This paper aims at changing the attributes of a face, without manipulating other aspects of the image, such as add/remove glasses, make a person young/old, changed the gender, and hence the name Fader Networks, similar to sliders of audio mixing tools that can change a value linearly to increase/decrease a feature. 

The model is shown below:

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

An image $x$ is passed to the encoder and the output of the encoder $E(x)$ is passed to the 
discriminator to distinguish whether a feature $y$ is in the latent space or not. The encoded features $E(x)$ and the feature $y$ is passed to the decoder to reconstruct the image $D(E(x))$.

The AE therefore has two loss: 1- The reconstruction loss between $x$ and $D(E(x))$, and 2- The gan loss to fool the discriminator on the feature $y$ in the encoded space $E(x)$.

The discriminator tries to distinguish whether a feature $y$ is in the encoded space $E(x)$ or not, while the encoder tries to fool the discriminator. This process leads to removal of the feature $y$ from the $E(x)$ by encoder. The encoded feature $E(x)$ therefore does not have any information on $y$. However, since the decoder needs to reconstruct the same input image, $E(x)$ has to maintain all information, except the feature $y$ and the decoder should get the feature $y$ from the input of the decoder.

The model is trained on binary $y$ features such as:
male/female, young/old, glasses Yes/No, mouth open Yes/No, eyes open Yes/No (some samples from test set below):
https://i.imgur.com/bj9wu6B.png

At test time, they can change the features continuously and show transition in the features:
https://i.imgur.com/XUD3ZTu.png

The performance of the model is measured using mechanical turks on two metrics: Naturalness of the images and the accuracy of swapping features on the image. In both FadNet shows better results compared to IcGAN, and FadNet shows very good results on accuracy, however on naturalness the performance drops when some features are swapped.

On Flowers dataset, FadNet can change colors of the flowers:
https://i.imgur.com/7nvBSEY.png


I find the following positive aspects about FadNet:

1- It can change some features while maintaining other features of the image such as identity of the person, background information, etc.

2- The model does not need paired data. In some cases it is impossible to gather paired data (e.g. male/female) or very difficult (young/old).

3- The gan loss is used to remove a feature in the latent space, where that feature can be later specified for reconstruction by decoder. Since GAN is applied to latent space, it can be used to remove features on the data that is discrete (where direct usage of disc on those data is not trivial).

I think these aspects need further work for improvement:
- When multiple features are changed the blurriness of the image shows up:
https://i.imgur.com/LD5cVbg.png
When only one feature changes the blurriness affect is much less, despite the fact that they use L2-loss for AE reconstruction. I guess also using a high resolution of 256*256 helps make the bluriness of the images less noticeable.

- The model should be first trained only on AE (no gan loss) and then the gan loss in AE is linearly increased to remove a feature. So, it requires a bit of care in training it properly.

Overall, I find it an interesting paper on how to change a feature in an image when one wants to keep other features unchanged.

#### Goal
+ Predict 128 diagnoses for intensive pediatric care patients.

#### Dataset:

+ Children's Hospital LA.
+ Episode is a multivariate time series that describes the stay of one patient in the intensive care unit.

Dataset properties  | Value 
---------|----------
Number of episodes | 10,401
Duration of episodes | From 12h to several months
Time series variables | Systolic blood pressure, Diastolic blood pressure,  Peripheral capillary refill rate, End tidal CO2, Fraction of inspired O2,  Glasgow coma scale,  Blood glucose,  Heart rate,  pH,  Respiratory rate, Blood O2 Saturation,  Body temperature,  Urine output.

+ Resampling and missing values:
  + Irregularly sampled time-series that is resampled to an hourly rate.
    + Mean measurement within each hour window is taken.
    + Forward- and back-filling are used to fill gaps created by the resampling.
  + When variable time series is missing entirely: imputation with a clinically *normal* value defined by domain experts.
  + This paper is followed by [Modeling Missing Data in Clinical Time Series with RNNs](http://www.shortscience.org/paper?bibtexKey=journals/corr/LiptonKW16) from the same research group.
  
+ Labels:
  + Each episode is associated with 0 or more diagnoses. (in-house taxonomy, ICD-9 based).
  + Dataset contains 429 diagnoses. The paper focuses on the 128 most frequent diagnoses that appear 50 or more times in the dataset.

#### Architecture:

+ LSTM with Target Replication:

![Architecture](https://raw.githubusercontent.com/tiagotvv/ml-papers/master/clinical-data/images/Lipton2016a_target.png?raw=true "Target Replication")

+ Loss function:
  + For the model with target replication, output y is generated at every sequence step. The loss function is then a convex combination of the final loss (log-loss in the case of this paper) and the average of the losses over all steps where T is the number of sequence steps and alpha is a hyperparameter.

![Loss function](https://raw.githubusercontent.com/tiagotvv/ml-papers/master/clinical-data/images/Lipton2016a_loss.png?raw=true "Loss function")


#### Experiments and Results:

**Methodology**:
+ Split dataset: 80% training, 10% validation, 10% test
+ LTSM trained for 100 epochs via gradient stochastic gradient (with momentum).
+ Regularization L2: 1e-6, obtained via validation dataset.

+ LSTM: 2 hidden layers with 64 cells or 128 cells (and 50% dropout)
+ Multiple combinations: target replication / auxiliary target variables (trained using the other 301 diagnoses and other clinical information as a target. Inferences are made only for the 128 major diagnoses.

+ Baselines for comparison:
  + Logistic Regression - L2 regularized
  + MLP with 3 hidden layers - ReLU - dropout 50%.
  + Baselines tested in the raw time-series and in a feature engineering version made by domain experts.

*Metrics*:
+ Micro AUC, Micro F1: calculated by adding the TPs, FPs, TNs and FNs for the entire dataset and for all classes.
+ Macro AUC, Macro F1: Arithmetic mean of AUCs and F1 scores for each of the classes.
+ Precision at 10: Fraction of correct diagnoses among the top 10 predictions of the model.
  + The upper bound for precision at 10 is 0.2281 since in the test set there are on average 2.281 diagnoses per patient.

*Results*:

![All Results](https://raw.githubusercontent.com/tiagotvv/ml-papers/master/clinical-data/images/Lipton2016a_allresults.png?raw=true "Performance metrics across all labels")

*Results for selected diagnoses*:

![Results for Selected Diseases](https://raw.githubusercontent.com/tiagotvv/ml-papers/master/clinical-data/images/Lipton2016a_selected.png?raw=true "Performance for selected diagnoses")


#### Discussion:

+ Auxiliary outputs improve performance at the expense of increased training time. Very unbalanced dataset for some of the remaining 301 labels makes it spend an entire epoch only to learn that one of the target variables can take values ​​other than 0.

+ Real-Time Predictions: In the future, the authors expect that the proposed solution could be used to make continuously updated real-time alerts and diagnoses.

This paper merges a GAN and VAE to improve pose estimation on depth hand images. 

They used paired data (where both depth image ($x$) and pose ($y$) is provided) and merge that with unlabelled data where only depth image ($x$) is given. The model is shown below:
https://i.imgur.com/BvjZekU.png

The VAE model takes $y$ and projects it to latent space ($z_y$) using encoder and then reconstructs it back to $\bar y$.

Ali is used to map between latent space of VAE $z_y$ and the latent space of GAN $z_x$.
The depth image synthesizer takes $z_x$ and generates a depth image $\bar x$.

The Discriminator does three tasks: 

1-$L_{gan}$: distinguishing between true ($x$) and generated sample ($\bar x$). 

2- $L_{pos}$: predicting the pose of the true depth image $x$. 

3: $L_{smo}$: a smoothing loss to enforce the difference between two latent spaces in the generator and the ones predicted by discriminator to be the same (see below for more details). 

$\textbf{Here is how the data flows and losses are defined:}$ Given a pair of labelled data $(x,y)$, the pose $y$ is projected to latent space $z_y$, then projected back to estimate pose $\bar y$. 
Using VAE model, a reconstruction loss $L_{recons}$ is defined on pose. 
Using Ali, the latent variable $z_y$ is projected to $z_x$ and then the depth image $\bar{x}$ is generated $\bar{x} = Gen(Ali({z_y}))$. A reconstruction loss between x and $\bar{x}$ is defined (d_{self}). 
A random noise is samples from pose latent space ($\hat{z_y}$) and projected to a depth map using $\hat{x} = Gen(Ali(\hat{z_y}))$. Discriminator then takes $x$ and $\hat{x}$. It estimates pose on $x$ using $L_{pos}$. It also distinguishes between $x$ and $\hat{x}$ with $L_{gan}$. Finally, it measures the $x$ and $\hat{x}$'s latent space difference $smo(x, \hat x)$, which should be similar to the distance between $z_y$ and $\hat{z_y}$, so the smo-loss is: $L_{smo} = || smo(x, \hat x) - (z_y - \hat{z_y})||^2 + d_{self}$.


In general the the VAE model and the depth image synthesizer can be considered as the Generator of the network. The total loss can be written as:

$L_G = L_{recons} + L_{smo} - L_{gan}\\$
$L_D = L_{pos} + L_{smo} - L_{gan}\\$

The generator loss contains pose reconstruction, smo-loss, and gan loss on generated depth maps.
The discriminator loss contains pose estimation loss, smo-loss, and gan loss on distinguishing fake and real depth images.

Note that in the gen and disc losses all except the gan loss need paired data and the un-labelled data can be used for only gan-loss. However, the unlabelled data would train the lowest layers of the disc (for pose estimation) and the image synthesis part of gen. But for pose estimation (the final target of the paper), training the VAE model, and also mapping between VAE and GAN using Ali, labelled data should be provided. Also note that $ L_{smo}$ trains both generator and discriminator parameters.

In terms of performance the model improves the results on partially labelled data. On fully labelled data it shows either improvement or comparable results w.r.t to previous models. I find the strongest aspect of the paper in semi-supervised learning where smaller portion of labelled data is provided, However, due to the way parameters are binded together, the model needs some labelled data to train the model completely.

#### Goal:
+ Development and validation of a continuous score for patient assessment (to be used both outside and inside intensive care).

+ Prior work: Modified Early Warning Score (MEWS) identifies 44% of intensive care transfers occurring within the next 12 hours. Generates 69 false positives for each correctly identified event.


#### Dataset:

Model Creation | Model Validation
---------------|------------------
22,265 patients admitted to the *Sarasota Memorial Hospital* (SMH) between Jan/2004 and Dec/2004 | 32341 patients admitted to the SMH between Sep/2007 and Jun/2009 
| 45,771 patients admitted to the SMH between Jan/2008 and May/2010  
| 32,416 patients admitted to *Abigton Memorial Hospital* (AMH) between Jul/2009 and Jun/2010  
| 19,402 patients admitted between Jul/2008 and Nov/2008 in *Hospital C*.

+ ~ 7000 variables, 500 laboratory tests.
+ Constraints:
  + Variables should be related to the patient's condition
  + Collected with some frequency
  + Susceptible to variation during patient stay in the hospital
  + Focus: "How the patient is" not "Who the patient is"
+ The constraints reduce the number of candidate variables to 43 (13 nurse assessments, 6 vital signs and 23 laboratory tests)

#### Rothman Index:

+ The Rothman Index is based on the "Excess Risk" associated with each of the variables:

+ The excess risk is determined by the increase (in percentage points) of the mortality at 1 year identified for that variable. In the best case, the "excess" risk is zero and the Rothman Index equals 100.

![Excess Risk](https://raw.githubusercontent.com/tiagotvv/ml-papers/master/clinical-data/images/Rothman2013_excess.png?raw=true "Excess Risk")


+ The excess risk somewhat resembles the *impact coding* for categorical variables. One must always be careful that there is no data snooping.

+ The index consists of the 26 variables below. They were chosen from the 43 candidates using a *forward stepwise logistic regression* with the patients of the model creation dataset (criterion p-value <0.05). Note that the logistic regression is used only to choose the variables. The Rothman Index is not a regression model itself.

![Variables](https://raw.githubusercontent.com/tiagotvv/ml-papers/master/clinical-data/images/Rothman2013_variables.png?raw=true "Variables used to derive Rothman Index")


+ The lab tests are collected less frequently. The score is divided into two parts (one that takes into account the laboratory variables and another that does not take into account).

![Formula](https://raw.githubusercontent.com/tiagotvv/ml-papers/master/clinical-data/images/Rothman2013_formula.png?raw=true "Rothman Index Formula")

+ *TimeSinceLabs* has a maximum value of 48 hours.

#### Results:

+ Outcomes:
  + Mortality in 24h
  + Unplanned readmission in 30 days
  + Discharge
+ Rothman Index is correlated with discharge category (Home, Home healthcare, Rehab, Skilled Nursing Facility, Hospice, Death)

|Mortality in 24h || Readmission in 30 days || Discriminates type of discharge| | 
|-------------|-|-----------------------|-|------------------------|-------------------------------|
| Hospital|  AUC |  Hospital | AUC | Hospital | AUC|
|SMH | 0.933  (0.915-0.930) | SMH | 0.62  (0.61-0.63) | SMH | 0.923 (0.915-0.930)|
|AMH | 0.948  (0.960-0.970) | AMH | *|  AMH | 0.965 (0.960-0.970)|
|C | 0.929 (0.919-0.940) | C | *| C| 0.915  (0.900-0.931) |

(*) in the case of readmission in 30 days it was possible to only identify the patients of the SMH hospital.

+ Tracking the Rothman Index and correlating it with events during hospital stay:

![Evolution](https://raw.githubusercontent.com/tiagotvv/ml-papers/master/clinical-data/images/Rothman2013_evolution.png?raw=true "Evolution of Rothman Index during patient stay")


#### Discussion:

+ Choice of 1-year mortality to calculate excess risk:
  + Instead of in-hospital death, which is relatively rare (approximately 1—2% of patients), the model is based on 1-year post discharge mortality, where death is far more common (approximately 10% of patients). 
  + Improve the *signal strength* to determine the relationships between clinical measures and risk.  
  + Outcome should be sufficiently frequent and a plausible surrogate for the patient condition. In this case, the risk tries to quantify *distance from death*. 
+ The Rothman index is not designed to predict any specific outcome.
+ Caveat: Results should have included precision/recall analysis. For risk assessment it is important to evaluate the rate of false alarms per one true positive.

This paper directly relies on understanding [Gumbel-Softmax][gs] ([Concrete][]) sampling.

The place to start thinking about this paper is in terms of a distribution over possible permutations. You could, for example, have a categorical distribution over all the permutation matrices of a given size. Of size 2 this is easy:

```
p(M)   0.1    0.9

M:     1, 0   0, 1
       0, 1   1, 0
```

You could apply the Gumbel-Softmax trick to this, and other selections of permutation matrices in small dimensions, but the number of possible permutations grows factorially with the dimension. If you want to infer the order of $100$ items, you now have a categorical over $100!$ variables, and you can't even store that number in floating point.

By breaking up and applying a normalised weight to each permutation matrix, we are effectively doing a [Naive Birkhoff-Von Neumann decomposition][naive] to return a sample from the space of Doubly Stochastic matrices. This paper proposes *much* more efficient ways to sample from this space in a way that is amenable to stochastic variational (read *SGD*) methods, such that they have an experiment working with permutations of 278 variables.

There are two ingredients to a good stochastic variational recipe:

1. A differentiable sampling method; for example (most famously): $x = \mu + \sigma \epsilon \text{ where } \epsilon \sim \mathcal{N}(0,1)$
2. A density over this sampling distribution; in the preceding example: $\mathcal{N}(\mu, \sigma)$

This paper presents two recipes: Stick-breaking transformations and Rounding towards permutation matrices.

Stick-breaking
--------------------

[Shakir Mohamed wrote a good blog post on stick-breaking methods.][sticks]

One problem, which you could guess from the categorical-over-permutations example above, is we can't possibly store a probability for each permutation matrix ($N!$ is a lot of numbers to store). Stick-breaking gives us another way to represent these probabilities implicitly through $B \in [0,1]^{(N-1)\times (N-1)}$. The row `x` gets recursively broken up like this:

```
    B_11    B_12*(1-x[:1].sum())     1-x[:2].sum()
x: |-------|------------------------|---------------------|
    x[0]    x[1]                     x[2]
    <---------------------------------------------------->
                               1.0
```

For two dimensions, this becomes a little more complicated (and is actually a novel part of this paper) so I'll just refer you to the paper and say: *this is also possible in two dimensions*.

OK, so now to sample from the distribution of Doubly Stochastic matrices, you just need to sample $(N-1) \times (N-1)$ values in the range $[0,1]$. The authors sample a Gaussian and pass it through a sigmoid. Along with a temperature parameter, the values get pushed closer to 0 or 1 and the result is a permutation matrix.

To get the density, the authors *appear to* (this would probably be annoying in high dimensions) automatically differentiate through the $N^2$ steps of the stick-breaking transformation to get the Jacobian and use change of variables.

Rounding
-------------

This method is more idiosyncratic, so I'll just copy the steps straight from the paper:

> 1. Input $Z \in R^{N \times N} $, $M \in R_+^{N \times N}$, and $V \in  R_+^{N \times N}$;
> 2. Map $M \to \tilde{M}$, a point in the Birkhoff polytope, using the [Sinkhorn-Knopp algorithm][sk];
> 3. Set $\Psi = \tilde{M} + V \odot Z$ where $\odot$ denotes elementwise multiplication;
> 4. Find $\text{round}(\Psi)$, the nearest permutation matrix to $\Psi$, using the [Hungarian algorithm][ha];
> 5. Output $X = \tau \Psi + (1- \tau)\text{round}(\Psi)$.

So you can just schedule $\tau \to 0$ and you'll be moving your distribution to be a distribution over permutation matrices.

The big problem with this is we *can't easily get the density*. Step 4 is not differentiable. However, the authors argue the function is still piecewise-linear so we can just get around this. Once they've done that, it's possible to evaluate the density by change of variables again.

Results
----------

On a synthetic permutation matching problem, the rounding method gets a better match to the true posterior (the synthetic problem is small enough to enumerate the true posterior). It also performs better than competing methods on a real matching problem; matching the activations in neurons of C. Elegans to the location of neurons in the known connectome.

[sticks]: http://blog.shakirm.com/2015/12/machine-learning-trick-of-the-day-6-tricks-with-sticks/
[naive]: https://en.wikipedia.org/wiki/Doubly_stochastic_matrix#Birkhoff_polytope_and_Birkhoff.E2.80.93von_Neumann_theorem
[gs]: http://www.shortscience.org/paper?bibtexKey=journals/corr/JangGP16
[concrete]: http://www.shortscience.org/paper?bibtexKey=journals/corr/1611.00712
[sk]: https://en.wikipedia.org/wiki/Sinkhorn%27s_theorem#Sinkhorn-Knopp_algorithm
[ha]: https://en.wikipedia.org/wiki/Hungarian_algorithm