ML Algorithms: One SD (σ)- Bayesian Algorithms (2022)

An intro to machine learning bayesian algorithms

ML Algorithms: One SD (σ)- Bayesian Algorithms (1)

The obvious questions to ask when facing a wide variety of machine learning algorithms, is “which algorithm is better for a specific task, and which one should I use?”

Answering these questions vary depending on several factors, including: (1) The size, quality, and nature of data; (2) The available computational time; (3) The urgency of the task; and (4) What do you want to do with the data.

This is one section of the many algorithms I wrote about in a previous article.
In this part I tried to display and briefly explain the main algorithms (though not all of them) that are available for bayesian tasks as simply as possible.

A family of algorithms where all of them share a common principle, i.e. every pair of features being classified is independent of each other. Naive Bayes classifiers are a collection of classification algorithms based on Bayes’ Theorem. Bayes’s formula provides relationship between P(A|B) and P(B|A)

ML Algorithms: One SD (σ)- Bayesian Algorithms (2)

·Naive Bayes

ML Algorithms: One SD (σ)- Bayesian Algorithms (3)

A Naive Bayes algorithm assumes that each of the features it uses are conditionally independent of one another given some class. It provides a way of calculating posterior probability P(c|x) from P(c), P(x) and P(x|c). For example, assume that you have few emails which are already classified as spam or ham. Now suppose that you want to classify a new email as spam or ham. Naïve Bayes sees this issue as “what is the probability that new email is spam/ham given that it contains particular words” (e.g. the probability that an email that contains the word “Viagra”, be classified as spam/ham).

Some things to consider:

(Video) 1. Solved Example Naive Bayes Classifier to classify New Instance PlayTennis Example Mahesh Huddar

Useful for very large data sets — you can use Naïve Bayes classification algorithm with a small data set but precision and recall will keep very low

Since the algorithm has an assumption of independence, you do lose the ability to exploit the interactions between features.

· Gaussian Naive Bayes

ML Algorithms: One SD (σ)- Bayesian Algorithms (4)

The general term Naive Bayes refers the independence assumptions in the model, rather than the particular distribution of each feature. Up to this point we have said nothing about the distribution of each feature, but in Gaussian Naïve Bayes, we assume that the distribution of probability is Gaussian (normal). Because of the assumption of the normal distribution, Gaussian Naive Bayes is used in cases when all our features are continuous. For example, if we consider the Iris dataset, the features are sepal width, petal width, etc. They can have different values in the dataset like width and length, hence we can’t represent them in terms of their occurrences and we need to use the Gaussian Naive Bayes here.

Some things to consider:

It assumes the distribution of features is normal

It is usually used when all our features are continuous

· Multinomial Naive Bayes

ML Algorithms: One SD (σ)- Bayesian Algorithms (5)

The term Multinomial Naive Bayes simply tells us that each feature has a multinomial distribution. It’s used when we have discrete data (e.g. movie ratings ranging 1 and 5 as each rating will have certain frequency to represent). In text learning we have the count of each word to predict the class or label. This algorithm is mostly used for document classification problem (whether a document belongs to the category of sports, politics, technology etc.). The features/predictors used by the classifier are the frequency of the words present in the document.

Some things to consider:

Used with discrete data

(Video) #43 Bayes Optimal Classifier with Example & Gibs Algorithm |ML|

Works well for data which can easily be turned into counts, such as word counts in text.

· Averaged One-Dependence Estimators (AODE)

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AODE is a semi-naive Bayesian Learning method. It was developed to address the attribute independence problem of the popular naive Bayes classifier. It does it by averaging over all of the models in which all attributes depend upon the class and a single other attribute. It frequently develops more accurate classifiers than naive Bayes at the cost of a small increase in the amount of computation.

Some things to consider:

Using it for nominal data is computationally more efficient than regular naïve bayes, and achieves very low error rates.

· Bayesian Belief Network (BBN)

ML Algorithms: One SD (σ)- Bayesian Algorithms (7)

A probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases (another example can be seen above in the image). A BBN is a special type of diagram (called a directed graph) together with an associated set of probability tables. Another example is tossing a coin. The coin can have two values- heads or tails with a 50% probability each. We call these probabilities “beliefs” (i.e. our belief that the state coin=head is 50%).

Some things to consider:

BBNs enable us to model and reason about uncertainty

The most important use of BBNs is in revising probabilities in the light of actual observations of events

Can be used to understand what caused a certain problem, or the probabilities of different effects given an action in areas like computational biology and medicine for risk analysis and decision support.

(Video) Introduction to Bayesian statistics, part 1: The basic concepts

· Bayesian Network (BN)

ML Algorithms: One SD (σ)- Bayesian Algorithms (8)

Bayesian networks are a type of Probabilistic Graphical Model (probabilistic because they are built from probability distributions). These networks can be used for predictions, anomaly detection, diagnostics, automated insight, reasoning, time series prediction and decision making under uncertainty. The goal of these networks is to model conditional dependence, and therefore causation. For example: if you’re outside of your house and it starts raining, there is a high probability that your dog will start barking. Which in turn, will increase the probability that the cat will hide under the couch. So you can see how info about one event (rain) allows you to make inferences about a seemingly unrelated event (the cat hiding under the couch).

Some things to consider:

You can use them to make future predictions

Useful for explaining observations

Bayesian networks are very convenient for representing similar probabilistic relationships between multiple events.

· Hidden Markov models (HMM)

ML Algorithms: One SD (σ)- Bayesian Algorithms (9)

HMM is a class of probabilistic graphical model that allow us to predict a sequence of unknown (hidden) variables from a set of observed variables. For example, predicting the weather (hidden variable) based on the type of clothes that someone wears (observed). This can be a swimsuit, an umbrella, etc. These are basically the evidence.

HMM are known for their use in in reinforcement learning and temporal pattern recognition such as handwriting, speech, part-of-speech tagging, gesture recognition, and bioinformatics.

HMM answers questions like: given a model, what is the likelihood of sequence S happening? Given a sequence S and number of hidden states, what is the optimal model which maximizes the probability of S?

Some things to consider:

(Video) 4.5 Bayesian Predictive Distributions (UvA - Machine Learning 1 - 2020)

HMM is suitable to be used in application that dealing with recognizing something based on sequence of feature.

HMMs can be used to model processes which consist of different stages that occur in definite (or typical) orders.

HMM needs to be trained on a set of seed sequences and generally requires a larger seed than the simple Markov models.

· Conditional random fields (CRFs)

ML Algorithms: One SD (σ)- Bayesian Algorithms (10)

A classical ML model to train sequential models. It is a type of discriminative classifier that model the decision boundary between the different classes. The difference between discriminative and generative models is that while discriminative models try to model conditional probability distribution, i.e., P(y|x), generative models try to model a joint probability distribution, i.e., P(x,y). Their underlying principle is that they apply Logistic Regression on sequential inputs. Hidden Markov Models share some similarities with CRFs, one in that they are also used for sequential inputs. CRFs are most used for NLP tasks.

Suppose you have a sequence of snapshots from a day in your friend’s life. Your goal is to label each image with the activity it represents (eating, sleeping, driving, etc.). One way to do it is to ignore the fact that the snapshots has a sequential nature, and to build a per-image classifier. For example, you can learn that dark images taken at 5am are usually related to sleeping, while images with food tends to be about eating, and so on. However, by ignoring the sequential aspect, we lose a lot of information. As an example, what happens if you see a close-up picture of a mouth — is it about talking or eating? If you know that the previous snapshot is a picture of your friend eating, then it’s more likely this picture is about eating. Hence, to increase the accuracy of our labeler, we should consider the labels of nearby photos, and this is precisely what a conditional random field does.

ML Algorithms: One SD (σ)- Bayesian Algorithms (11)

Some things to consider:

CRF predicts the most likely sequence of labels that correspond to a sequence of inputs

Compared to HMM, since CRF does not have as strict independence assumptions as HMM does, it can accommodate any context information.

CRFs also avoid the label bias problem.

CRF is highly computationally complex at the training stage of the algorithm. It makes it very difficult to re-train the model when newer data becomes available.

(Video) [12-min poster] BART: Bayesian Additive Regression Trees - A Methodology Study

If you’re interested in more of my work you can check out my Github, my scholar page, or my website


What is Bayesian algorithm in machine learning? ›

Naïve Bayes Classifier is one of the simple and most effective Classification algorithms which helps in building the fast machine learning models that can make quick predictions. It is a probabilistic classifier, which means it predicts on the basis of the probability of an object.

What are Bayesian algorithms? ›

A family of algorithms where all of them share a common principle, i.e. every pair of features being classified is independent of each other. Naive Bayes classifiers are a collection of classification algorithms based on Bayes' Theorem.

What are the algorithms of ML? ›

Common machine learning algorithms

Linear regression, aka least squares regression (for numeric data) Logistic regression (for binary classification) Linear discriminant analysis (for multi-category classification) Decision trees (for both classification and regression)

Which algorithm is used for prediction in ML? ›

Naive Bayes is a simple but surprisingly powerful algorithm for predictive modeling. The model consists of two types of probabilities that can be calculated directly from your training data: 1) The probability of each class; and 2) The conditional probability for each class given each x value.

What is Bayesian network in AI? ›

"A Bayesian network is a probabilistic graphical model which represents a set of variables and their conditional dependencies using a directed acyclic graph." It is also called a Bayes network, belief network, decision network, or Bayesian model.

What is Bayes Theorem example? ›

Bayes theorem is also known as the formula for the probability of “causes”. For example: if we have to calculate the probability of taking a blue ball from the second bag out of three different bags of balls, where each bag contains three different colour balls viz. red, blue, black.

Why Bayes theorem is used? ›

Bayes' theorem provides a way to revise existing predictions or theories (update probabilities) given new or additional evidence. In finance, Bayes' Theorem can be used to rate the risk of lending money to potential borrowers.

What is Bayesian analysis used for? ›

Bayesian analysis, a method of statistical inference (named for English mathematician Thomas Bayes) that allows one to combine prior information about a population parameter with evidence from information contained in a sample to guide the statistical inference process.

What is Bayesian statistics used for? ›

Bayesian statistics is a particular approach to applying probability to statistical problems. It provides us with mathematical tools to update our beliefs about random events in light of seeing new data or evidence about those events.

Which is the best algorithm in ML? ›

List of Popular Machine Learning Algorithms
  1. Linear Regression. ...
  2. Logistic Regression. ...
  3. Decision Tree. ...
  4. SVM (Support Vector Machine) Algorithm. ...
  5. Naive Bayes Algorithm. ...
  6. KNN (K- Nearest Neighbors) Algorithm. ...
  7. K-Means. ...
  8. Random Forest Algorithm.
21 Sept 2022

What are the 3 types of machine learning? ›

The three machine learning types are supervised, unsupervised, and reinforcement learning.

How many algorithms are there in ML? ›

There are four types of machine learning algorithms: supervised, semi-supervised, unsupervised and reinforcement.

What are the 4 types of algorithm? ›

Introduction To Types of Algorithms

Brute Force algorithm. Greedy algorithm. Recursive algorithm. Backtracking algorithm.

What is the 5 popular algorithm in machine learning? ›

To recap, we have covered some of the the most important machine learning algorithms for data science: 5 supervised learning techniques- Linear Regression, Logistic Regression, CART, Naïve Bayes, KNN.

How do Bayesian networks work? ›

A Bayesian network is a probability model defined over an acyclic directed graph. It is factored by using one conditional probability distribution for each variable in the model, whose distribution is given conditional on its parents in the graph.

How a Bayesian network is constructed in AI? ›

It is also known as a belief network or a causal network. It consists of directed cyclic graphs (DCGs) and a table of conditional probabilities to find out the probability of an event happening. It contains nodes and edges, where edges connect the nodes.

What are the advantages of Bayesian networks? ›

Bayesian Networks are more extensible than other networks and learning methods. Adding a new piece in the network requires only a few probabilities and a few edges in the graph. So, it is an excellent network for adding a new piece of data to an existing probabilistic model. The graph of a Bayesian Network is useful.

How do you use Bayesian formula? ›

To find the conditional probability P(A|B) using Bayes' formula, you need to:
  1. Make sure the probability P(B) is non-zero.
  2. Take the probabilities P(B|A) and P(A) and compute their product.
  3. Divide the result from Step 2 by P(B) .
  4. That's it! You've just successfully applied Bayes' theorem!
31 Aug 2022

Where is Bayes Theorem used in real life? ›

Bayes' theorem does not only apply in mathematics, but it also has many real life applications such as in Internet Marketing to profile visitors to a website, in Decision Analysis and Decision Trees, the “Two Child Problem” explained in the text above.

What is the correct formula for Bayes Theorem? ›

Formula for Bayes' Theorem

P(A|B) – the probability of event A occurring, given event B has occurred. P(B|A) – the probability of event B occurring, given event A has occurred. P(A) – the probability of event A. P(B) – the probability of event B.

How is Bayes Theorem derived? ›

Bayes Theorem Formula

Bayes Theorem formulas are derived from the definition of conditional probability. It can be derived for events A and B, as well as continuous random variables X and Y.

Who invented Bayes Theorem? ›

Bayes's theorem, in probability theory, a means for revising predictions in light of relevant evidence, also known as conditional probability or inverse probability. The theorem was discovered among the papers of the English Presbyterian minister and mathematician Thomas Bayes and published posthumously in 1763.

Why is Bayesian statistics better? ›

Frequentist statistics never uses or calculates the probability of the hypothesis, while Bayesian uses probabilities of data and probabilities of both hypothesis. Frequentist methods do not demand construction of a prior and depend on the probabilities of observed and unobserved data.

How is Bayesian inference used in machine learning? ›

Bayesian machine learning is a subset of Bayesian statistics that makes use of Bayes' theorem to draw inferences from data. Bayesian inference can be used in Bayesian machine learning to predict the weather with more accuracy, recognize emotions in speech, estimate gas emissions, and much more!

Is Bayesian data analysis useful? ›

Bayesian hypothesis testing enables us to quantify evidence and track its progression as new data come in. This is important because there is no need to know the intention with which the data were collected.

What is Bayesian p value? ›

The p-value quantifies the discrepancy between the data and a null hypothesis of interest, usually the assumption of no difference or no effect. A Bayesian approach allows the calibration of p-values by transforming them to direct measures of the evidence against the null hypothesis, so-called Bayes factors.

What is the opposite of Bayesian? ›

Frequentist statistics (sometimes called frequentist inference) is an approach to statistics. The polar opposite is Bayesian statistics. Frequentist statistics are the type of statistics you're usually taught in your first statistics classes, like AP statistics or Elementary Statistics.

What is Bayesian modeling in data analysis? ›

In Bayesian analysis, expert scientific opinion is encoded in a probability distribution for the unknown parameters; this distribution is called the prior distribution. The data are modeled as coming from a sampling distribution given the unknown parameters.

Which algorithm is best for prediction? ›

  • Time Series Model. The time series model comprises a sequence of data points captured, using time as the input parameter. ...
  • Random Forest. Random Forest is perhaps the most popular classification algorithm, capable of both classification and regression. ...
  • Gradient Boosted Model (GBM) ...
  • K-Means. ...
  • Prophet.
1 Jan 2022

What is the simplest machine learning algorithm? ›

K-means clustering

K-means clustering is one of the simplest and a very popular unsupervised machine learning algorithms.

What are the different ML models? ›

Amazon ML supports three types of ML models: binary classification, multiclass classification, and regression.

What are 5 examples of algorithms? ›

Examples of Algorithms in Everyday Life
  • Tying Your Shoes. Any step-by-step process that is completed the same way every time is an algorithm. ...
  • Following a Recipe. ...
  • Classifying Objects. ...
  • Bedtime Routines. ...
  • Finding a Library Book in the Library. ...
  • Driving to or from Somewhere. ...
  • Deciding What to Eat.
18 Aug 2022

How many algorithms are there? ›

There are seven different types of programming algorithms: Sort algorithms. Search algorithms. Hashing.

What are AI algorithms? ›

Essentially, an AI algorithm is an extended subset of machine learning that tells the computer how to learn to operate on its own. In turn, the device continues to gain knowledge to improve processes and run tasks more efficiently. Need an example of where this is incredibly common?

How many algorithms are there in deep learning? ›

Whether you are a beginner or a professional, these top three deep learning algorithms will help you solve complicated issues related to deep learning: CNNs or Convolutional Neural Networks, LSTMs or Long Short Term Memory Networks and RNNs or Recurrent Neural Networks (RNNs).

How does Bayesian learning impact machine learning? ›

Bayesian methods assist several machine learning algorithms in extracting crucial information from small data sets and handling missing data. They play... Bayesian methods assist several machine learning algorithms in extracting crucial information from small data sets and handling missing data.

What is means by Bayesian learning in deep learning? ›

A Bayesian Neural Network (BNN) is simply posterior inference applied to a neural network architecture. To be precise, a prior distribution is specified for each weight and bias. Because of their huge parameter space, however, inferring the posterior is even more difficult than usual.

What is Bayes Theorem show how it is used for classification? ›

Bayes Theorem

P(B/A) is a conditional probability that explains the occurrence of event B when A is true. Similarly, P(A/B) is a conditional probability that explains the occurrence of event A when B is true.

What is Bayesian optimization used for? ›

Bayesian Optimization is an approach that uses Bayes Theorem to direct the search in order to find the minimum or maximum of an objective function. It is an approach that is most useful for objective functions that are complex, noisy, and/or expensive to evaluate.

Is all machine learning Bayesian? ›

Strictly speaking, Bayesian inference is not machine learning. It is a statistical paradigm (an alternative to frequentist statistical inference) that defines probabilities as conditional logic (via Bayes' theorem), rather than long-run frequencies.

Where is Bayesian machine learning used? ›

Bayesian machine learning has become increasingly popular because it can be used for real-world applications such as credit card fraud detection and spam filtering.

Is Bayesian modeling machine learning? ›

The Bayesian framework for machine learning states that you start out by enumerating all reasonable models of the data and assigning your prior belief P(M) to each of these models. Then, upon observing the data D, you evaluate how probable the data was under each of these models to compute P(D|M).

What are the features of Bayesian learning method? ›

Features of Bayesian learning methods:

a probability distribution over observed data for each possible hypothesis. New instances can be classified by combining the predictions of multiple hypotheses, weighted by their probabilities.

Is Bayesian a neural network? ›

What is Bayesian Neural Network? Bayesian neural network (BNN) combines neural network with Bayesian inference. Simply speaking, in BNN, we treat the weights and outputs as the variables and we are finding their marginal distributions that best fit the data.

What is Bayesian thinking in simple terms? ›

In simple terms, Bayesian statistics apply probabilities to statistical problems to update prior beliefs in light of the evidence of new data. The probability expresses a degree of belief in a specific event.

What are the applications of Bayes classifier? ›

Applications of Naive Bayes Algorithm

As this algorithm is fast and efficient, you can use it to make real-time predictions. This algorithm is popular for multi-class predictions. You can find the probability of multiple target classes easily by using this algorithm.

What is the application of Bayes Theorem in data analysis? ›

The Bayes theorem is a mathematical formula for calculating conditional probability in probability and statistics. In other words, it's used to figure out how likely an event is based on its proximity to another.

Why do we use naive Bayes algorithm? ›

Naive Bayes uses a similar method to predict the probability of different class based on various attributes. This algorithm is mostly used in text classification and with problems having multiple classes.

Is Bayesian optimization better than random search? ›

Bayesian optimization methods are efficient because they select hyperparameters in an informed manner. By prioritizing hyperparameters that appear more promising from past results, Bayesian methods can find the best hyperparameters in lesser time (in fewer iterations) than both grid search and random search.

How does Bayesian search work? ›

Bayesian Optimization differs from Random Search and Grid Search in that it improves the search speed using past performances, whereas the other two methods are uniform (or independent) of past evaluations. In that sense, Bayesian Optimization is like Manual Search.

Who invented Bayesian optimization? ›

The term is generally attributed to Jonas Mockus and is coined in his work from a series of publications on global optimization in the 1970s and 1980s.


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3. Efficient Bayesian inference with Hamiltonian Monte Carlo -- Michael Betancourt (Part 1)
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6. Bayes Theorem Explained with Solved Example in Hindi ll Machine Learning Course
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