Research map / Learning theory and algorithms / Sample complexity
Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Random initialization of EM (initial centers drawn from the mixture) versus converging to global optimum: EM converges to a bad critical point with probability at least 1-e^{-cM} | EM algorithm on population likelihood of well-separated uniform spherical GMM · population GMM, M>=3 components, random initialization | probability of converging to bad critical point | Hurt |
| Gradient-based first-order EM with constant step size s in (0,1) under random initialization | first-order EM on population GMM likelihood · population GMM, M>=3 components, random initialization | probability of converging to bad critical point | Hurt |
| Constant step size first-order EM (s in (0,1)) avoids convergence to strict saddle points | first-order EM on population GMM likelihood · population GMM, random initialization | probability of converging to a strict saddle point | Helped |
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