An Example Post

Informal justifications

In Auto-Encoding Variational Bayes, (missing reference), Kingma presents an unbiased, differentiable, and scalable estimator for the ELBO in variational inference. A key idea behind this estimator is the reparameterization trick. But why do we need this trick in the first place? When first learning about variational autoencoders (VAEs), I tried to find an answer online but found the explanations too informal…

$e = mc^2. \tag{1}$

$\begin{aligned} &= \end{aligned}$

Cool!

import numpy as np
import jax.numpy as jnp
from jax import grad, jit, vmap
from jax import random
import os
import sys


# check executable path
print(sys.executable)

There are something:

$\mathbb{P}(X=2) = \frac{1}{3}$

wish you can do

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Citations

According to (Bishop, 2006), machine learning … You can cite another one (Vaswani et al., 2017). You can also do inline citation, Bishop (2006) argues that …

Figures

Without zoom

Figure 1. Diagram of rejection sampling. The density $q(\mathbf{z})$ must be always greater than $p(\mathbf{x})$. A new sample is rejected if it falls in the gray region and accepted otherwise. These accepted samples are distributed according to $p(\mathbf{x})$. This is achieved by sampling $z_i$ from $q(\mathbf{z})$, and then sampling uniformly from $[0, k q(z_i)]$. Samples under the curve $p(z_i)$ are accepted.

With zoom

Figure 1. OECD HAN database structure: there are four tables, in which HAN_PERSON is the correspondence table which include all cleaned names.

Tables

Table and figure aligned

Top 5 IPC class	Count
B29C70-38	14
B29C70-54	13
G08G5-00	13
B64C39-02	13
G05D1-00	12

Figure 4. The IPC distribution of Airbus Defence (DE)'s patents; section B is about performing operations and transport; section H is electricity; section G is about physics. Remark : the total number of granted patents is 538 but the count of total IPC classes is 1763, which means some patents are assigned to multiple classes.

Table over flow if you need it