A very simple (but impractical) discrete model of subclonal evolution would include the following events:

* Division of a cell to create two cells:
    * **Mutation** at a location in the genome of the new cells
* Cell death at a new timestep
* Cell survival at a new timestep

Because measurements of mutations are usually taken at one time point, this is taken to be at the end of a time series of these events, where a tiny of subset of cells are observed and a **genotype matrix** $A$ is produced, in which mutations and cells are arbitrarily indexed such that $A_{i,j} = 1$ if mutation $j$ exists in cell $i$. What this matrix allows us to see is the proportion of cells which *both have mutation $j$*.

Unfortunately, I don't get to observe $A$, in practice $A$ has been corrupted by IID binary noise to produce $A'$. This paper focuses on difference inference problems given $A'$, including *inferring $A$*, which is referred to as **`noise_elimination`**. The other problems involve inferring only properties of the matrix $A$, which are referred to as:

* **`noise_inference`**: predict whether matrix $A$ would satisfy the *three gametes rule*, which asks if a given genotype matrix *does not describe a branching phylogeny* because a cell has inherited mutations from two different cells (which is usually assumed to be impossible under the infinite sites assumption). This can be computed exactly from $A$.
* **Branching Inference**: it's possible that all mutations are inherited between the cells observed; in which case there are *no branching events*. The paper states that this can be computed by searching over permutations of the rows and columns of $A$. The problem is to predict from $A'$ if this is the case.

In both problems inferring properties of $A$, the authors use fully connected networks with two hidden layers on simulated datasets of matrices. For **`noise_elimination`**, computing $A$ given $A'$, the authors use a network developed for neural machine translation called a [pointer network][pointer]. They also find it necessary to map $A'$ to a matrix $A''$, turning every element in $A'$ to a fixed length row containing the location, mutation status and false positive/false negative rate.

Unfortunately, reported results on real datasets are reported only for branching inference and are limited by the restriction on input dimension. The inferred branching probability reportedly matches that reported in the literature.

[pointer]: https://arxiv.org/abs/1409.0473

Main purpose:
* This work proposes a software-based resolution augmentation method which is more agile and simpler to implement than hardware engineering solutions.
* The paper examines three deep learning single image super resolution techniques on pCLE images 
* A video-registration based method is proposed to estimate ground truth HR pCLE images (this can be assumed as the main objective of the paper)

Highlights:
* The papers emphasise that this is the first work to address the image resolution problem in pCLE image acquisitions
* The paper introduces useful information on how pCLE devices work
* Strong related work 
* Clear story
* Comprehensive evaluation

Main Idea:
* Use video-registration based techniques to estimate the HR images (real ground truth HR image is not available)
* Simulate LR images from estimate HR images with help of Voronoi diagram and Delaunay-based linear interpolation.
* Train an Exemplar-based SR model (EBSR -- DL-based approach) to learn the mapping between simulated LR and estimate HR images. 

Methodology Details
* To estimate the HR images, a video-registration based mosaicking techniques (by the same authors in MIA 2006) is used which fuses a collection of input images by averaging the temporal information. 
* Since mosaicking generates  single large filed-of-view mosaic image from LR images, the mosaic-to-image diffeomorphic spatial transformation is used which results from the mosaicking process to propagate and crop the fused information from the mosaic back into each input LR image space. 
* At this point, the authors observe that the misalignment between input LR images (used in the video-registration based mosaicking technique) and estimate HR cause training problem for the EBSR model. So, they treat the HR images as realistic and chose to simulate LR images from them!!!!
* Simulated LR images by obtained using the Voronoi diagram (averaging the Voronoi cell on HR image) + additive noise on estimate HR images. 
* Finally, they build to experimental datasets 1) LR_org and HR and 2) LR_synth and HR and train three CNN SR models on these twor datasets. 
* They train FSRCNN, EDSR, SRGAN
* The networks are trained using L1+SSIM loss functions

Experiment Notes:
* SSIM and GCF are used to quantitatively assess the performance of the models.
* A composite score is also used to take SSIM and GCF into account jointly
* In the ideal case, when the models are trained and etsted on simulated LR and HR images, the quantitative results are convincing.  
* "From this experiment, it is possible to conclude that the proposed solution is capable of performing SR reconstruction when the models are trained on synthetic data with no domain gap at test time"
* When models are trained and tested on original LR and estimate HR images, the performance is not reasonable
* When the models are trained on simulated LR images and tested on original LR images, the results become better compared to the previous case, 
* For a solid conclusion, and MOS study was carried out. The models are trained on simulated LR images. 

When machine learning models need to run on personal devices, that implies a very particular set of constraints: models need to be fairly small and low-latency when run on a limited-compute device, without much loss in accuracy. A number of human-designed architectures have been engineered to try to solve for these constraints (depthwise convolutions, inverted residual bottlenecks), but this paper's goal is to use Neural Architecture Search (NAS) to explicitly optimize the architecture against latency and accuracy, to hopefully find a good trade-off curve between the two. 

This paper isn't the first time NAS has been applied on the problem of mobile-optimized networks, but a few choices are specific to this paper. 

1. Instead of just optimizing against accuracy, or optimizing against accuracy with a sharp latency requirement, the authors here construct a weighted loss that includes both accuracy and latency, so that NAS can explore the space of different trade-off points, rather than only those below a sharp threshold.  
2. They design a search space where individual sections or "blocks" of the network can be configured separately, with the hope being that this flexibility helps NAS trade off complexity more strongly in the early parts of the network, where, at a higher spatial resolution, it implies greater computation cost and latency, without necessary dropping that complexity later in the network, where it might be lower-cost. Blocks here are specified by the type of convolution op, kernel size, squeeze-and-excitation ratio, use of a skip op, output filter size, and the number of times an identical layer of this construction will be repeated to constitute a block. 

Mechanically, models are specified as discrete strings of tokens (a block is made up of tokens indicating its choices along these design axes, and a model is made up of multiple blocks). These are represented in a RL framework, where a RNN model sequentially selects tokens as "actions" until it gets to a full model specification . This is repeated multiple times to get a batch of models, which here functions analogously to a RL episode. These models are then each trained for only five epochs (it's desirable to use a full-scale model for accurate latency measures, but impractical to run its full course of training). After that point, accuracy is calculated, and latency determined by running the model on an actual Pixel phone CPU. These two measures are weighted together to get a reward, which is used to train the RNN model-selection model using PPO. 

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

Across a few benchmarks, the authors show that models found with MNasNet optimization are able to reach parts of the accuracy/latency trade-off curve that prior techniques had not.

When humans classify images, we tend to use high-level information about the shape and position of the object. However, when convolutional neural networks classify images,, they tend to use low-level, or textural, information more than high-level shape information. This paper tries to understand what factors lead to higher shape bias or texture bias. 

To investigate this, the authors look at three datasets with disagreeing shape and texture labels. The first is GST, or Geirhos Style Transfer. In this dataset, style transfer is used to render the content of one class in the style of another (for example, a cat shape in the texture of an elephant). In the Navon dataset, a large-scale letter is rendered by tiling smaller letters. And, in the ImageNet-C dataset, a given class is rendered with a particular kind of distortion; here the distortion is considered to be the "texture label". In the rest of the paper, "shape bias" refers to the extent to which a model trained on normal images will predict the shape label rather than the texture label associated with a GST image. The other datasets are used in experiments where a model explicitly tries to learn either shape or texture. 

https://i.imgur.com/aw1MThL.png

To start off, the authors try to understand whether CNNs are inherently more capable of learning texture information rather than shape information. To do this, they train models on either the shape or the textural label on each of the three aforementioned datasets. On GST and Navon, shape labels can be learned faster and more efficiently than texture ones. On ImageNet-C (i.e. distorted ImageNet), it seems to be easier to learn texture than texture, but recall here that texture corresponds to the type of noise, and I imagine that the cardinality of noise types is far smaller than that of ImageNet images, so I'm not sure how informative this comparison is. Overall, this experiment suggests that CNNs are able to learn from shape alone without low-level texture as a clue, in cases where the two sources of information disagree 

The paper moves on to try to understand what factors about a normal ImageNet model give it higher or lower shape bias - that is, a higher or lower likelihood of classifying a GST image according to its shape rather than texture. Predictably, data augmentations have an effect here. When data is augmented with aggressive random cropping, this increases texture bias relative to shape bias, presumably because when large chunks of an object are cropped away, its overall shape becomes a less useful feature. Center cropping is better for shape bias, probably because objects are likely to be at the center of the image, so center cropping has less of a chance of distorting them. On the other hand, more "naturalistic" augmentations like adding Gaussian noise or distorting colors lead to a higher shape bias in the resulting networks, up to 60% with all the modifications. However, the authors also find that pushing the shape bias up has the result of dropping final test accuracy. 

https://i.imgur.com/Lb6RMJy.png

Interestingly, while the techniques that increase shape bias seem to also harm performance, the authors also find that higher-performing models tend to have higher shape bias (though with texture bias still outweighing shape) suggesting that stronger models learn how to use shape more effectively, but also that handicapping models' ability to use texture in order to incentivize them to use shape tends to hurt performance overall. 

Overall, my take from this paper is that texture-level data is actually statistically informative and useful for classification - even in terms of generalization - even if is too high-resolution to be useful as a visual feature for humans. CNNs don't seem inherently incapable of learning from shape, but removing their ability to rely on texture seems to lead to a notable drop in accuracy, suggesting there was real signal there that we're losing out on.

Wu et al. provide a framework (behavior regularized actor critic (BRAC)) which they use to empirically study the impact of different design choices in batch reinforcement learning (RL). Specific instantiations of the framework include BCQ, KL-Control and BEAR. 

Pure off-policy rl describes the problem of learning a policy purely from a batch $B$ of one step transitions collected with a behavior policy $\pi_b$. The setting allows for no further interactions with the environment. This learning regime is for example in high stake scenarios, like education or heath care, desirable. 

The core principle of batch RL-algorithms in to stay in some sense close to the behavior policy. The paper proposes to incorporate this firstly via a regularization term in the value function, which is denoted as **value penalty**. In this case the value function of BRAC takes the following form:

$
V_D^{\pi}(s) = \sum_{t=0}^{\infty} \gamma ^t \mathbb{E}_{s_t \sim P_t^{\pi}(s)}[R^{pi}(s_t)- \alpha D(\pi(\cdot\vert s_t) \Vert \pi_b(\cdot \vert s_t)))], 
$

where $\pi_b$ is the maximum likelihood estimate of the behavior policy based upon $B$. 
This results in a Q-function objective:
$\min_{Q} = \mathbb{E}_{\substack{(s,a,r,s') \sim D \\ a' \sim \pi_{\theta}(\cdot \vert s)}}\left[(r + \gamma \left(\bar{Q}(s',a')-\alpha D(\pi(\cdot\vert s) \Vert \pi_b(\cdot \vert s) \right) - Q(s,a) \right]  
$

and the corresponding policy update:
$
\max_{\pi_{\theta}} \mathbb{E}_{(s,a,r,s') \sim D} \left[ \mathbb{E}_{a^{''} \sim \pi_{\theta}(\cdot \vert s)}[Q(s,a^{''})] - \alpha  D(\pi(\cdot\vert s) \Vert \pi_b(\cdot \vert s)  \right] 
$
 
The second approach is **policy regularization** . Here the regularization weight $\alpha$ is set for value-objectives (V- and Q) to zero and is non-zero for the policy objective.

It is possible to instantiate for example the following batch RL algorithms in this setting:
- BEAR: policy regularization with sample-based kernel MMD as D and min-max mixture of the two ensemble elements for $\bar{Q}$
- BCQ: no regularization but policy optimization over restricted space

Extensive Experiments over the four Mujoco tasks Ant, HalfCheetah,Hopper Walker show:
1. for a BEAR like instantiation there is a  modest advantage of keeping $\alpha$ fixed
2. using a mixture of a two or four Q-networks ensemble as target value yields better returns that using one Q-network
3. taking the minimum of ensemble Q-functions is slightly better than taking a mixture (for Ant, HalfCeetah & Walker, but not for Hooper
4. the use of value-penalty yields higher return than the policy-penalty
5. no choice for D (MMD, KL (primal), KL(dual) or Wasserstein (dual)) significantly outperforms the other (note that his contradicts the BEAR paper where MMD was better than KL)
6. the value penalty version consistently outperforms BEAR which in turn outperforms BCQ with improves upon a partially trained baseline. 

This large scale study of different design choices helps in developing new methods. It is however surprising to see, that most design choices in current methods are shown empirically to be non crucial. This points to the importance of agreeing upon common test scenarios within a community to prevent over-fitting new algorithms to a particular setting.