features.md
Title: Markdown Example
Date: 2020-02-21 16:19:46
publications_src: content/pages/zotero_single.bib
toc_run: true
Status: hidden
## Links
[Markdown quick reference](https://github.com/adam-p/markdown-here/wiki/Markdown-Cheatsheet)
## Table (Playing with Kaggle; uses Markdown includes)
--- snip ---
{! includes/ffe/table.md !}
--- snap ---
(1) augmented: one additional variant per image rotated randomly in [-5,5] degree.
(2) bn: batch-norm
## Mathematics
_Inline Math:_ $f_{i}(x) = \int_{\tau(\pi)}^\infty e(x,y)dy$
_Display Math:_
$$
\begin{bmatrix}
a_{11} & a_{12} & \dots \\
\vdots & \ddots & \\
a_{n1} & & a_{nn}
\end{bmatrix}
$$
_Inline Math:_ $(\Omega,\mathcal{F},P) \coloneqq (\Omega^+\times\Omega^-,\mathcal{F^+}\otimes\mathcal{F^-},P^+\times P^-)$
_Display Math:_
The Wiener process in $(\Omega,\mathcal{F},P)$ is defined by
$$
\omega(t) \coloneqq
\left\{
\begin{array}{cc}
(\omega^+(t),0) & t\geq 0 \\
(0,\omega^-(t)) & t<0
\end{array}
\right.
$$
More math...
$$
\tag{3.1a}
\begin{aligned}
dy_t &= \sum_{i=1}^n \frac{x_t^i}{\|x_t\|^2} \left( \sum_{j=1}^n
u_{ij} x_t^i\,dt + \sum_{k=1}^m \sum_{j=1}^n v_{ij}^k
x_t^j\circ dW_t^k\right) + \cdots\\
\cdots &+ \frac{1}{2} \sum_{i,j}^n \left( \frac{\delta_{ij}}{\|x_t\|^2} -
\frac{2x_t^i x_t^j}{\|x_t\|^4} \right)\; \sum_k^m \sum_{l,p}^n
v_{il}^k v_{jp}^k\, x_t^l x_t^p\;dt
\end{aligned}
$$
With $z_t \coloneqq \frac{x_t}{\|x_t\|}$ we get the following differential equation on the unit sphere:
$$
\tag{3.1b}
\begin{aligned}
y_t &= y_0 + \int_0^t z_t^TUz_t- \|z_t\|^{-2}
z_t^T\hat{V}\hat{V}^T z_t + \frac{1}{2}\text{ trace
}(\hat{V}\hat{V}^T)\,dt +\cdots\\
\cdots &+ \sum_{k=1}^m \int_0^t z_t^TV^kz_t\circ dW_t^k
\end{aligned}
$$
### Outline as partial TeX file inclusion
Line block - takes only the inner part of a LaTeX display-math environment by specifying row delimiters for the included LaTeX file:
--- snip ---
$$
{! includes/ffe/formulas.tex [ln:6-12] !}
$$
--- snap ---
Single line (as inline): start include ->
$
{! includes/ffe/formulas.tex [ln:16] !}
$
<- stop include
## Footnotes
Footnotes are possible, like using [^1] and [^2].
[^1]: First footnote
[^2]: Second footnote
## Citations
- Cited text 1: [@@touchetteBasicIntroductionLarge2012]
- Cited text 2[^3]: [@dematteisRogueWavesLarge2018]
[^3]: Interesting in terms of content, by the way
## SVG Image
Embedded using Markdown extension (*attr_list*) and table (for caption):
||
|:-:|
|{: style="width:80%"; class="align-center"}|
|Neuron image - 80%|
## Code
### Verbatim file inclusion
```
{! includes/ffe/features.py !}
```
### Normal code block
```
from torch.utils.data import TensorDataset
from torch import Tensor, LongTensor, FloatTensor
def loadData(path) -> Tuple[np.ndarray, np.ndarray]:
'''
Load data from kaggle mnist set.
path -- input csv
Return scaled images [0,1] and labels (if available)
as numpy arrays (dtype: float32, int64)
'''
# Read
df = pd.read_csv(str(path)) # 40.000 entries
# tdata = pd.read_csv(data_raw_dir + sep + 'train.csv') # 28.000 entries
has_labels = True if 'label' in df.columns else False
```
Some `inline code`.
table.md
| Model | Epochs | bs | lr | Momentum | Result (local) | Result (Kaggle) | Remarks |
| :-------------: | ------ | --- | ------ | -------- | -------------- | --------------- | ------------- |
| SimpleNet | 50 | 20 | 0.007 | 0.9 | ~97 | | |
| ConvNet | 50 | 25 | 0.008 | 0.9 | | 99.257 | |
| " | 50 | 17 | 0.008 | 0.9 | 99.1964 | | augmented |
| " | 50 | 17 | 0.008 | 0.9 | 99.3143 | 99.342 | augmented bn |
| Binary Ensemble | 25 | 17 | 0.007 | 0.9 | >99 | | |
| " | 22 | 17 | 0.0085 | 0.9 | 99.23928 | 99.328 | augmented |
| " | 22 | 17 | 0.0085 | 0.9 | 99.34643 | 99.357 | augmented bn |