CS3491 – ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING

[Audio] We will discuss probabilistic reasoning techniques for managing uncertainty including Bayesian inference naïve Bayes models Bayesian networks exact inference in Bayesian networks approximate inference in Bayesian networks causal networks and the importance of probability theory in uncertainty handling. We will also examine sources of uncertainty in the real world and the role of probabilistic reasoning in addressing these uncertainties. By the end of this presentation you will have a better understanding of how to apply probabilistic reasoning in your own work in artificial intelligence and machine learning. Therefore let us proceed!.

[Audio] Probabilistic reasoning is a fundamental concept in this field. In this topic we will discuss various methods for acting under uncertainty including Bayesian inference and naïve Bayes models. We will also examine Bayesian networks and the exact and approximate inference methods used within them. Lastly we will delve into causal networks which are used to represent relationships between variables in a probabilistic context. By mastering these probabilistic reasoning techniques you will be better prepared to handle problems in artificial intelligence and machine learning..

[Audio] Uncertainty and ignorance are two different concepts. Uncertainty refers to situations where information is incomplete or unknown. However uncertainty is not a straightforward concept without a description. It can arise due to incompleteness or incorrectness in agents understanding the environment. To represent uncertain knowledge uncertain reasoning or probabilistic reasoning is necessary. In this presentation we will discuss the different types of probabilistic reasoning and their applications..

[Audio] Agents in complex or uncertain environments cannot find definitive answers.

[Audio] Probability theory can summarize uncertainty caused by our laziness and ignorance. Probability statements have no evidence semantics so it can help in making better decisions and predictions..

[Audio] We use probability theory and logic to manage uncertainty in higher education. Some individuals may approach probabilistic reasoning sluggishly or with ignorance but we use probability to handle this uncertainty. Probability is a crucial tool for anyone seeking to comprehend artificial intelligence and machine learning..

[Audio] Probabilistic reasoning is a way of using uncertain knowledge to solve problems. It's especially useful when there are unpredictable outcomes when specifications or possibilities of predicates becomes too large to handle or when an unknown error occurs during an experiment. There are two main ways to solve problems with uncertain knowledge using probabilistic reasoning: Bayes' rule and Bayesian Statistics. These methods allow us to make predictions and make decisions based on the available data even when we don't have all the information we need. Understanding the basics of probabilistic reasoning is important if you're working with (A-I ). It's a powerful tool that can help you make more informed decisions and solve complex problems..

[Audio] Probability is a measure of the likelihood that an uncertain event will occur. It is defined as the numerical measure of the likelihood that an event will occur. The value of probability always remains between 0 and 1 representing ideal uncertainties..

[Audio] We can define an event as a possible outcome of a variable. For example a coin can have two events: heads or tails. The sample space is the collection of all possible events. For example the sample space of a coin can be heads and tails. Random variables are used to represent events and objects in the real world. For example a person's height can be a random variable. Prior probability is the probability computed before observing new information. It is a way of making a guess or prediction about the likelihood of an event happening. Posterior probability is the probability that is calculated after all evidence or information has taken into account. It is a combination of prior probability and new information. For example if we knew that the coin was fair the prior probability of heads would be 0.5 and the prior probability of tails would also be 0.5. If we flip the coin and get heads the posterior probability of heads would be 0.5 but the posterior probability of tails would now be 0..

[Audio] We will discuss the concept of conditional probability in probability theory. Conditional probability is the probability of an event occurring under specific conditions. For example if we want to determine the probability of a person going to the doctor based on whether they have a fever we would use conditional probability. We can calculate the probability of a person going to the doctor given that they have a fever using the formula: P(A⋀B) = P(A and B) / P(B) where P(A⋀B) denotes the probability of A given B P(A) denotes the probability of A and P(B) denotes the probability of B This formula enables us to determine the probability of an event occurring under specific circumstances which is useful in many scenarios..

[Audio] We need to understand how to calculate the probability of an event given that another event has a probability. This can be done using the formula: P(A⋀B) = P(A) * P(B|A) / P(B). This formula involves representing A and B as sets using Venn diagrams. If event B happens the sample space is decreased to set B and we can calculate the probability of event A given that event B has already occurred by dividing P(A⋀B) by P(B). This is an essential concept in probabilistic reasoning and is widely used in many areas such as machine learning and artificial intelligence..

[Audio] Discuss the topic of probabilistic reasoning..

[Audio] Bayes' theorem establishes a relationship between the conditional probability and marginal probabilities of two random events. Through Bayesian inference we can calculate the probability of an event with uncertain knowledge. With this knowledge we can update our probability prediction of an event by observing new information from the real world..

[Audio] Bayes' theorem is a tool that calculates the probability of an event occurring based on prior knowledge and observed evidence. In the context of cancer diagnosis Bayes' theorem can be used to calculate the probability of a person having cancer given their age and other relevant information. Using Bayes' theorem doctors can make more accurate diagnoses and provide more effective treatment options. To calculate the probability of cancer using Bayes' theorem we need to know the prior probability of having cancer which is often estimated based on age and other risk factors. We also need to know the conditional probability of having cancer given age and other relevant information. Once we have these probabilities we can use Bayes' theorem to calculate the posterior probability of having cancer which represents the updated probability of having cancer based on the observed evidence. This posterior probability can be used to inform treatment decisions and guide patient care. In summary Bayes' theorem is a powerful tool that can be used to accurately determine the probability of cancer diagnosis. By using this theorem we can provide more effective treatment options and improve patient outcomes..

[Audio] Posterior probability is the probability of hypothesis A given evidence B It is calculated as P(A|B) = P(B|A) \* P(A) / P(B). This means that we calculate the probability of hypothesis A given evidence B by considering both the probability of evidence B given hypothesis A and the prior probability of hypothesis A Likelihood is the probability of evidence B given that hypothesis A is true and is calculated as P(B|A). Understanding these concepts is essential for developing effective probabilistic models in artificial intelligence and machine learning..

[Audio] Bayes' rule is a fundamental concept in probabilistic reasoning. It enables us to compute the probability of an event given some evidence particularly useful when we have good probability of the evidence. In the context of perception Bayes' rule enables us to determine the cause of some unknown event by using the evidence of the effect such as computing the probability that the cause of a tree falling in a forest was a lightning strike. Bayes' rule is a powerful tool in artificial intelligence and machine learning with many applications..

[Audio] We will discuss example-1 which looks at the probability of a patient having meningitis with a stiff neck. Specifically we will examine the probability of a patient having meningitis given that they have a stiff neck. The known probability of a patient having meningitis is 1/30 000 which means that P(a|b) = 0.8 where P(a) is the probability of having meningitis and P(b) is the probability of having a stiff neck. Therefore we can conclude that 1 patient out of 750 patients has meningitis with a stiff neck which gives us a probability of 2%. This example is a great way to understand how probability can be used in artificial intelligence. By understanding the probability of certain events happening we can make better decisions and predictions..

[Audio] Consider a standard deck of playing cards where there is a king card in 4 out of 52 cards. Now imagine that a single card is drawn from the deck and it is revealed to be a face card. The probability that the face card is the king card is 4/52 which can be calculated as the ratio of the number of king cards to the total number of cards in the deck. To calculate the posterior probability of the event occurring we use Bayes' theorem which states that P(A|B) = P(B|A) * P(A) / P(B) In this case A represents the event of the face card being the king card and B represents the drawn face card. The probability of the event A occurring is P(A) = 4/52 which is the probability of drawing a king card. The probability of the event B occurring given that A occurs is P(B|A) = 1 which means that if the drawn face card is the king card it is certain that the event B will occur. The probability of the event B occurring is P(B) = P(B|A) * P(A) = 4/52 which is the probability of drawing a face card. Finally we can calculate the posterior probability of the event A occurring given the observed event B as P(A|B) = P(B|A) * P(A) / P(B) = 4/52 * 4/52 / 4/52 = 1 which means that given the observed event B it is certain that the event A occurred. This example demonstrates how to calculate the posterior probability of an event occurring given prior knowledge using Bayes' theorem..

[Audio] 1. Remove the welcome sentences: We will discuss the solution to a problem involving card probabilities. 2. Rewrite the text: We will look at the probability of the card being a King the probability of the card being a face card and the probability of a face card given that it is a King. These probabilities will be calculated using the formula P(A or B) = P(A) plus P(B) P(A and B). We will start by looking at the probability of the card being a King. The probability of a card being a King is 1/13. Next we will look at the probability of the card being a face card. The probability of a card being a face card is 3/13. Finally we will look at the probability of a face card given that it is a King. The probability of a face card given that it is a King is 1. To put all of these values in equation (i) we can use the formula P(A or B) = P(A) plus P(B) P(A and B). This will give us: P(king or face) = 1/13 plus 3/13 0 = 16/13. So the probability of the card being a King or a face card is 16/13..

[Audio] Bayes' theorem is a powerful tool that can be used to calculate the next step of the robot when the already executed step is given. It is particularly useful in weather forecasting where it can help predict the likelihood of certain weather patterns occurring. Additionally Bayes' theorem can be used to solve the Monty Hall problem a classic problem in probability theory. It is also a valuable tool in the field of Artificial Intelligence that can help us make more informed decisions and improve the performance of our machines..

[Audio] Bayesian Networks are a type of probabilistic graphical model that represent a set of variables and their conditional dependencies using a directed acyclic graph. They are also known as belief networks decision networks or Bayesian models. One of the key features of Bayesian networks is that they are probabilistic meaning that they are built from a probability distribution and use probability theory for prediction and anomaly detection. Bayesian networks can be used for tasks such as classification prediction and decision making..

[Audio] Bayesian Networks are a fundamental concept in probabilistic reasoning. They are used for building models from data and expert opinions and consist of two parts: a Directed Acyclic Graph and a Table of conditional probabilities. Bayesian Networks use nodes to represent variables and edges to represent the relationships between them. The Directed Acyclic Graph shows the causal relationships between these variables and the Table of conditional probabilities stores the probability of each variable given its parents allowing to calculate the probability of any variable given its parents useful for making predictions and solving decision problems. Bayesian Networks are a powerful tool for building models in various fields including healthcare finance and engineering and can be used to model complex systems and make decisions based on uncertain knowledge..

[Audio] Today we will discuss Bayesian Networks. Bayesian networks are useful for probabilistic reasoning and can be applied in various fields..

[Audio] We will discuss probabilistic reasoning and its importance in understanding the relationships between random variables represented by nodes in a network graph. We can see from the diagram that there are links between nodes A B C and D and each node represents a random variable. The arrows in the diagram indicate the direction of influence between the nodes. If there is a directed link between nodes A and B then A is considered the parent of B meaning A has an influence on B On the other hand if there is no directed link between A and C then A and C are independent of each other. Understanding these relationships between random variables is crucial in probabilistic reasoning. By analyzing the probabilities of different outcomes we can make predictions and make informed decisions. In summary probabilistic reasoning is an important tool in understanding the relationships between random variables in a network graph. By analyzing the probabilities of different outcomes we can make predictions and make informed decisions..

[Audio] The joint probability distribution in Bayesian networks describes the probability of all possible outcomes of a set of random variables. This distribution is used to determine the probability of each node given its parent nodes. To calculate the joint probability of each node we multiply the condition probability distribution of its parent nodes and the likelihood function of the node. The likelihood function describes the probability of observing the data given the state of the random variable. With the joint probability distribution we can make predictions and perform causality reasoning in Bayesian networks..

[Audio] When we have variables x1 x2 x3 ..... xn the probabilities of different combinations of x1 x2 x3.. xn are known as Joint probability distribution. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities of different combinations of variables when more than one variable is involved. Joint probability distribution is used to determine the probabilities.

[Audio] Discuss Bayesian networks and their real-world applications..

[Audio] The probability that the alarm has sounded is 20.4%..

[Audio] Probabilistic reasoning is a technique used in (A-I ) and ML to make predictions and decisions based on the probability of different outcomes. In the context of (A-I ) and ML probabilistic reasoning can be used to predict the likelihood of different events occurring such as a burglary or an earthquake. The image shows probabilities of different outcomes for various events. In this case the probability of burglary is 0.998 while the probability of earthquake is 0.75. Probabilistic reasoning can also be used to make decisions based on these probabilities such as installing an alarm to prevent burglary. Overall probabilistic reasoning is an important tool in (A-I ) and ML for making predictions and decisions based on the likelihood of different outcomes..

[Audio] Discuss observed probabilities for the Burglary and earthquake components. Examine values of P(B= True) = 0.002 P(B= False)= 0.998 P(E= True) = 0.001 and P(E= False)= 0.999. These probabilities can be used to make predictions and decisions about the potential occurrence of these events..

[Audio] 1. Discuss the conditional probability of Alarm A in the context of burglar and earthquake. 2. 3. Discuss.

[Audio] We will discuss the mathematical concepts behind conditional probability tables. These concepts are widely used in the telecommunications industry. In the context of David calls the random variables are the different events that can occur during a call such as the caller's location the type of call and the duration of the call. The conditional probability table for David calls shows the probabilities of different events occurring given the state of a call. For example the table can show the probability of a call lasting a certain duration given the caller's location. Understanding conditional probability tables is crucial for building accurate and reliable David call models. With conditional probability tables we can make predictions about the likelihood of different events occurring during a call based on the state of the call..

[Audio] The conditional probability table for Sophia Calls shows the probability of Sophia making a specific call based on the presence or absence of certain attributes and conditions. The table includes mutually exclusive attributes such as B and E as well as the probability of Sophia making a call based on the presence or absence of certain conditions such as S and D The table is calculated by multiplying the probabilities of each individual attribute and condition which helps to provide a more accurate representation of Sophia's behavior and decision-making process..

34. Thank you.