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Related Concept Videos

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...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
Noncompartmental Analysis: Statistical Moment Theory00:56

Noncompartmental Analysis: Statistical Moment Theory

Noncompartmental analyses leverage statistical moment theory to examine time-related changes in macroscopic events, encapsulating the collective outcomes stemming from the constituent elements in play. Statistical moment theory is a mathematical approach used to describe the time course of drug concentration in the body without assuming a specific compartmental model. SMT provides insights into drug absorption, distribution, metabolism, and elimination by treating drug concentration versus time...
Relative Motion Analysis using Rotating Axes - Acceleration01:22

Relative Motion Analysis using Rotating Axes - Acceleration

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame. The absolute velocity of point B is determined by adding the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the effects caused by the angular velocity within the rotating frame.
Time differentiation is...
Two-Way ANOVA01:17

Two-Way ANOVA

The two-way ANOVA is an extension of the one-way ANOVA. It is a statistical test performed on three or more samples categorized by two factors - a row factor and a column factor. Ronald Fischer mentioned it in 1925 in his book 'Statistical Methods for Researchers.'
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Related Experiment Videos

Automatic relevance determination in nonnegative matrix factorization with the β-divergence.

Vincent Y F Tan1, Cédric Févotte

  • 1Institute for Infocomm Research, A*STAR, Singapore and National Universityof Singapore, Singapore. vtan@nus.edu.sg

IEEE Transactions on Pattern Analysis and Machine Intelligence
|May 18, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a Bayesian approach for estimating latent dimensions in nonnegative matrix factorization (NMF) using β-divergence. The method effectively prunes spurious components, balancing data fidelity and overfitting for improved model order selection.

Related Experiment Videos

Area of Science:

  • Machine Learning
  • Data Science
  • Statistical Modeling

Background:

  • Nonnegative Matrix Factorization (NMF) is crucial for dimensionality reduction.
  • Estimating the optimal latent dimensionality (model order) is essential to prevent overfitting and maintain data fidelity.
  • Existing methods for β-divergence-based NMF lack robust model order selection.

Purpose of the Study:

  • To develop a Bayesian method for estimating latent dimensionality in NMF with β-divergence.
  • To introduce a novel approach for automatic relevance determination (ARD) within the NMF framework.
  • To propose efficient algorithms for maximum a posteriori (MAP) estimation.

Main Methods:

  • A Bayesian model incorporating Automatic Relevance Determination (ARD) is proposed.
  • Scale parameters in the priors of dictionary and activation matrices are tied.
  • Majorization-Minimization (MM) algorithms are developed for MAP estimation.
  • Inference drives a subset of scale parameters to a lower bound, pruning components.

Main Results:

  • The proposed ARD-based Bayesian NMF effectively estimates latent dimensionality.
  • The MM algorithms efficiently perform MAP estimation.
  • Experimental results on synthetic and real-world datasets demonstrate robustness and efficacy.
  • The method successfully prunes spurious components, improving model interpretability.

Conclusions:

  • The developed Bayesian NMF with ARD offers a principled approach to model order selection.
  • The proposed MM algorithms provide an efficient solution for parameter estimation.
  • This method enhances the performance and reliability of NMF across various applications.