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What is latent variable in EM algorithm?
Joint probability model parameterized by θ ∈ Θ: p(x,z | θ) Definition A latent variable model is a probability model for which certain variables are never observed. e.g. The Gaussian mixture model is a latent variable model.
What is the role of e step in EM algorithm?
The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step.
What is a latent variable machine learning?
Latent variable models aim to model the probability distribution with latent variables. Latent variables are a transformation of the data points into a continuous lower-dimensional space. Intuitively, the latent variables will describe or “explain” the data in a simpler way.
Which is the first mode of the EM algorithm?
The first mode attempts to estimate the missing or latent variables, called the estimation-step or E-step. The second mode attempts to optimize the parameters of the model to best explain the data, called the maximization-step or M-step. E-Step.
If you think of an image (ex. human face) as the observed variable x then, the latent variable z could encode the features of the face (which are not seen during training), like it can encode whether the face is happy or sad, male or female etc. LVMs can also help us to deal with missing data. The previous point and this one are related.
What is exp 3 for latent variable mixing coefficients?
Exp 3: Marginal distribution over latent variable. Now the mixing coefficients and latent variables z, all fall into a place when we consider the marginal distribution over z is specified in terms of the mixing coefficients as defined in the expression above.
How is the expectation maximization algorithm used in machine learning?
The Expectation-Maximization Algorithm, or EM algorithm for short, is an approach for maximum likelihood estimation in the presence of latent variables. A general technique for finding maximum likelihood estimators in latent variable models is the expectation-maximization (EM) algorithm. — Page 424, Pattern Recognition and Machine Learning, 2006.