Say we have a problem where we need to learn a function:

$f(\mathbf{x} \in \mathbf{R}^p) \rightarrow \mathbf{y} \in \mathbf{R}^q$

where $\mathbf{x}$ and $\mathbf{y}$ are vectors representing time series.

We have multiple examples of this mapping, i.e.:

$$\begin{pmatrix}\mathbf{x_0}\\...\\\mathbf{x_N}\end{pmatrix}\rightarrow \begin{pmatrix}\mathbf{y_0}\\...\\\mathbf{y_N} \end{pmatrix} $$

What type of problem is this? Is it a regression problem? If so, what metrics (loss functions) and methods would be appropiate for this problem? Anything specifically available in Python?

Say we want to learn a function:

$f(\mathbf{x} \in \mathbf{R}^p) \rightarrow \mathbf{y} \in \mathbf{R}^q$

where $\mathbf{x}$ and $\mathbf{y}$ are vectors representing time series.

We have multiple examples of this mapping, i.e.:

$$\begin{pmatrix}\mathbf{x_0}\\...\\\mathbf{x_N}\end{pmatrix}\rightarrow \begin{pmatrix}\mathbf{y_0}\\...\\\mathbf{y_N} \end{pmatrix} $$

What type of problem is this? Is it a regression problem? If so, what metrics (loss functions) and methods would be appropiate for this problem? Anything specifically available in Python?

Say we have a problem where we need to learn a function:

$f(\mathbf{t}_{X} \in \mathbf{R}^N) \rightarrow \mathbf{t_Y} \in \mathbf{R}^M$

where both $\mathbf{t}_x$ and $\mathbf{t}_Y$ are time-series.

We have multiple examples, so we can constuct $X \rightarrow Y$ as:

$$\begin{pmatrix}\mathbf{t}_{X_0}\\...\\\mathbf{t}_{X_N}\end{pmatrix}\rightarrow \begin{pmatrix}\mathbf{t}_{Y_0}\\...\\\mathbf{t}_{Y_N} \end{pmatrix} $$

We can also assume that:

• all $\mathbf{t}_{Xi}$ have the same dimensionality (i.e. length in time), e.g. $N$
• all $\mathbf{t}_{Yi}$ have the same dimensionality (i.e. length in time), e.g. $M$

One important note is that the time-series $t_{Xi}$ and $t_{Yi}$ are not consecutive (there is a gap in time between them).

What type of problem is this? Is it a regression problem? If so, what metrics (loss functions) and methods would be appropiate for this problem?

Say we have a problem where we need to learn a function:

$f(\mathbf{x} \in \mathbf{R}^p) \rightarrow \mathbf{y} \in \mathbf{R}^q$

where $\mathbf{x}$ and $\mathbf{y}$ are vectors representing time series.

We have multiple examples of this mapping, i.e.:

$$\begin{pmatrix}\mathbf{x_0}\\...\\\mathbf{x_N}\end{pmatrix}\rightarrow \begin{pmatrix}\mathbf{y_0}\\...\\\mathbf{y_N} \end{pmatrix} $$

What type of problem is this? Is it a regression problem? If so, what metrics (loss functions) and methods would be appropiate for this problem? Anything specifically available in Python?