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Knot placement details, cross referencing etc.

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Jonathan Berrisch
2025-06-01 12:09:05 +02:00
parent 78b6846eef
commit 91f578bcf1
2 changed files with 63 additions and 31 deletions
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16
assets/library.bib
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@@ -168,4 +168,20 @@
doi = {10.1016/j.egyai.2023.100236},
issn = {2666-5468},
keywords = {Electricity peak load, Generalized additive models, Artificial neural networks, Prediction, Combination, Weather effects, Seasonality}
}
@book{johnson1995continuous,
title = {Continuous univariate distributions, volume 2},
author = {Johnson, Norman L and Kotz, Samuel and Balakrishnan, Narayanaswamy},
year = {1995},
publisher = {John wiley \& sons},
volume = {289}
}
@article{li2022general,
title = {General P-splines for non-uniform B-splines},
author = {Li, Zheyuan and Cao, Jiguo},
year = {2022},
journal = {arXiv preprint},
publisher = {Cornell University},
doi = {10.48550/arXiv.2201.06808},
url = {https://arxiv.org/abs/2201.06808}
}

78
index.qmd
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@@ -36,7 +36,7 @@ revealjs-plugins:
- pointer
---
## Outline
## Outline {.center}
<!--
Render with: quarto preview /home/jonathan/git/PHD-Presentation/25_07_phd_defense/index.qmd --no-browser --port 6074
@@ -48,20 +48,17 @@ $$
$$
:::
<br/>
:::: {style="font-size: 150%;"}
<i class="fa fa-fw fa-rocket" style="color:var(--col_grey_9);"></i> &ensp; [Research Motivation](#motivation)
<i class="fa fa-fw fa-book" style="color:var(--col_grey_9);"></i> &ensp; Overview of the Thesis
<i class="fa fa-fw fa-book" style="color:var(--col_grey_9);"></i> &ensp; [Overview of the Thesis](#sec-overview)
<i class="fa fa-fw fa-code-merge" style="color:var(--col_grey_9);"></i> &ensp; Online Aggregation
<i class="fa fa-fw fa-layer-group" style="color:var(--col_grey_9);"></i> &ensp; [Online Aggregation](#sec-crps-learning)
<i class="fa fa-fw fa-fire-flame-simple" style="color:var(--col_grey_9);"></i> &ensp; Probabilistic Forecasting of European Carbon and Energy Prices
<i class="fa fa-fw fa-newspaper" style="color:var(--col_grey_9);"></i> &ensp; Contributions & Outlook
<i class="fa fa-fw fa-chart-line" style="color:var(--col_grey_9);"></i> &ensp; [Probabilistic Forecasting of European Carbon and Energy Prices](#sec-voldep)
<i class="fa fa-fw fa-newspaper" style="color:var(--col_grey_9);"></i> &ensp; [Contributions & Outlook](#sec-conclusion)
:::
@@ -101,7 +98,7 @@ col_yellow <- "#FCE135"
## Motivation
## Overview of the Thesis {transition="fade" transition-speed="slow"}
## Overview of the Thesis {transition="fade" transition-speed="slow" #sec-overview}
<table style="width: 100%; border-collapse: separate; border-spacing: 0 1em; border: none;">
<tr style="border: none;">
@@ -162,7 +159,7 @@ col_yellow <- "#FCE135"
</tr>
</table>
## Overview of the Thesis {transition="fade" transition-speed="slow"}
## Overview of the Thesis {transition="fade" transition-speed="slow"}
<table style="width: 100%; border-collapse: separate; border-spacing: 0 1em; border: none;">
<tr style="border: none;">
@@ -589,7 +586,7 @@ ggplot() +
::::
# CRPS Learning
# CRPS Learning {#sec-crps-learning}
Berrisch, J., & Ziel, F. [-@BERRISCH2023105221]. *Journal of Econometrics*, 237(2), 105221.
@@ -2627,27 +2624,21 @@ chart = {
::: {.column width="48%"}
Basis specification `b_smooth_pr` is internally passed to `make_basis_mats()`:
Non-central beta distribution @johnson1995continuous:
```{r, echo = TRUE, eval = FALSE, cache = TRUE}
mod <- online(
y = Y,
experts = experts,
tau = 1:99 / 100,
b_smooth_pr = list(
knots = 9,
mu = 0.3, # NEW
sigma = 1,
nonc = 0,
tailweight = 1,
deg = 3
)
)
::: {style="font-size: 70%;"}
\begin{equation*}
\mathcal{B}(x, a, b, c) = \sum_{j=0}^{\infty} e^{-c/2} \frac{\left( \frac{c}{2} \right)^j}{j!} I_x \left( a + j , b \right)
\end{equation*}
::::
```{r, fig.align="center", echo=FALSE, out.width = "1000px", cache = TRUE}
knitr::include_graphics("assets/mcrps_learning/knot_placement.svg")
```
Knots are distributed using the generalized beta distribution.
TODO: Add actual algorithm to backup slides
<i class="fa fa-fw fa-triangle-exclamation" style="color:var(--col_orange_9);"></i> Penalty and $\lambda$ need to be adjusted accordingly @li2022general
:::
@@ -2657,6 +2648,27 @@ TODO: Add actual algorithm to backup slides
::: {.column width="48%"}
Using non equidistant knots in `profoc` is straightforward:
```{r, echo = TRUE, eval = FALSE, cache = TRUE}
mod <- online(
y = Y,
experts = experts,
tau = 1:99 / 100,
b_smooth_pr = list(
knots = 9,
mu = 0.3,
sigma = 1,
nonc = 0,
tailweight = 1,
deg = 3
)
)
```
Basis specification `b_smooth_pr` is internally passed to `make_basis_mats()`.
<i class="fa fa-fw fa-check" style="color:var(--col_green_9);"></i> Profoc adjusts penatly and $\lambda$
:::
@@ -2716,7 +2728,7 @@ Pubications:
::::
# Modeling Volatility and Dependence of European Carbon and Energy Prices
# Modeling Volatility and Dependence of European Carbon and Energy Prices {#sec-voldep}
Berrisch, J., Pappert, S., Ziel, F., & Arsova, A. (2023). *Finance Research Letters*, 52, 103503.
@@ -3482,6 +3494,10 @@ Accounting for heteroscedasticity or stabilizing the variance via log transforma
::::
## Conclusion
## Contributions and Outlook {#sec-conclusion}
## References