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Related Concept Videos

Probability Distributions01:32

Probability Distributions

13.5K
 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
13.5K
Binomial Probability Distribution01:15

Binomial Probability Distribution

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A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
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Poisson Probability Distribution01:09

Poisson Probability Distribution

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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
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Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

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Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
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Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
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Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Related Experiment Video

Updated: Jun 4, 2026

End-To-End Deep Neural Network for Salient Object Detection in Complex Environments
03:31

End-To-End Deep Neural Network for Salient Object Detection in Complex Environments

Published on: December 15, 2023

A Non-Negative Deep VAE: The Generalized Gamma Belief Network.

Zhibin Duan, Tiansheng Wen, Muyao Wang

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |April 6, 2026
    PubMed
    Summary

    Generalized Gamma Belief Networks (Generalized GBN) enhance topic modeling by introducing non-linear generative models for deeper insights. This approach improves data variability and disentangled representation learning in text corpora.

    Related Experiment Videos

    Last Updated: Jun 4, 2026

    End-To-End Deep Neural Network for Salient Object Detection in Complex Environments
    03:31

    End-To-End Deep Neural Network for Salient Object Detection in Complex Environments

    Published on: December 15, 2023

    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Natural Language Processing

    Background:

    • Gamma Belief Networks (GBN) are deep probabilistic topic models effective for multi-layer latent representations in text.
    • Their strength lies in gamma-distributed latent variables capturing sparsity and hierarchical structures.
    • Existing GBNs are limited by linear generative models, restricting expressiveness.

    Purpose of the Study:

    • Introduce Generalized Gamma Belief Network (Generalized GBN) with a non-linear generative model.
    • Address limitations of linear generative models in existing GBNs.
    • Enhance expressiveness and applicability of deep probabilistic topic models.

    Main Methods:

    • Developed Generalized GBN with a non-linear generative model.
    • Proposed an upward-downward Weibull inference network for approximating posterior distributions.
    • Jointly trained generative and inference network parameters within a variational inference framework.

    Main Results:

    • Demonstrated Generalized GBN's effectiveness in modeling data variability through theoretical analysis.
    • Showcased Generalized GBN's ability to achieve disentangled representations via inherent sparsity modeling.
    • Empirically evaluated Generalized GBN against Gaussian variational autoencoders on expressivity and disentangled representation learning tasks.

    Conclusions:

    • Generalized GBN offers a more expressive and applicable alternative to traditional GBNs.
    • The proposed Weibull inference network effectively handles non-analytic posteriors.
    • Generalized GBN shows promise for advanced document modeling and representation learning.