CS3491 – ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING

[Audio] As a teacher in higher education I am thrilled to discuss the significance of probability theory in dealing with uncertainty and the diverse techniques employed in probabilistic reasoning. We will cover topics such as Bayesian inference naïve bayes models exact inference in Bayesian networks approximate inference in Bayesian networks causal networks acting under uncertainty causes of uncertainty and real-world examples of its application. I trust that you will find this presentation enlightening and valuable and I eagerly anticipate addressing any inquiries you may have..

[Audio] Discussing probabilistic reasoning in the context of artificial intelligence and machine learning Bayesian inference is a key concept. Naïve Bayes models are a type of Bayesian inference commonly used in machine learning. Assuming features in a dataset are conditionally independent of each other they are based on this assumption. Bayesian networks are another important tool for probabilistic reasoning. Approximate inference in Bayesian networks is a technique used when exact inference is not feasible. It is based on sampling from the distribution of the network and approximating the results. Causal networks are a type of Bayesian network designed to model causal relationships between variables. Diagnosis and prediction are useful for tasks such as. Probabilistic reasoning is a powerful tool for artificial intelligence and machine learning. It allows making predictions and drawing conclusions based on uncertain data..

[Audio] Discussing the concept of uncertainty in Artificial Intelligence and Machine Learning. Uncertainty refers to a situation where information is incomplete or unknown. It is important to note that uncertainty is not always unintelligible. In some cases uncertainty can arise due to incompleteness or incorrectness in the agent's understanding of the environment. In these cases we need to use probabilistic reasoning which involves making decisions based on the likelihood of different outcomes. This allows us to represent uncertain knowledge and make informed decisions in situations where we are not entirely sure about the predicates. It is important to differentiate ignorance from uncertainty as ignorance refers to a lack of knowledge about the factors that influence the issues whereas uncertainty refers to a situation where information is incomplete or unknown..

[Audio] We present our findings on the reasons for uncertainty in environments due to lack of full knowledge. We show that such uncertainty arises due to two main reasons: laziness and ignorance. Agents cannot always find a categorical answer and uncertainty can also arise due to incompleteness or incorrectness in their understanding of the environment's properties. Therefore it is impossible to completely eliminate uncertainty in such environments..

[Audio] Probability statements provide a clear and rigorous framework for expressing uncertainty..

[Audio] We will discuss the concept of probability and its application to knowledge representation in the presentation. By combining probability theory with logic we can better handle the uncertainty in our knowledge and make informed decisions. The use of probability in probabilistic reasoning allows us to quantify this uncertainty and make more accurate predictions..

[Audio] Probabilistic reasoning is a crucial aspect of artificial intelligence. It helps (A-I ) systems make informed decisions based on available data and uncertainty. When there are uncertain outcomes specifications or predictions become too large to handle or an unknown error occurs during an experiment probabilistic reasoning plays an essential role in (A-I )..

[Audio] Probability is a numerical measure that represents ideal uncertainties and ranges from 0 to 1. The probability of an event A is represented by P(A) and the probability of a not happening event is represented by P(¬A). Understanding the concepts of probability is essential for comprehending (A-I ) and machine learning..

[Audio] Probability theory is the study of basic concepts such as events sample spaces and random variables. An event is a possible outcome of a variable while a sample space is the set of all possible events. Random variables are used to represent events and objects in the real world. Prior probability is calculated before observing new information and posterior probability is calculated after all evidence or information has been taken into account. Posterior probability is a combination of prior probability and new information..

[Audio] Conditional probability is a measure of the likelihood of an event occurring under a given set of conditions. It is a useful tool in artificial intelligence and machine learning algorithms as it allows us to make predictions based on prior knowledge. Let's use an example to understand this concept better. Suppose we have a dataset of students' performance in a particular course and we want to predict the probability of a student passing the course given their performance in the first exam. We can use conditional probability to calculate the probability of a student passing the course given their performance in the first exam. The probability of a student passing the course is given by:.

[Audio] We can calculate the probability of event B given the probability of event A using the Venn diagram method. This formula is useful when we want to find the probability of an event occurring given the probability of another event occurring. By using the Venn diagram method we can visualize the relationship between the two events and see how they intersect to calculate the probability of event B..

[Audio] We will introduce probabilistic reasoning. We have two events A and B where A represents a student liking Mathematics and B represents a student liking English. Using probabilistic reasoning we can determine the probability of a student liking English also liking Mathematics represented by event C To do this we use the formula for conditional probability: P(A and B) = P(A|B) x P(B). We want to find the probability of a student liking English and Mathematics which is represented by event C Applying the formula we determine that the probability of a student liking English and Mathematics is: P(C) = P(A and B) = P(A|B) x P(B) = 0.4 x 0.7 = 0.28. The probability of a student liking English and Mathematics is 28%..

[Audio] Bayes' theorem is a fundamental concept in probability theory that relates the conditional probability and marginal probabilities of two random events. This theorem is named after Thomas Bayes. We will discuss Bayesian inference an application of Bayes' theorem. This is a way to calculate the probability of an event given new information from the real world. Bayesian inference allows updating the probability prediction of an event. In probabilistic reasoning Bayes' theorem and Bayesian inference are crucial concepts that are fundamental to Bayesian statistics..

[Audio] We can determine the probability of cancer more accurately using Bayes' theorem. The theorem can be derived using the product rule and the conditional probability of event A with known event B Using the product rule we can write P(A ⋀ B)= P(A|B)P(B) or similarly the probability of event B with known event A: P(A ⋀ B)= P(B|A)P(A). Equating the right-hand side of both equations we will get: P(A ⋀ B)= P(B|A)P(A). This equation helps us determine the probability of cancer more accurately based on age. Therefore Bayes' theorem is a powerful tool in determining the probability of cancer more accurately and it is widely used in healthcare..

[Audio] We will discuss the terms probability of hypothesis A when evidence B has occurred likelihood prior probability and marginal probability. These four terms are essential in probabilistic reasoning which is a fundamental concept in artificial intelligence and machine learning. Students in higher education should have a solid understanding of these concepts in order to better understand the algorithms and models that we use to make predictions and decisions. As a teacher it is important to ensure that your students have a solid understanding of these concepts..

[Audio] Bayes' rule is a powerful tool for probabilistic reasoning especially in higher education. It allows us to calculate the probability of an event B given that event A has occurred. This is done by taking into account the probability of event A given event B the probability of event B and the probability of event A For example suppose we want to determine the probability of a certain cause given an observed variable. Bayes' rule can be used to calculate this probability. By using Bayes' rule we can determine the probability of the unknown cause given the observed variable. In summary Bayes' rule is a valuable tool for probabilistic reasoning in higher education. It can be applied in many different contexts to determine the probability of unknown variables given observed variables..

[Audio] In this example we will calculate the probability of a patient having meningitis disease based on given data. We will specifically look at the case of a patient with meningitis disease and a stiff neck. We will calculate the probability that a patient has meningitis disease and a stiff neck using Bayes' theorem..

[Audio] We will present Example-2 which involves drawing a single card from a standard deck of playing cards. The probability of drawing a king card is 4/52. However we want to calculate the posterior probability P(King|Face) which means that the drawn face card is a king card. To calculate this probability we need to consider the prior probability of drawing a king card which is 0 since we don't have any information about the card before it is drawn. We also need to consider the likelihood of drawing a face card given that the card is a king which is 1 since a king is always a face card. Finally we need to divide the likelihood by the total number of possible outcomes which is 52 to get the posterior probability. P(King|Face) = (1 x 4/52) / 52 = 2/52 = 1/26 = 0.0385 Therefore the posterior probability of drawing a king card given that the card is a face card is 0.0385 or approximately 0.0385..

[Audio] Probability of card being King is 1/13. Probability of card being Face card is 3/13..

[Audio] Discuss Bayes' theorem in artificial intelligence and how it is used to calculate the next step of a robot. Explore Bayes' theorem in weather forecasting and the Monty Hall problem. By the end of discussion you should understand Bayes' theorem's role in artificial intelligence..

[Audio] Bayesian networks are a way to represent variables and their relationships using a directed acyclic graph. They are used for predicting and detecting anomalies. They are based on probability because they are constructed from a probability distribution..

[Audio] * Bayesian Networks are a powerful tool for building models from data and expert opinions. They consist of a Directed Acyclic Graph and a table of conditional probabilities. These components work together to allow Bayesian Networks to represent and solve decision problems under uncertain knowledge. * The generalized form of Bayesian Network known as an Influence diagram provides even more flexibility and can be used to model a wide range of complex decision problems. * Bayesian Networks can offer something to data scientists experts in various fields and those seeking to make more informed decisions..

[Audio] Bayesian Networks represent random variables which can be continuous or discrete and use directed arrows between nodes to represent conditional probabilities. This allows for complex relationships between variables to be easily modeled and reasoned about. Bayesian networks are popular for decision making and natural language processing due to their ability to model and reason about uncertainty..

[Audio] today we will discuss probabilistic reasoning in the context of artificial intelligence and machine learning. We will examine the relationship between nodes in a network graph and how this information can be used to make predictions and decisions. Let's start by taking a closer look at the nodes. There are four nodes represented in the network graph: A B C and D Each node is a random variable. Next let's examine the directed links between the nodes. The directed links represent the influence one node has on another node. In this case node B is connected with node A by a directed arrow which means that node A is the parent of node B It's important to note that node C is independent of node A This means that the value of node C does not depend on the value of node A Overall this network graph provides us with valuable information about how nodes are related and can be used to make predictions and decisions. We will explore this concept further in the coming slides..

[Audio] We will discuss the joint probability distribution..

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[Audio] The alarm has been installed at Harry's home. The alarm responds to detecting a burglary but also responds to minor earthquakes. Harry's two neighbors David and Sophia are responsible for informing him at work when they hear the alarm. David always calls Harry when he hears the alarm but sometimes he gets confused with the phone ringing and calls at that time too. On the other hand Sophia likes to listen to high music so sometimes she misses to hear the alarm. We compute the probability of a burglary using Bayesian network. By computing the probability of the random variable given the evidence we can determine the likelihood of a burglary occurring. Bayesian networks are widely used in various fields including artificial intelligence and machine learning. They provide a powerful tool for reasoning about uncertainty and making predictions based on available evidence..

[Audio] We need to identify all of the events in this network. These events include Burglary (B) Earthquake(E) Alarm(A) David Calls(D) and Sophia Calls(S)..

[Audio] Discuss the results of our probabilistic reasoning model on the given data. We can see from the table that the model predicts that a burglary is the most likely event to occur with a probability of 0.998. This means that there is a 99.8% chance that a burglary will occur. The model also predicts that an alarm will occur with a probability of 0.999 meaning that there is a 99.9% chance that an alarm will occur. These results show the effectiveness of our probabilistic reasoning model in predicting events with high accuracy. It is important to note that these predictions are based on the given data and may not necessarily reflect real-world scenarios. As a result further testing and validation of the model is necessary to ensure its reliability..

[Audio] We use probabilities to determine the likelihood of certain events occurring. These probabilities are critical in various fields such as insurance and finance..

[Audio] Examine the conditional probability table for Alarm A and the correlation between Alarm A and two events: Burglar and Earthquake. This table will help us improve our decision-making and predictive abilities concerning Alarm A's probability of activation..

[Audio] Conditional probability tables are a vital resource for individuals working in artificial intelligence and machine learning. By utilizing a conditional probability table one can determine the likelihood of an event occurring under specified conditions. The table offers a straightforward and systematic way to depict the interrelationships between various events and variables..

[Audio] We will discuss conditional probability tables. We will discuss conditional probability tables. We will discuss conditional probability tables. We will discuss conditional probability tables. We will discuss conditional probability tables. We will discuss conditional probability tables. We will discuss conditional probability tables. We will discuss conditional probability tables..

34. Thank you.