

![0_image_0.png](0_image_0.png)

outlier detection mechanism, each switch i k  is a binary indicator variable specifying whether the onset yk is an outlier or not. We assume that all indicators are independent a-priori and have a uniform prior. The observation model is given by p( yk | ik, τk ) = N (0, R ik ) °.

Since the score γ 1 : κ is known, the only unknown discrete quantities are the indicators i 0 : κ . We have used greedy filtering followed by iterative improvement to find the MAP state of indicators io: K and eliminated outliers in our further studies. For many performances, there were around 2 - 4 outliers, less than 1% of all the notes. The resulting dataset can be downloaded from the url http://www.snn.kun.nl/~cemgil .

## 4.2.2 Parameter Estimation

We have trained tempo tracking models with different dimensionality D , where D denotes the dimension of the hidden variable z . In all of the models, we use a transition matrix that has the form in Eq. 8.

Since the true score is known, i.e., the quantization location ck of ea onset yk is given, we can clamp all the discrete variables in the model. Consequently, we can estimate the observation noise variance R, the transition noise variance Q and the transition matrix coefficients A from data.

We have optimized the parameters by Expectation-Maximization (EM) for the linear dynamical systems (Shumway & Stoffer, 1982; Ghahramani & Hinton, 1996) using all perfor-