The reconstruction of high-fidelity resolution brain MR images is especially challenging because of the highly complex brain structure. Most promising approaches for this task are autoencoders and generative models such as Variational Autoencoders (VAE) or Generative Adversarial Networks (GAN). In Unsupervised Anomaly Detection (UAD), these architectures are only trained with images of healthy brain anatomy and not with images containing anomalies such as lesions. Therefore, processing an anomalous input image $\pmb{x}$ with an architecture trained to reconstruct healthy MR images should produce a high reconstruction error $r$ indicating that the input MR image is likely to exhibit anomalies.

So far developed models for this task are either limited to low resolution reconstructions so that quite a lot of information is lost or to only small image regions. Baur et al. hypothesize that these restrictions are caused by the low dimensionality of the latent space of the models even though a high capacity would be necessary to reconstruct highly complex brain MR images. Thus, Baur et al. introduce skip connections in the autoencoder to enable detailed high resolution reconstructions due to the enhanced gradient flow. In addition, the application of dropout on the skip connections shall prevent the model from learning the identity of the input image since only the corresponding healthy anatomy of the possibly anomalous input image shall be reconstructed. Sampling the networks parameter $\pmb{\theta}$ from a Bernoulli distribution $\pmb{\theta} \sim \mathcal{B}(p)$ with $p$ being the dropout rate  also turns the Skip-Autoencoder into a Bayesian neural network by using a Monte Carlo dropout at test time.
The proposed Skip Autoencoder and the Bayesian Skip-Autoencoder are tested on Mutiple Sclerosis and Glioblastoma datasets and evaluated using the Precision-Recall-Curve (PRC), the AUPRC, and the Dice Score. An investigation of the Bernoulli dropout yields that no input identity is learnt independent on the dropout. A random weight initialization seems to be sufficient. Considering the skip-connections, the best performance is achieved by a single skip-connection close to the bottleneck layer. Applying more skip connections improves the performance on the Glioblastoma test set but reduces the performance on the Multiple Sclerosis test set.

In general, the non-Bayesian Skip-Autoencoder exceeds the performance of the Bayesian Skip-Autoencoder because in the calculation of the reconstruction residual $r = \rvert \pmb{x} - \pmb{\hat{x}} \rvert$ for the Bayesian Skip-Autoencoder the predictive mean of $n$ Monte Carlo samples is applied as reconstructed image $\pmb{\hat{x}}$ which causes a blurriness in the reconstructions  $\pmb{\hat{x}}$. However, the Bayesian Skip-Autoencoder enables to quantify the epistemic uncertainty because the pixels of hyperintense anomalies have a low variance compared to normal tissue.

For a machine learning model to be trusted/ used one would need to be confident in its capabilities of dealing with all possible scenarios. To that end, designing unit test cases for more complex and global problems could be costly and bordering on impossible to create.

**Idea**: We need a basic guideline that researchers and developers can adhere to when defining problems and outlining solutions, so that model interpretability can be defined accurately in terms of the problem statement.

**Solution**: This paper outlines the basics of machine learning interpretability, what that means for different users, and how to classify these into understandable categories that can be evaluated. This paper highlights the need for interpretability, which arises from *incompleteness*,either of the problem statement, or the problem domain knowledge. This paper provides three main categories to evaluating a model/ providing interpretations:
- *Application Grounded Evaluation*: These evaluations are more costly, and involve real humans evaluating real tasks that a model would take up. Domain knowledge is necessary for the humans evaluating the real task handled by the model.
- *Human Grounded Evaluation:* these evaluations are simpler than application grounded, as they simplify the complex task and have humans evaluate the simplified task. Domain knowledge is not necessary in such an evaluation. 
- *Functionally Grounded Evaluation:* No humans are involved in this version of evaluation, here previously evaluated models are perfected or tweaked to optimize certain functionality. Explanation quality is measured by a formal definition of interpretability.

This paper also outlines certain issues with the above three evaluation processes, there are certain questions that need answering before we can pick an evaluation method and metric. 
-To highlight the factors of interpretability, we are provided with the Data-driven approach. Here we analyze each task and the various methods used to fulfill the task and see which of these methods and tasks are most significant to the model.
- We are introduced to the term latent dimensions of interpretability, i.e. dimensions that are inferred not observed. These are divided into task related latent dimensions and method related latent dimensions, these are a long list of factors that are task specific or method specific.

Thus this paper provides a basic taxonomy for how we should evaluate our model, and how these evaluations differ from problem to problem.  The ideal scenario outlined is that researchers provide the relevant information to evaluate their proposition correctly (correctly in terms of the domain and the problem scope).

During the development of neural circuitry, neurons of different kinds establish specific synaptic connections by selecting appropriate targets from large numbers of alternatives. The range of alternative targets is reduced by well organised patterns of growth, termination, and branching that deliver the terminals of appropriate pre- and postsynaptic partners to restricted volumes of the developing nervous system. We use the axons of embryonic Drosophila sensory neurons as a model system in which to study the way in which growing neurons are guided to terminate in specific volumes of the developing nervous system. The mediolateral positions of sensory arbors are controlled by the response of Robo receptors to a Slit gradient. Here we make a genetic analysis of factors regulating position in the dorso-ventral axis. We find that dorso-ventral layers of neuropile contain different levels and combinations of Semaphorins. We demonstrate the existence of a central to dorsal and central to ventral gradient of Sema 2a, perpendicular to the Slit gradient. We show that a combination of Plexin A (Plex A) and Plexin B (Plex B) receptors specifies the ventral projection of sensory neurons by responding to high concentrations of Semaphorin 1a (Sema 1a) and Semaphorin 2a (Sema 2a). Together our findings support the idea that axons are delivered to particular regions of the neuropile by their responses to systems of positional cues in each dimension.

This paper learns deep local patch descriptor (for replacing SIFT) by hard negative mining using current mini-batch. It outperforms SIFT and deep competitors on Oxford5K and Paris6K retrieval datasets.

This paper introduces triangle-GAN ($\triangle$-GAN) that aims at cross-domain joint distribution matching: The model is shown below

https://i.imgur.com/boIDOMu.png

Having two domains of data $x$ and $y$, there are two generators:

1- $G_x(y)$ which takes $y$ and generates $\tilde{x}$

2- $G_y(x)$ which takes $x$ and generates $\tilde{y}$

There are two discriminators in the model:

1- $D_1 (x,y)$ a discriminator that distinguishes between $(x, y)$ and either of $(x, \tilde{y})$ or $(\tilde{x}, y)$.

2- $D_2 (x,y)$ a discriminator that distinguishes between $(x, \tilde{y})$ and $(\tilde{x}, y)$.

The second discriminator is ALI and can be used on un-paired sets of data.
The first discriminator is equivalent to a conditional discriminator where the true paired data $(x, y)$ is compared to either $(x, \tilde{y})$ or $(\tilde{x}, y)$, where one element in the pair is sampled. This discriminator needs paired $(x, y)$ data for training. 

This model can be used for semi-supervised settings, where a small set of paired data is provided. In this paper it is used for:

-  semi-supervised image classification, where a small subset of CIFAR10 is labelled. $x$ and $y$ are images and class labels here.

- image to image translation on edge2shoes dataset, where only a subset of dataset is paired.

- attribute conditional image generation where $x$ and $y$ domains are image and attributes. CelebA and COCO datasets are used here. In one experiment test-set images are projected to attributes and then given those attributes new images are generated:

On celebA:
https://i.imgur.com/EX5tDZ0.png

On COCO:
https://i.imgur.com/GRpvjGx.png

In another experiment some attributes are chosen (as samples shown below in the first row with different noise) and then another feature is added (using the same noise) to generate the samples in the second row:
 https://i.imgur.com/KeHL8Ye.png

The triangle gan demonstrates improved performance compared to triple gan in the experiments shown in the paper. It has been also compared with Disco gan (a model that can be trained on un-paired data) and shows improved performance when some percentage of paired data is provided. In an experiment they pair each MNIST digit with its transposed (as $x$, $y$ pairs). Disco-GAN cannot learn correct mapping between them, while triangle-GAN can learn correct mapping since it leverages paired data.

https://i.imgur.com/Vz9Zfhu.png

In general this model is a useful approach for semi-supervised cross-domain matching and can leverage un-paired data (using ALI) as well as paired data (using conditional discriminator).