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Probability Histograms01:17

Probability Histograms

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A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
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Histogram01:05

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The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data represents (for instance, distance from your home to school). The vertical y-axis is labeled either frequency or relative frequency (or percent frequency or probability).
A histogram graph consists of contiguous (adjoining) boxes. The heights of the bars correspond to frequency values. The graph will have the same shape with respective labels. The...
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One-Way ANOVA: Equal Sample Sizes01:15

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One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
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Relative Frequency Histogram01:14

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The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. Like the histogram, a relative frequency histogram also has the same shape with a horizontal scale (the x-axis), but the vertical scale (the y-axis) is marked with relative frequencies (percentages of the whole) instead of actual frequencies. A relative frequency histogram is a graphical representation of a frequency distribution where the...
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Electric Field of Two Equal and Opposite Charges01:30

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Atoms generally contain the same number of positively and negatively charged particles, protons, and electrons. Hence, they are electrically neutral. However, the centers of the positive and negative charges do not always coincide. In such a scenario, the electric field of an atom may not be zero.
A separation of the positive and negative charges can lead to a weak, remnant effect of the positive and negative charges. The expectation is that the more the distance between the positive and...
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What are Estimates?01:06

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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
The estimate for the mean of a sample is denoted by ͞x, whereas the mean of the population is designated as μ. Further, parameters such...
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Related Experiment Video

Updated: Feb 13, 2026

Author Spotlight: Investigating the Impact of Emotional Prosodies on Voice Recognition and Perception
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Author Spotlight: Investigating the Impact of Emotional Prosodies on Voice Recognition and Perception

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Histogram equalization with Bayesian estimation for noise robust speech recognition.

Youngjoo Suh1, Hoirin Kim1

  • 1School of Electrical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Republic of Korea.

The Journal of the Acoustical Society of America
|March 3, 2018
PubMed
Summary

This study introduces a Bayesian estimation method for histogram equalization to improve automatic speech recognition (ASR) systems. The enhanced technique boosts performance in deep neural network-hidden Markov model (DNN-HMM) systems, especially when data is limited.

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Area of Science:

  • Speech Recognition
  • Machine Learning
  • Signal Processing

Background:

  • Histogram equalization is an efficient feature normalization technique for noise-robust automatic speech recognition (ASR).
  • Conventional methods degrade performance under specific test conditions or due to overfitting with insufficient data.
  • Class-based histogram equalization improved noise robustness but still faced overfitting issues.

Purpose of the Study:

  • To address the limitations of existing histogram equalization methods in ASR.
  • To improve the performance of speech recognition systems, particularly those using deep neural network-hidden Markov models (DNN-HMMs).
  • To enhance feature normalization techniques for better robustness and accuracy in diverse acoustic environments.

Main Methods:

  • The proposed histogram equalization technique utilizes Bayesian estimation for cumulative distribution function estimation.
  • The method was evaluated on speech recognition systems, including Gaussian mixture model-hidden Markov models (GMM-HMMs) and deep neural network-hidden Markov models (DNN-HMMs).
  • Fusion of proposed features with mel-frequency cepstral coefficients (MFCCs) was explored.

Main Results:

  • The Bayesian estimation approach demonstrated substantial performance gains in GMM-HMM based systems on the Aurora-4 task.
  • Meaningful performance improvements were observed in DNN-HMM systems compared to conventional maximum likelihood estimation methods.
  • Fusion with MFCCs provided additional gains in DNN-HMM systems, mitigating degradation in clean test conditions.

Conclusions:

  • The proposed Bayesian estimation-based histogram equalization is effective for enhancing ASR performance, particularly in DNN-HMM systems.
  • This technique offers a solution to overfitting problems and improves robustness in challenging acoustic environments.
  • Feature fusion further boosts performance, highlighting the adaptability of the proposed method to current ASR architectures.