Search results for "Artificial Intelligence"

A Gentle Introduction to Maximum a Posteriori (MAP) for Machine Learning

A Gentle Introduction to Maximum a Posteriori (MAP) for Machine Learning

Density estimation is the problem of estimating the probability distribution for a sample of observations from a problem domain. Typically, estimating the entire distribution is intractable, and instead, we are happy to have the expected value of the distribution, such as the mean or mode. Maximum a Posteriori or MAP for short is a Bayesian-based […]

Continue Reading 0
A Gentle Introduction to Markov Chain Monte Carlo for Probability

A Gentle Introduction to Markov Chain Monte Carlo for Probability

Probabilistic inference involves estimating an expected value or density using a probabilistic model. Often, directly inferring values is not tractable with probabilistic models, and instead, approximation methods must be used. Markov Chain Monte Carlo sampling provides a class of algorithms for systematic random sampling from high-dimensional probability distributions. Unlike Monte Carlo sampling methods that are […]

Continue Reading 4
Histogram Plots of Differently Sized Monte Carlo Samples From the Target Function

A Gentle Introduction to Monte Carlo Sampling for Probability

Monte Carlo methods are a class of techniques for randomly sampling a probability distribution. There are many problem domains where describing or estimating the probability distribution is relatively straightforward, but calculating a desired quantity is intractable. This may be due to many reasons, such as the stochastic nature of the domain or an exponential number […]

Continue Reading 8
Histogram of Dataset Constructed From Two Different Gaussian Processes

A Gentle Introduction to Expectation-Maximization (EM Algorithm)

Maximum likelihood estimation is an approach to density estimation for a dataset by searching across probability distributions and their parameters. It is a general and effective approach that underlies many machine learning algorithms, although it requires that the training dataset is complete, e.g. all relevant interacting random variables are present. Maximum likelihood becomes intractable if […]

Continue Reading 5
A Gentle Introduction to Logistic Regression With Maximum Likelihood Estimation

A Gentle Introduction to Logistic Regression With Maximum Likelihood Estimation

Logistic regression is a model for binary classification predictive modeling. The parameters of a logistic regression model can be estimated by the probabilistic framework called maximum likelihood estimation. Under this framework, a probability distribution for the target variable (class label) must be assumed and then a likelihood function defined that calculates the probability of observing […]

Continue Reading 4
Plot of Probability Distribution vs Entropy

A Gentle Introduction to Information Entropy

Information theory is a subfield of mathematics concerned with transmitting data across a noisy channel. A cornerstone of information theory is the idea of quantifying how much information there is in a message. More generally, this can be used to quantify the information in an event and a random variable, called entropy, and is calculated […]

Continue Reading 2
A Gentle Introduction to Bayesian Belief Networks

A Gentle Introduction to Bayesian Belief Networks

Probabilistic models can define relationships between variables and be used to calculate probabilities. For example, fully conditional models may require an enormous amount of data to cover all possible cases, and probabilities may be intractable to calculate in practice. Simplifying assumptions such as the conditional independence of all random variables can be effective, such as […]

Continue Reading 2