Reorganize files
3
.gitignore
vendored
@@ -86,4 +86,5 @@ data/*
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# Ignore html files for now
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# TODO: Remove later
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*.html
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25_07_phd_defense/index_cache
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index_cache
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index_files
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4
.vscode/settings.json
vendored
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{
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"files.autoSave": "off",
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"files.exclude": {
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"**/.git": true,
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".git": true
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"**/.git": false,
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".git": false
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},
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"todo-tree.tree.hideTreeWhenEmpty": false
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}
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Before Width: | Height: | Size: 2.3 MiB After Width: | Height: | Size: 2.3 MiB |
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Before Width: | Height: | Size: 4.2 MiB After Width: | Height: | Size: 4.2 MiB |
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Before Width: | Height: | Size: 692 KiB After Width: | Height: | Size: 692 KiB |
@@ -10,7 +10,7 @@ affiliations:
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name: University of Duisburg-Essen, House of Energy, Climate and Finance
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format:
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revealjs:
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embed-resources: true
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embed-resources: false
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footer: ""
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logo: assets/logos_combined.png
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theme: [default, sydney.scss, custom.scss]
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@@ -808,65 +808,10 @@ We receive the constant solution for high values of $\lambda$ when setting $d=1$
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## The Proposed CRPS-Learning Algorithm
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:::: {.columns}
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```{r, fig.align="left", echo=FALSE, out.width = "1000px", cache = TRUE}
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knitr::include_graphics("assets/crps_learning/algorithm_1.svg")
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```
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::: {.column width="48%"}
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**Initialization:**
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Array of expert predicitons: $\widehat{X}_{t,k,p}$
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Vector of Prediction targets: $Y_t$
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Starting Weights: $w_0=(w_{0,1},\ldots, w_{0,K})$,
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Penalization parameter: $\lambda\geq 0$
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B-spline and penalty matrices $B$ and $D$ on $\mathcal{P}= (p_1,\ldots,p_M)$
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Hat matrix: $$\mathcal{H} = B(B'B+ \lambda D'D)^{-1} B'$$
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Cumulative Regret: $R_{0,k} = 0$
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Range parameter: $E_{0,k}=0$
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:::
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::: {.column width="2%"}
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:::
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::: {.column width="48%"}
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**Core**:
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for(t in 1:T) { for(p in $\mathcal{P}$) {
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$\widetilde{X}_{t,k}(p) = \sum_{k=1}^K w_{t-1,k,p} \widehat{X}_{t,k}(p)$ .grey[\# Prediction]
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for(k in 1:K){
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$r_{t,k,p} = \text{QL}_p^{\nabla}(\widehat{X}_{t,k}(p),Y_t) - \text{QL}_p^{\nabla}(\widetilde{X}_{t}(p),Y_t)$
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$E_{t,k,p} = \max(E_{t-1,k,p}, |r_{t,k,p}|)$
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$\eta_{t,k,p}=\min\left(1/2E_{t,k,p}, \sqrt{\log(K)/ \sum_{i=1}^t (r^2_{i, k,p})}\right)$
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$R_{t,k,p} = R_{t-1,k,p} + \frac{1}{2} \left( r_{t,k,p} \left( 1+ \eta_{t,k,p} r_{t,k,p} \right) + 2E_{t,k,p} \mathbb{1}(\eta_{t,k,p}r_{t,k,p} > \frac{1}{2}) \right)$
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$w_{t,k,p} = \eta_{t,k,p} \exp \left(- \eta_{t,k,p} R_{t,k,p} \right) w_{0,k,p} / \left( \frac{1}{K} \sum_{k = 1}^K \eta_{t,k,p} \exp \left( - \eta_{t,k,p} R_{t,k,p}\right) \right)$
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}.grey[\#k]}.grey[\#p]
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for(k in 1:K){
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$w_{t,k} = \mathcal{H} w_{t,k}(\mathcal{P})$ .grey[\# Smoothing]
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} .grey[\#k]} .grey[\#t]
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:::
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::::
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## Simulation Study
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@@ -3182,7 +3127,10 @@ Accounting for heteroscedasticity or stabilizing the variance via log transforma
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## References
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::: {.scrollable}
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```{r refs1, echo=FALSE, results="asis"}
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PrintBibliography(my_bib, .opts = list(style = "text"))
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```
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::::
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