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Update documentation
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arturtoshev committed Jan 9, 2024
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25 changes: 20 additions & 5 deletions _sources/about.md
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Expand Up @@ -11,6 +11,26 @@ The course breaks down into an introduction to the topic, followed by 4 core con

> Questions should preferably be posted in the Moodle, or else be sent to Artur Toshev.

## Outline

```{tableofcontents}
```


## Contributors

Thanks to all contributors! Github names, if available.

### Contributed content

1. Armin Illerhaus - Notebooks on Windows

### Content fixes

1. Andreas Steger (AndSte01)


## Citation

Please cite this work as:
Expand All @@ -24,11 +44,6 @@ Please cite this work as:
}
```

## Outline

```{tableofcontents}
```

<br>
<br>

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1 change: 1 addition & 0 deletions _sources/faq.md
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Expand Up @@ -9,6 +9,7 @@ There exist a number of resources to run the tutorials online, and also work on
2. [**AWS SageMaker Studio Lab**](https://aws.amazon.com/sagemaker/studio-lab/) new-ish competitor to Google Colab. Pretty much the same as Google Colab, just running on Amazon Web-Services.
3. [**PaperSpace Gradient**](https://www.paperspace.com/gradient) Hosted JuPyter runtime on the cloud with pre-installed machine learning packages.

Look at [](software.md) for more details on the software setup.

## 2. I have a question which is not suitable for the Moodle, who should I contact?

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4 changes: 2 additions & 2 deletions _sources/lecture/gmm.md
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Expand Up @@ -251,7 +251,7 @@ In the E-step, we compute the posterior probability of $z^{(i)}_k$ given the dat
$$
\begin{aligned}
p(z^{(i)}=k| x^{(i)},\pi,\mu,\Sigma) &= \frac{p(x^{(i)}|z^{(i)}=k, \mu, \Sigma)p(z^{(i)}=k,\pi)}{\sum_{l=1}^K p(x^{(i)}|z^{(i)}=l, \mu, \Sigma)p(z^{(i)}=l,\pi)} \\
&= \frac{\pi_k \mathcal{N}(x^{(i)}|\mu_K, \Sigma_k)}{\sum_{l=1}^K \pi_l \mathcal{N}(x^{(i)}|\mu_l, \Sigma_l)}
&= \frac{\pi_k \mathcal{N}(x^{(i)}|\mu_k, \Sigma_k)}{\sum_{l=1}^K \pi_l \mathcal{N}(x^{(i)}|\mu_l, \Sigma_l)}
\end{aligned}$$ (gmm_responsibilities)

The values of $p(x^{(i)}|z^{(i)}=k, \mu, \Sigma)$ can be computed by evaluating the $k$th Gaussian with parameters $\mu_k$ and $\Sigma_k$. And $p(z^{(i)}=k,\pi)$ is just $\pi_k$.
Expand All @@ -273,7 +273,7 @@ Most limitations of this approach arive from the assumption that the indivudual
- If the data does not follow a Gaussian distribution, e.g. heavy-tailed ditribution with outliers, then too much weight will be given to the outliers
- If there is an outlier, eventually one mode will focus only on this one data point. But if a Gaussian describes only one data point, then its variance will be zero and we recover a singularity/Dirac function.
- The choice of $K$ is crucial and this parameters need to be optimized in a outer loop.
- GMMs do now scale well to high dimensions.
- GMMs do not scale well to high dimensions.


## Further References
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