Bayesian Networks: A Clear and Practical Introduction

Bayesian Networks: A Clear and Practical Introduction

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  BAYESIAN NETWORK Presented by Presentedto Nusrat -E- Fariya Silvia Sifath Tasmia Chowdhury Trust University, Barishal page 1
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  Bayesian Network "A BayesianNetwork (BN) is a probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG)." Rain Sprinkler Grass Wet Wet Ground Rain Car Wash Slip page 2
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  There are twobasic types of Bayesian network models for dynamic processes: • State based • Event based State based models represent the state of each variable at discrete time intervals, so that the networks consist of a series of time slices, where each time slice indicates the value of each variable at time t - Dynamic Bayesian Networks Event based models represent the changes in state of each state variable; each temporal variable will then correspond to the time in which a state change occurs - event networks or temporal networks. Bayesian Network Model 1 2 3 4 page 3
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  1. Nodes (Variables): Eachnode represents a random variable. It may be discrete (e.g., “Rain: Yes/No”) or continuous. 2. Edges (Directed): A link between nodes A B means that A directly influences B, → in probabilistic terms. 3. Conditional Probability Tables (CPTs): Each node has an associated CPT if it is discrete (or conditional probability density if continuous) that specifies the probability of the node given the states of its parent nodes. Structure of a Bayesian Network A B C D page 4
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  Rain Sprinkler Grass Wet Rain R 0.2 0.8 ~R Sprinkler S 0.4 0.6 ~S F T0.01 0.99 Grass Wet W 0.0 1 ~W ~R R 0.8 0.2 ~S 0.6 0.99 ~R R ~S S S 0.1 0.01 Visual Example of a Simple Bayesian Network: Rain page 5
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  Conditional Probability P(A|B) =(P(B|A) × P(A)) / P(B) [Baye’s Theorem] P(W,S,R ) P(W S R) = P(W/S,R) × P(S/R) × P(R) ∩ ∩ = 0.99 × 0.01 × 0.2 = 0.00198 P(W,~S,~R) P(W ~S ~R) = P(W/~S,~R) × P(~S/~R) × P(~R) ∩ ∩ = 0 × 0.6 × 0.8 = 0 Rain Sprinkler Grass Wet page 6 https://youtu.be/DVnubVOjZtg?si=CmY-WcXv2sh4GL- J
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  Real-World Applications ofBayesian Networks The Bayesian framework, with its ability to incorporate prior knowledge and quantify uncertainty, has found broad application across diverse fields. Its flexibility makes it a powerful tool for complex, real-world problems. Robots and intelligent agents use BNs to make decisions in uncertain environments (e.g., reasoning about unseen obstacles). Applied to gene regulatory networks, protein interactions, and genetic disorder analysis to capture complex biological dependencies. Search engines and recommender systems employ BNs to personalize results based on observed user behavior and inferred preferences. In finance, insurance, and engineering, BNs predict risks, system failures, or investment outcomes by integrating multiple uncertain factors. Robotics and AI Bioinformatics Web Search & Recommendation Risk & Decision Support Medical Diagnosis Fault Diagnosis and Monitoring In manufacturing, aerospace, and IT, BNs predict equipment failures or system faults in advance using sensor data and maintenance logs. Used to model disease–symptom relationships, helping doctors reason probabilistically when not all data is available (e.g., “What is the probability a patient has disease X given symptoms Y and Z?”). page 7
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  Challenges and Limitations Despitetheir strengths, Bayesian Networks present several challenges: Structure Identification: Complexity in Inference: Data Requirements: Learning the optimal structure from data can be computationally intensive, particularly as the number of variables increases. Exact inference is often NP-hard for large, densely-connected networks, making it impractical in some real-world scenarios. BNs require significant amounts of data to accurately estimate parameters, especially when variables have many discrete states. Sensitivity to Model Misspecification: Assumption of Acyclicity: Data Scarcity & Quality Issues BNs do not allow cycles in the graph, which limits modeling feedback loops unless reformulated. Incorrect dependencies can spread errors or mislead results, requiring domain expertise or hybrid methods to overcome. Scarce, noisy, or incomplete data can lead to unreliable probabilities and weaken predictive power. page 8
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  Dynamic Bayesian networks DynamicBayesian networks (DBNs) are an extension of Bayesian networks to model dynamic processes A DBN consists of a series of time slices that represent the state of all the variables at a certain time, t For each temporal slice, a dependency structure between the variables at that time is defined, called the base network Additionally, there are edges between variables from different slices, with their directions following the direction of time, defining the transition network Dynamic Bayesian Networks are used for varied domains with the implementation of time steps at different states. Three types of reasoning processes where they are used are - Causal Reasoning Diagnostic Reasoning Mixed Reasoning. page 9
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  Types of Inference Predictcurrent state based on past observations page 11 1. Filtering Inference in Dynamic Bayesian Networks (DBNs) refers to estimating hidden states or predicting future states based on observed data over time. There are four main types; Predict future states based on past observations. 2. Prediction Estimate current states using both past and future observations 3. Smoothing Find the most likely sequence of hidden states given all observations. 4. Decoding
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  How does aDynamic Bayesian Networks Works They contain multi variable nodes and it is useful as it makes use of temporal nodes as a simplified structure, and makes inference faster, also easier implementation.They model events that include both, temporal and ambient aspects. It consists of a series of time slices that represent the state of all the variables at a certain time t, and for each temporal slice a dependency structure between the variables at that time is the base network. Hence, There are edges between varaibles from different slices, with their direcitons following the direction of time, which defines the transition network. The state variables at time t depend only on the state variables at time t- 1 and the other variables at time t and the structure and parameters of the model do not change over time. While making inference, we consider different cases as follows -> Filtering is where we predict the next state based on past observations, Prediction is that type of inference where we predict the future states based on the past observations Two other types of inferences that we consider would be of Smoothing where we estimate the current state based on past and future observations which comes in very handy for models based on learning, and the other type of inference is Decoding where we find the most likely sequence of hidden variables given the observations, page 10
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  Choosing the RightModel Use a Bayesian Network (BN) when: • The relationships in your problem domain are static—they do not change or repeat over time. • You're interested in probabilistic reasoning or diagnosis based on a “snapshot” of information. • You want a compact, interpretable model, and your data is not sequential in nature. Use a Dynamic Bayesian Network (DBN) when: • The problem is explicitly time-dependent—states or observations naturally form a sequence. • You require temporal prediction, filtering, or smoothing (e.g., tracking an object over time). • You're modeling systems where present states depend on past states (e.g., speech, video, industrial monitoring). page 12
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  Thank You!