach using signal approximations will be termed distributed signal analytics in this work. Overpredictive signal approximations may be desired for distributed signal analytics, especially in network demand (capacity) planning applications motivated by federated learning. In this work, we propose algorithms that compute an overpredictive signal approximation at the client devices using an efficient convex optimization framework. Tradeoffs between communication cost, sampling rate, and the signal approximation error are quantified using mathematical analysis. We also show the performance of the proposed distributed algorithms on a publicly available residential energy consumption dataset.

Overpredictive Signal Analytics in Federated Learning: Algorithms and Analysis

TL;DR

This work addresses privacy and communication constraints in federated learning by introducing overpredictive signal analytics that compute envelope approximations at edge devices using a convex optimization framework based on a Fourier-basis representation. The server aggregates these envelopes to produce analytics such as the aggregate signal and the empirical CDF via Glivenko–Cantelli theory, without accessing raw data. The authors derive bounds on the envelope approximation error and the resulting CDF estimation error, revealing tradeoffs between the bandwidth parameter and accuracy, including order-optimality results for and envelopes and subsampling effects. Experiments on a publicly available residential energy dataset validate the theoretical bounds and demonstrate practical applicability for energy-demand analytics in smart-city contexts.

Abstract

Edge signal processing facilitates distributed learning and inference in the client-server model proposed in federated learning. In traditional machine learning, clients (IoT devices) that acquire raw signal samples can aid a data center (server) learn a global signal model by pooling these distributed samples at a third-party location. Despite the promising capabilities of IoTs, these distributed deployments often face the challenge of sensitive private data and communication rate constraints. This necessitates a learning approach that communicates a processed approximation of the distributed samples instead of the raw signals. Such a decentralized learning approach using signal approximations will be termed distributed signal analytics in this work. Overpredictive signal approximations may be desired for distributed signal analytics, especially in network demand (capacity) planning applications motivated by federated learning. In this work, we propose algorithms that compute an overpredictive signal approximation at the client devices using an efficient convex optimization framework. Tradeoffs between communication cost, sampling rate, and the signal approximation error are quantified using mathematical analysis. We also show the performance of the proposed distributed algorithms on a publicly available residential energy consumption dataset.
Paper Structure (20 sections, 3 theorems, 40 equations, 2 figures, 1 table, 1 algorithm)

This paper contains 20 sections, 3 theorems, 40 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Prior Literature
  3. Distributed Signal Model and Background Concepts
  4. Federated Learning Signal Model
  5. Signal Representation
  6. Problem Formulation and Related Definitions
  7. Choice of the distance metric
  8. Algorithms for Overpredictive Signal Analytics
  9. Algorithms at the Clients
  10. Aggregation at the server
  11. Federated learning algorithm for over-predictive signal analytics
  12. Performance Bounds on Optimal Envelope Approximation
  13. A Naïve Envelope Approximation Scheme
  14. Envelope Approximation Analysis
  15. CDF of the Envelope Signal Approximation
  16. ...and 5 more sections

Key Result

Theorem 1

The approximation errors of the optimal envelope signal and the naïve envelope signal, viz.$\hbox{SA}_q$ and $\hbox{SA}'_q$ respectively for $q \in \{1,2\}$, are shown to be order optimal for a specific class of $p$-times differentiable signals as stated below.

Figures (2)

  • Figure 1: The figure illustrates federated learning for overpredictive signal analytics in a smart city with $D$ electricity consumers. The power consumption time-series recorded at the consumer's smart meters are converted to compressed signal representations, $\{\vec{\mathbf{v}}_1,\vec{\mathbf{v}}_2,\ldots,\vec{\mathbf{v}}_D\}$ using edge signal processing. These signal representations are communicated to the central server for computing signal analytics that overpredict the actual demand time-series.
  • Figure 2: The system overview of a federated learning model adapted from Anavangot:2020. In this model, the $D$ participating client devices communicate an approximation of the observed signal, and the central server aggregates these signal approximations to learn global signal statistics such as histogram, signal peak, and device clusters.

Theorems & Definitions (5)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • proof
  • proof