Real-time Anomaly Detection

System Overview

A real-time anomaly detection system using a temporal convolutional attention model and Stacked Autoencoder with ELBO-based uncertainty quantification.

Real-time Processing

Detect anomalies in streaming data with minimal latency

TCNATT Model

Temporal convolutional network with self-attention

Uncertainty Quantification

Gaussian Process-based uncertainty estimation

Uncertainty Quantification

GP Multivariate Distribution Analysis

Our approach leverages Gaussian Process (GP) modeling to quantify uncertainty in anomaly detection. The visualization shows the GP multivariate distribution across three principal components, with uncertainty levels indicated by color intensity.

Explained Variance Ratios:

  • PC1: 0.235 - Primary variance component
  • PC2: 0.054 - Secondary variance component
  • PC3: 0.026 - Tertiary variance component

ELBO-based Uncertainty Quantification

We employ the Evidence Lower Bound (ELBO) to optimize our variational inference:

ELBO = 𝔼[log p(x|z)] - KL(q(z|x)||p(z))

Where:

  • 𝔼[log p(x|z)] represents the expected log-likelihood
  • KL(q(z|x)||p(z)) is the Kullback-Leibler divergence
  • q(z|x) is the variational distribution
  • p(z) is the prior distribution
GP Multivariate Distribution with Uncertainties 3D Distribution of variance uncertainty estimates for multivariate distribution
Anomaly Detection with Uncertainty

Vibration data generated from a motor where anomaly detection has been made coupled with ELBO-based uncertainty quantification. Every dot represents an anomaly along the time series data and red represents high uncertainty, i.e false alarms.

Gaussian Mixture Model Component Analysis

Gaussian Mixture Model Components

Our uncertainty quantification system uses a 4-component GMM to classify prediction confidence levels:

Traffic Light Zones:

  • Green Zone (x < -0.5):
    • Highest confidence predictions
    • Dominant peak indicating reliable model performance
    • Represents standard operating conditions
  • Yellow Zone (-0.5 ≤ x < 1.0):
    • Moderate uncertainty level
    • Transition region between confident and uncertain predictions
    • Requires increased monitoring
  • Red Zone (x ≥ 1.0):
    • High uncertainty predictions
    • Two distinct components for different types of uncertainty
    • Indicates potential anomalies or edge cases

Model Metrics:

  • ELBO: 4534 (Evidence Lower Bound)
  • BIC: 9068 (Bayesian Information Criterion)
  • AIC: 8998 (Akaike Information Criterion)
  • Entropy: 1308 (Distribution Uncertainty)

GMM components showing uncertainty distribution across traffic light zones

Component Distribution:

  • Component 1: Very low uncertainty (3.7%)
  • Component 2: Low uncertainty (15.8%)
  • Component 3: Medium uncertainty (57.2%)
  • Component 4: High uncertainty (23.4%)

Run Inference on Your Data

or drag and drop files here

Requirements:

  • CSV format only
  • Time series data in columns
  • Maximum file size: 100MB