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Related Concept Videos

State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
State Space to Transfer Function01:21

State Space to Transfer Function

The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
Variance01:15

Variance

The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.The standard deviation measures the spread in the same units as the data.
Vectors in Space: Problem Solving01:26

Vectors in Space: Problem Solving

A chandelier suspended by multiple cables can be analyzed using principles of three-dimensional static equilibrium. In this setup, a chandelier weighing 1000 N is positioned at the origin of a three-dimensional coordinate system, while three ceiling anchor points are fixed at known locations above it. Each cable connects the chandelier to one anchor point and transmits a tensile force along its length.To find out the forces in the cables, the spatial direction of each cable must first be...
Variability: Analysis01:11

Variability: Analysis

Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
The range is a simple measure of variability, indicating the difference between the highest and...
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...

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Related Experiment Video

Updated: Jun 28, 2026

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
07:05

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

Latent-space variational bayes.

Jaemo Sung1, Zoubin Ghahramani, Sung-Yang Bang

  • 1Department of Computer Science and Engineering, Pohang University of Science and Technology, Pohang, Kyungbuk, South Korea. emtidi@postech.ac.kr

IEEE Transactions on Pattern Analysis and Machine Intelligence
|November 8, 2008
PubMed
Summary
This summary is machine-generated.

Latent-Space Variational Bayes (LSVB) offers improved Bayesian inference for probabilistic models over Variational Bayesian Expectation-Maximization (VBEM). A new First-order LSVB (FoLSVB) algorithm provides comparable complexity and better estimates.

Related Experiment Videos

Last Updated: Jun 28, 2026

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
07:05

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

Area of Science:

  • Machine Learning
  • Statistical Inference
  • Probabilistic Modeling

Background:

  • Variational Bayesian Expectation-Maximization (VBEM) is a standard approximate inference technique for Bayesian models.
  • VBEM relies on factorizing over latent variables and model parameters.

Purpose of the Study:

  • Introduce a more general approximate inference framework, Latent-Space Variational Bayes (LSVB), for conjugate-exponential family models.
  • Compare LSVB with VBEM, highlighting LSVB's advantages in estimating model evidence and latent variable distributions.

Main Methods:

  • Developed Latent-Space Variational Bayes (LSVB) by exactly integrating out model parameters.
  • Proposed a practical First-order LSVB (FoLSVB) algorithm to approximate the latent variable distribution.
  • Demonstrated LSVB's generalization of collapsed variational methods to conjugate-exponential families.

Main Results:

  • LSVB provides superior estimates of model evidence and latent variable distributions compared to VBEM.
  • The FoLSVB algorithm achieves comparable computational complexity to VBEM.
  • Illustrative examples using Gaussian and Bernoulli mixtures show LSVB's advantages over VBEM.

Conclusions:

  • LSVB is a more general and effective approximate inference framework for conjugate-exponential models.
  • FoLSVB offers a practical and efficient implementation of LSVB.
  • The proposed method advances approximate Bayesian inference techniques.