docfix aressler38

doc/user_guide.rst

@@ -15,7 +15,7 @@ Learning multivariate sequential data with the sliding window method is useful i
 Time Series Data
 ----------------
 
-Sequence and time series data have a general formulation as sequence pairs :math:`\{(\mathbf{X}_i,\mathbf{y}_i)\}_{i=1}^{N}`, where each :math:`\mathbf{X}_i` is a multivariate sequence with :math:`T_i` samples :math:`\langle \mathbf{x}_{i,1}, \mathbf{x}_{i,2},...,\mathbf{x}_{i,T_i} \rangle` and each :math:`\mathbf{y}_i` target is a univariate sequence with :math:`T_i` samples :math:`\langle \mathbf{x}_{i,1}, \mathbf{x}_{i,2},...,\mathbf{x}_{i,T_i} \rangle`. The targets :math:`\mathbf{y}_i` can either be sequences of categorical class labels (for classification problems), or sequences of continuous data (for regression problems). The number of samples :math:`T_i` varies between the sequence pairs in the data set. Time series' with a regular sampling period may be treated equivalently to sequences. Irregularly sampled time series are formulated with an additional sequence variable :math:`\mathbf{t}_i` that increases monotonically and indicates the timing of samples in the data set :math:`\{(\mathbf{t}_i, \mathbf{X}_i,\mathbf{y}_i)\}_{i=1}^{N}`.
+Sequence and time series data have a general formulation as sequence pairs :math:`\{(\mathbf{X}_i,\mathbf{y}_i)\}_{i=1}^{N}`, where each :math:`\mathbf{X}_i` is a multivariate sequence with :math:`T_i` samples :math:`\langle \mathbf{x}_{i,1}, \mathbf{x}_{i,2},...,\mathbf{x}_{i,T_i} \rangle` and each :math:`\mathbf{y}_i` target is a univariate sequence with :math:`T_i` samples :math:`\langle y_{i,1}, y_{i,2},...,y_{i,T_i} \rangle`. The targets :math:`\mathbf{y}_i` can either be sequences of categorical class labels (for classification problems), or sequences of continuous data (for regression problems). The number of samples :math:`T_i` varies between the sequence pairs in the data set. Time series' with a regular sampling period may be treated equivalently to sequences. Irregularly sampled time series are formulated with an additional sequence variable :math:`\mathbf{t}_i` that increases monotonically and indicates the timing of samples in the data set :math:`\{(\mathbf{t}_i, \mathbf{X}_i,\mathbf{y}_i)\}_{i=1}^{N}`.
 
 Important sub-classes of the general sequence learning problem are sequence classification and sequence prediction. In sequence classification problems (eg song genre classification), the target for each sequence is a fixed class label :math:`y_i` and the data takes the form :math:`\{(\mathbf{X}_i, y_i)\}_{i=1}^{N}`. Sequence prediction involves predicting a future value of the target :math:`(y_{i,t+f})` or future values :math:`\langle y_{i,t+1}, y_{i,t+2},..., y_{i,t+f} \rangle`, given :math:`\langle \mathbf{x}_{i,1}, \mathbf{x}_{i,2},...,\mathbf{x}_{i,t} \rangle, \langle y_{i,1}, y_{i,2},..., y_{i,t} \rangle`, and sometimes also :math:`\langle \mathbf{x}_{i,t+1}, \mathbf{x}_{i,t+2},...,\mathbf{x}_{i,t+f} \rangle`.