Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

454
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
454
Variability: Analysis01:11

Variability: Analysis

609
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...
609
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

20.4K
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...
20.4K
Summation Notation01:25

Summation Notation

292
Sigma notation, also known as summation notation, provides a concise method for representing the sum of a sequence of terms that follow a regular pattern. It utilizes the uppercase Greek letter sigma (∑), A typical expression is:In this form, k the index of summation is 1, the starting value, and n the ending value. The term ak​ represents the general term of the sequence.For example, the increasing sequence 5, 7, 9, ..., 23 over 10 terms can be expressed as:This simplifies the...
292
Integration of Synaptic Events01:28

Integration of Synaptic Events

5.3K
Synaptic integration mainly includes the summation of graded potentials. Graded potentials, regardless of their type, cause subtle alterations in membrane voltage, resulting in either depolarization or hyperpolarization. These incremental changes, when combined or summed, can propel the neuron toward its threshold. Consider, for example, a membrane experiencing a +15 mV shift, causing it to depolarize from -70 mV to -55 mV. In this scenario, graded potentials govern the membrane's ability to...
5.3K
Superposition Theorem01:18

Superposition Theorem

1.6K
The superposition principle is a fundamental concept stating that in a linear circuit, the voltage across (or current through) an element can be determined by summing the individual contributions of each independent source acting in isolation. When dealing with linear circuits containing multiple independent sources, this principle serves as a valuable tool for analysis. To apply the superposition principle effectively, one should focus on a single independent source at a time while...
1.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Adaptive Variational Inference: Beyond Bethe, Tree-Reweighted, and Convex Free Energies.

IEEE transactions on pattern analysis and machine intelligence·2026
Same author

Usability and User Experience of a Digital Platform Prototype (Healthy Bone) to Promote Pharmacological and Nonpharmacological Treatment in Patients With Osteoporosis: Mixed Methods Study.

JMIR formative research·2025
Same author

Acoustic COVID-19 Detection Using Multiple Instance Learning.

IEEE journal of biomedical and health informatics·2024
Same author

Dataset of directional room impulse responses for realistic speech data.

Data in brief·2024
Same author

The ADAM17 sheddase complex regulator iTAP/Frmd8 modulates inflammation and tumor growth.

Life science alliance·2023
Same author

Self-Guided Belief Propagation - A Homotopy Continuation Method.

IEEE transactions on pattern analysis and machine intelligence·2022

Related Experiment Video

Updated: Mar 11, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.7K

On the Latent Variable Interpretation in Sum-Product Networks.

Robert Peharz, Robert Gens, Franz Pernkopf

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |November 23, 2016
    PubMed
    Summary

    Sum-Product networks (SPNs) with augmented latent variables (LVs) resolve model incompleteness. This approach validates EM and MPE algorithms for SPNs, confirmed by experiments.

    More Related Videos

    Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
    06:52

    Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

    Published on: September 17, 2019

    6.8K
    Measuring Attention and Visual Processing Speed by Model-based Analysis of Temporal-order Judgments
    13:00

    Measuring Attention and Visual Processing Speed by Model-based Analysis of Temporal-order Judgments

    Published on: January 23, 2017

    10.4K

    Related Experiment Videos

    Last Updated: Mar 11, 2026

    Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
    10:44

    Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

    Published on: December 7, 2021

    2.7K
    Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
    06:52

    Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

    Published on: September 17, 2019

    6.8K
    Measuring Attention and Visual Processing Speed by Model-based Analysis of Temporal-order Judgments
    13:00

    Measuring Attention and Visual Processing Speed by Model-based Analysis of Temporal-order Judgments

    Published on: January 23, 2017

    10.4K

    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Probabilistic Graphical Models

    Background:

    • Sum-Product networks (SPNs) interpret sum nodes as marginalized latent variables (LVs).
    • This interpretation enables EM algorithm application and efficient MPE inference.
    • Existing LV interpretation methods conflict with SPN completeness and model specification.

    Purpose of the Study:

    • To address the conflict in existing LV interpretation for SPNs.
    • To propose a novel method, SPN augmentation, for introducing LVs.
    • To formally establish the probabilistic interpretation and algorithmic validity within augmented SPNs.

    Main Methods:

    • SPN augmentation: Modifying the approach for introducing LVs.
    • Conditional independence analysis in augmented SPNs.
    • Formal derivation of the EM algorithm for SPNs.
    • Proof of correctness for Viterbi-style MPE inference in selective and augmented SPNs.

    Main Results:

    • SPN augmentation resolves completeness and model specification issues.
    • Formal probabilistic interpretation of sum-weights and Bayesian network equivalence established.
    • A sound derivation of the EM algorithm for SPNs is presented.
    • The Viterbi-style MPE algorithm is proven correct for selective and augmented SPNs.

    Conclusions:

    • SPN augmentation provides a theoretically sound framework for LVs in SPNs.
    • This framework validates key algorithms like EM and MPE inference.
    • Experimental results on synthetic and real-world data confirm the theoretical findings.