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| Hamiltonian Monte Carlo z brakującymi danymi× | Wariacyjna inferencja z brakującymi danymi× | |
|---|---|---|
| Dziedzina | Statystyka bayesowska | Statystyka bayesowska |
| Rodzina | Bayesian methods | Bayesian methods |
| Rok powstania≠ | 1996–2011 | 1994–2008 |
| Twórca≠ | Radford M. Neal (HMC, 1996/2011); missing-data treatment via Bayesian data augmentation (Tanner & Wong, 1987) | Ghahramani & Jordan; Wainwright & Jordan (formal foundations) |
| Typ≠ | Bayesian computational sampler | Approximate Bayesian inference |
| Źródło pierwotne≠ | Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In S. Brooks, A. Gelman, G. Jones & X.-L. Meng (Eds.), Handbook of Markov Chain Monte Carlo (pp. 113-162). CRC Press. ISBN: 978-1420079418 | Ghahramani, Z. & Jordan, M. I. (1994). Supervised learning from incomplete data via an EM approach. In Cowan, J. D., Tesauro, G. & Alspector, J. (Eds.), Advances in Neural Information Processing Systems 6 (pp. 120–127). Morgan Kaufmann. link ↗ |
| Inne nazwy | HMC with missing data, HMC data augmentation, Bayesian HMC imputation, HMC with data augmentation | VI with missing data, variational EM with missing data, VB missing data, mean-field VI for incomplete data |
| Pokrewne≠ | 6 | 4 |
| Podsumowanie≠ | Hamiltonian Monte Carlo with missing data extends the gradient-based HMC sampler to handle incomplete observations by treating missing values as additional unknown parameters. The posterior over model parameters and missing values is sampled jointly in one efficient pass, exploiting gradient information to explore the high-dimensional joint space with far fewer rejected proposals than random-walk MCMC. | Variational inference with missing data is a scalable Bayesian approach that simultaneously approximates the posterior over latent variables and model parameters while imputing missing observations. Instead of integrating over all possible values of the missing entries exactly, it posits a tractable approximate distribution and optimises it to be as close as possible to the true joint posterior, yielding fast, principled inference even in high-dimensional incomplete datasets. |
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