CS 5313/7313: Advanced AI Probabilistic Reasoning over time The problems in this set will require you to implement algorithms, collect test/training data, and report analysis of experimental results1. Submit code, data, and reports with detailed analysis and supporting documentation including graphs and tables as necessary. Hidden Markov Models (HMMs): Solve Exercise 15.13 and develop an HMM model. You will also implement the following algorithms: • exact HMM smoothing algorithm using constant space, the forward-backward Country-Dance algorithm, and • the online fixed-lag smoothing algorithm in Figure 15.6, • the most likely sequence of states, using the Viterbi algorithm. You will use these algorithms to compute the state estimation, smoothing, and fixed- lag smoothing (report results from lag values over the range [2,5]) probabilities for the scenarios in Exercise 15.14 but for all t ∈ {1 . . . 25}. Dynamic Bayesian Networks (DBN): For the domain presented in Figure 15.7, con- sider the DBN formulation where each state consists of a 〈location, direction〉 pair which results in a state space size of 42 = 168. Use the environment simulator pro- vided to obtain the sequence of observations. Implement the the particle filtering algorithm (Figure 15.17) for approximate inference in DBNs and compute the filtering probabilities of the posterior distribution of the robot state from observations received for each time step t = [1, . . . , 100]. 1Numbered exercises are from the Russell & Norvig textbook (3rd Edition). 1
