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 […]
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 […]
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 […]
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 […]
In this tutorial you are going to learn about the k-Nearest Neighbors algorithm including how it works and how to implement it from scratch in Python (without libraries). A simple but powerful approach for making predictions is to use the most similar historical examples to the new data. This is the principle behind the k-Nearest Neighbors […]
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 […]
Cross-entropy is commonly used in machine learning as a loss function. Cross-entropy is a measure from the field of information theory, building upon entropy and generally calculating the difference between two probability distributions. It is closely related to but is different from KL divergence that calculates the relative entropy between two probability distributions, whereas cross-entropy […]
In this tutorial you are going to learn about the Naive Bayes algorithm including how it works and how to implement it from scratch in Python (without libraries). We can use probability to make predictions in machine learning. Perhaps the most widely used example is called the Naive Bayes algorithm. Not only is it straightforward […]
It is often desirable to quantify the difference between probability distributions for a given random variable. This occurs frequently in machine learning, when we may be interested in calculating the difference between an actual and observed probability distribution. This can be achieved using techniques from information theory, such as the Kullback-Leibler Divergence (KL divergence), or […]
Information gain calculates the reduction in entropy or surprise from transforming a dataset in some way. It is commonly used in the construction of decision trees from a training dataset, by evaluating the information gain for each variable, and selecting the variable that maximizes the information gain, which in turn minimizes the entropy and best […]
