Explore foundational concepts of probabilistic reasoning with a focus on Bayesian Networks and Markov Models. This quiz covers key terms, structural principles, and real-world examples relevant to inference and uncertainty in artificial intelligence.
What is the primary structure of a Bayesian Network used for representing probabilistic relationships among variables?
Explanation: A Bayesian Network is structured as a directed acyclic graph (DAG), where nodes represent variables and directed edges represent probabilistic dependencies. An undirected cyclic graph is characteristic of Markov networks, not Bayes nets. A linear sequence does not capture complex dependencies, and a hierarchical tree is more restrictive than required for Bayes nets.
In a Bayes Net modeling three variables A, B, and C where A points to B and B points to C, which statement about independence is generally true?
Explanation: In this configuration, A and C are conditionally independent given B due to the Markov property. B and C are only dependent through the network, so ‘always independent’ is inaccurate. A and B are not independent given C in this structure. C and A are not always dependent; their dependency is influenced by B.
Which phrase best describes the Markov property in the context of Markov Models, such as Markov Chains?
Explanation: The Markov property asserts that the future is independent of the past given the present state, meaning future states depend only on the current state. States are not all interconnected directly; transitions typically occur between adjacent states. The next state does not depend on both past and present states nor does the initial state alone predict all futures.
If weather is a hidden variable and observed data is whether someone carries an umbrella, what kind of probabilistic model is suitable for this scenario?
Explanation: A Hidden Markov Model (HMM) is well-suited for problems where the underlying state (the weather) is hidden and we observe related signals (carrying an umbrella). Logistic Regression and Decision Trees do not naturally model sequential hidden states. A Naive Bayes Classifier ignores dependencies between sequential states, so it is less appropriate here.
What is the main goal when performing inference in a Bayesian Network?
Explanation: Inference in a Bayesian Network is primarily about calculating conditional probabilities given certain observations. Building an undirected model is not the focus of Bayes nets. Increasing node numbers is not an objective, and it is common for many nodes to be unobserved in real applications.
Which of the following situations can best be modeled by a Markov Chain?
Explanation: Markov Chains are suited for systems where the next state depends only on the current state, as in modeling sleep transitions hour by hour. Relating age and height is not a sequential state problem. Image classification and tracking multiple people require more complex models than a simple Markov Chain.
What does Bayes' Rule enable you to compute in the context of Bayesian Networks?
Explanation: Bayes' Rule is used for updating and calculating posterior probabilities in light of new evidence. Shortest paths and spanning trees are concepts from graph algorithms, not from probabilistic inference. Maximum likelihood estimation is a broader statistical concept and not the specific result of applying Bayes' Rule.
What information is stored in the transition matrix of a Markov Model?
Explanation: A transition matrix contains probabilities for transitioning from one state to another in a Markov Model. It does not define what each state means (state variable definitions). Initial observations are separate from the transition matrix, and posterior probabilities are computed afterward using the model.
How does a Naive Bayes classifier differ from a general Bayesian Network?
Explanation: Naive Bayes classifiers make the simplifying assumption that all features are conditionally independent given the class label. They do not use undirected edges—that describes Markov Models. Naive Bayes does not model time-dependence, and it does not explicitly represent all possible dependencies among variables.
Which is a typical real-world application of a Bayesian Network?
Explanation: Bayesian Networks are commonly used for diagnosis, such as inferring disease likelihoods from observed symptoms. Image compression and sorting are unrelated to probabilistic graphical models. Predicting chemical bond strength might use other modeling techniques, but is not a standard use case for Bayes nets.