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 […]

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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 […]

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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 […]

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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 […]

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Probabilistic Model Selection Measures AIC, BIC, and MDL

Probabilistic Model Selection with AIC, BIC, and MDL

Model selection is the problem of choosing one from among a set of candidate models. It is common to choose a model that performs the best on a hold-out test dataset or to estimate model performance using a resampling technique, such as k-fold cross-validation. An alternative approach to model selection involves using probabilistic statistical measures […]

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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 […]

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A Gentle Introduction to Maximum Likelihood Estimation for Linear Regression

A Gentle Introduction to Linear Regression With Maximum Likelihood Estimation

Linear regression is a classical model for predicting a numerical quantity. The parameters of a linear regression model can be estimated using a least squares procedure or by a maximum likelihood estimation procedure. Maximum likelihood estimation is a probabilistic framework for automatically finding the probability distribution and parameters that best describe the observed data. Supervised […]

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A Gentle Introduction to Maximum Likelihood Estimation for Machine Learning

A Gentle Introduction to Maximum Likelihood Estimation for Machine Learning

Density estimation is the problem of estimating the probability distribution for a sample of observations from a problem domain. There are many techniques for solving density estimation, although a common framework used throughout the field of machine learning is maximum likelihood estimation. Maximum likelihood estimation involves defining a likelihood function for calculating the conditional probability […]

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