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Inference algorithms are computational procedures used to derive new information, conclusions, or predictions from existing data and models, often involving probabilistic or statistical techniques. They play a crucial role in machine learning, enabling systems to make decisions or understand patterns from inputs without explicit programming.
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Probabilistic Graphical Models (PGMs) are a rich framework for encoding probability distributions over complex domains using graphs to represent the conditional dependencies between random variables. They combine the strengths of probability theory and graph theory to provide a compact and intuitive representation of joint probability distributions, enabling efficient inference and learning in large-scale systems.
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Bayesian inference is a statistical method that updates the probability of a hypothesis as more evidence or information becomes available, utilizing Bayes' Theorem to combine prior beliefs with new data. It provides a flexible framework for modeling uncertainty and making predictions in complex systems, often outperforming traditional methods in scenarios with limited data or evolving conditions.
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Monte Carlo Methods are a class of computational algorithms that rely on repeated random sampling to obtain numerical results, often used to model phenomena with significant uncertainty in inputs. These methods are widely used in fields such as finance, physics, and engineering to simulate complex systems and evaluate integrals or optimization problems where analytical solutions are difficult or impossible to obtain.
The Expectation-Maximization (EM) Algorithm is an iterative method used to find maximum likelihood estimates of parameters in statistical models with latent variables. It alternates between estimating the expected value of the latent variables (E-step) and maximizing the likelihood function given these expectations (M-step), improving the parameter estimates with each iteration until convergence.
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Markov Chain Monte Carlo (MCMC) is a class of algorithms used to sample from probability distributions by constructing a Markov Chain that has the desired distribution as its equilibrium distribution. It is particularly useful in Bayesian statistics and computational physics for approximating complex integrals and distributions that are difficult to compute directly.
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Variational inference is a technique in Bayesian statistics that approximates complex posterior distributions through optimization, offering a scalable alternative to traditional sampling methods like Markov Chain Monte Carlo. It transforms the inference problem into an optimization problem by introducing a family of simpler distributions and finding the closest match to the true posterior using the Kullback-Leibler divergence.
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Belief propagation is an algorithm used for performing inference on graphical models, such as Bayesian networks and Markov random fields, by iteratively updating and passing messages between nodes. It is particularly effective for computing marginal distributions and finding the most probable configurations in tree-structured graphs, but can also be applied to loopy graphs with approximate results.
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Conditional Random Fields (CRFs) are a type of probabilistic graphical model used for structured prediction, where the goal is to predict a sequence of labels for a sequence of input data. Unlike Hidden Markov Models, CRFs model the conditional probability of the label sequence given the input sequence, allowing them to relax independence assumptions and incorporate a wide range of contextual information.
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Hidden Markov Models (HMMs) are statistical models that represent systems with unobservable (hidden) states through observable events, using probabilities to model transitions between these states. They are widely used in temporal pattern recognition, such as speech, handwriting, gesture recognition, and bioinformatics, due to their ability to handle sequences of data and uncover hidden structures.
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Neural networks are computational models inspired by the human brain, designed to recognize patterns and solve complex problems by learning from data. They consist of interconnected layers of nodes, or 'neurons', that process input data and iteratively adjust their weights to minimize error and improve accuracy.
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Conditional Random Fields (CRFs) are a type of discriminative probabilistic model used for structured prediction, especially in sequence labeling tasks where context is important. They model the conditional probability of a label sequence given an observation sequence, capturing dependencies between labels using undirected graphical models, which allows them to consider the entire input sequence for each prediction.
Conditional Random Fields (CRFs) are a class of statistical modeling methods used for structured prediction, particularly in sequence data, where they model the conditional probability of a label sequence given an observation sequence. Unlike Hidden Markov Models, CRFs are discriminative models that do not assume independence between observations, allowing them to capture complex dependencies in the data.
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Markov Networks, also known as Markov Random Fields, are graphical models used to represent the joint distribution of a set of variables. Unlike Bayesian Networks, they use undirected graphs to encode the dependencies, which makes them particularly useful for modeling scenarios where the direction of causality is not of interest or undetermined.
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Clique potentials are functions defined on subsets of variables, usually called cliques, in probabilistic graphical models. They represent local coherence or compatibility among the variables within a clique, influencing the joint distribution over the entire set of variables in the model.
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In the context of probabilistic graphical models, a factor node is a component of a factor graph that represents a relationship or constraint among a set of variables. They are crucial for performing calculations in inference algorithms, such as message passing, by connecting variable nodes through factors that capture joint probabilities or functions over these variables.
Probabilistic Graphical Models (PGMs) are frameworks that leverage graph theory to succinctly capture the complex dependencies among random variables in probabilistic systems. By using nodes to represent variables and edges to depict conditional dependencies, PGMs enable efficient computation and inference, making them invaluable in domains such as machine learning, natural language processing, and computer vision.
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