Estimation of Gaussian mixture models via tensor moments with application to online learning
| Autor: | Akiko Takeda, Damien Fay, Donya Rahmani, Mahesan Niranjan, Jacek Brodzki |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Covariance matrix
Computer science MathematicsofComputing_NUMERICALANALYSIS 02 engineering and technology Method of moments (statistics) Mixture model 01 natural sciences Moment (mathematics) Artificial Intelligence 0103 physical sciences Signal Processing 0202 electrical engineering electronic engineering information engineering Benchmark (computing) Applied mathematics 020201 artificial intelligence & image processing Computer Vision and Pattern Recognition Tensor 010306 general physics Gradient descent Software Second derivative |
| Popis: | In this paper, we present an alternating gradient descent algorithm for estimating parameters of a spherical Gaussian mixture model by the method of moments (AGD-MoM). We formulate the problem as a constrained optimisation problem which simultaneously matches the third order moments from the data, represented as a tensor, and the second order moment, which is the empirical covariance matrix. We derive the necessary gradients (and second derivatives), and use them to implement alternating gradient search to estimate the parameters of the model. We show that the proposed method is applicable in both a batch as well as in a streaming (online) setting. Using synthetic and benchmark datasets, we demonstrate empirically that the proposed algorithm outperforms the more classical algorithms like Expectation Maximisation and variational Bayes. |
| Databáze: | OpenAIRE |
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