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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 […]

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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 […]

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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 […]

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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 […]

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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 […]

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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 […]

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In this tutorial, you will discover how to implement the Bayesian Optimization algorithm for complex optimization problems. Global optimization is a challenging problem of finding an input that results in the minimum or maximum cost of a given objective function. Typically, the form of the objective function is complex and intractable to analyze and is […]

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Classification is a predictive modeling problem that involves assigning a label to a given input data sample. The problem of classification predictive modeling can be framed as calculating the conditional probability of a class label given a data sample. Bayes Theorem provides a principled way for calculating this conditional probability, although in practice requires an […]

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Bayes Theorem provides a principled way for calculating a conditional probability. It is a deceptively simple calculation, although it can be used to easily calculate the conditional probability of events where intuition often fails. Although it is a powerful tool in the field of probability, Bayes Theorem is also widely used in the field of […]

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Probability for Machine Learning Crash Course.Get on top of the probability used in machine learning in 7 days. Probability is a field of mathematics that is universally agreed to be the bedrock for machine learning. Although probability is a large field with many esoteric theories and findings, the nuts and bolts, tools and notations taken […]

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