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Thesis update

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Radu C. Martin 2021-06-25 06:22:43 +02:00
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9
30_Gaussian_Processes_Background.tex
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@ -130,7 +130,7 @@ observations and the fixed mean function:
The choice of the kernel is an important part for any kernel machine class
algorithm. It serves the purpose of shaping the behaviour of the \acrshort{gp}
by imposing a desired level of smoothness of the resulting functions, a
prediodicity, linearity, etc. This extends the use cases of the \acrshort{gp}
periodicity, linearity, etc. This extends the use cases of the \acrshort{gp}
models while including any available prior information of the system to be
modeled.
@ -148,8 +148,7 @@ continuous. The basic version of the \acrshort{se} kernel has the following form
\mathbf{x'}}^2}{l^2}\right)}
\end{equation}
with the parameters $\sigma^2$ (model variance) and $l$ (lengthscale).
with the model variance $\sigma^2$ and lengthscale $l$ as parameters.
With the model variance $\sigma^2$ and lengthscale $l$ as parameters.
The lengthscale indicates how fast the correlation diminishes as the two points
get further apart from each other.
@ -178,7 +177,7 @@ value of the hyperparameters. This is the \acrfull{ard} property.
\subsubsection*{Rational Quadratic Kernel}
The \acrfull{rq} Kernel can be intepreted as an infinite sum of \acrshort{se}
The \acrfull{rq} Kernel can be interpreted as an infinite sum of \acrshort{se}
kernels with different lengthscales. It has the same smooth behaviour as the
\acrlong{se} Kernel, but can take into account the difference in function
behaviour for large scale vs small scale variations.
@ -340,7 +339,7 @@ The \acrshort{noe} structure is therefore a \textit{simulation model}.
In order to get the best simulation results from a \acrshort{gp} model, the
\acrshort{noe} structure would have to be employed. Due to the high algorithmic
complexity of training and evaluating \acrshort{gp} models, this approach is
computationally untractable. In practice a \acrshort{narx} model will be trained,
computationally intractable. In practice a \acrshort{narx} model will be trained,
which will be validated through multi-step ahead prediction.
\clearpage