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Approximate inference in machine learning refers to the process of estimating complex probabilistic models when exact inference is computationally intractable. Many machine learning models involve dealing with probability distributions over a large number of variables, and computing the exact posterior distribution can be challenging or impossible due to the complexity of the model. In cases where exact inference is too computationally expensive or impractical, approximate inference methods are used to provide a close approximation of the true posterior distribution. These methods trade accuracy for computational efficiency, allowing practitioners to make reasonable approximations and gain insights into the model's behavior. 

Some common techniques for approximate inference include: 

1. Variational Inference: 

   This approach formulates the inference problem as an optimization problem, where the goal is to find a simpler distribution that is close to the true posterior. Variational methods aim to minimize the divergence between the true distribution and the approximating distribution. 

2. Monte Carlo Methods: 

   Monte Carlo methods use random sampling to estimate complex integrals or expectations. Markov Chain Monte Carlo (MCMC) is a popular technique that generates a Markov chain whose stationary distribution is the target posterior distribution. 

3. Expectation-Maximization (EM): 

   EM is an iterative optimization algorithm used to find maximum likelihood estimates of parameters in the presence of latent variables. It alternates between the E-step (expectation), where the expected values of the latent variables are computed given the observed data and current parameter estimates, and the M-step (maximization), where the parameters are updated to maximize the expected log-likelihood. 

4. Sampling Methods: 

   Various sampling methods, such as importance sampling, rejection sampling, and Gibbs sampling, are employed to draw samples from the posterior distribution, facilitating the estimation of desired quantities. 

These methods allow practitioners to make probabilistic inferences even when exact solutions are challenging. The choice of the approximate inference method depends on the specific characteristics of the model and the computational resources available. 

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