Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Probability Laws

Probability Laws

Probability Distributions

Probability Distributions

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 probability...

Poisson Probability Distribution

Poisson Probability Distribution

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...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

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...

Probability in Statistics

Probability in Statistics

Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...

Probability Histograms

Probability Histograms

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.

You might also read

Related Articles

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

Sort by

Same author

A knowledge-poor approach to chemical-disease relation extraction.

Database : the journal of biological databases and curation·2016

Same author

Unsupervised entity and relation extraction from clinical records in Italian.

Computers in biology and medicine·2016

Same author

Unsupervised information extraction from italian clinical records.

Studies in health technology and informatics·2014

See all related articles

Search research articles

Related Experiment Video

Updated: Jul 14, 2026

Experimental Paradigm for Measuring the Effect of Induced Emotion on Grammar Learning

Experimental Paradigm for Measuring the Effect of Induced Emotion on Grammar Learning

Published on: January 29, 2020

Probabilistic context-free grammars estimated from infinite distributions.

Anna Corazza¹, Giorgio Satta

¹Department of Physics, University of Naples Federico II, via Cinthia, Napoli, Italy. corazza@na.infn.it

IEEE Transactions on Pattern Analysis and Machine Intelligence

|June 15, 2007

Summary

This study explores training probabilistic context-free grammars (PCFGs) using cross-entropy minimization for infinite distributions. It reveals a key equivalence between grammar cross-entropy and derivational entropy, impacting PCFG estimation.

Related Experiment Videos

Last Updated: Jul 14, 2026

Experimental Paradigm for Measuring the Effect of Induced Emotion on Grammar Learning

Experimental Paradigm for Measuring the Effect of Induced Emotion on Grammar Learning

Published on: January 29, 2020

Area of Science:

Computational Linguistics
Machine Learning
Formal Language Theory

Background:

Probabilistic Context-Free Grammars (PCFGs) are vital for statistical natural language parsing.
Training PCFGs on infinite data distributions presents computational challenges.
Existing methods may not fully capture the complexities of natural language generation.

Purpose of the Study:

To investigate training PCFGs on infinite tree or sentence distributions via cross-entropy minimization.
To explore theoretical properties of PCFGs estimated through this method.
To establish a novel equivalence between grammar cross-entropy and derivational entropy.

Main Methods:

Minimizing cross-entropy between grammar-defined distributions and input distributions.
Theoretical analysis of PCFG properties under cross-entropy minimization.
Examining implications for maximum-likelihood estimation and finite-state models.

Main Results:

Demonstrated theoretical properties of PCFGs trained via cross-entropy minimization.
Established the equivalence between grammar cross-entropy and derivational entropy.
Highlighted consequences for standard maximum-likelihood estimation on finite samples.

Conclusions:

The cross-entropy minimization approach offers valuable theoretical insights into PCFG training.
The identified equivalence simplifies understanding and potentially improves PCFG estimation.
Results have implications for applying PCFGs and related finite-state models in practice.