Zhang and Sabuncu propose a generalized cross entropy loss for robust learning on noisy labels. The approach is based on the work by Gosh et al. [1] showing that the mean absolute error can be robust to label noise. Specifically, they show that a symmetric loss, under specific assumptions on the label noise, is robust. Here, symmetry corresponds to

$\sum_{j=1}^c \mathcal{L}(f(x), j) = C$ for all $x$ and $f$

where $c$ is the number of classes and $C$ some constant. The cross entropy loss is not symmetric, while the mean absolute error is. The mean absolute error however, usually results in slower learning and may reach lower accuracy. As alternative, the authors propose

$\mathcal{L}(f(x), e_j) = \frac{(1 – f_j(x)^q)}{q}$.

Here, $f$ is the classifier which is assumed to contain a softmax layer at the end. For $q \rightarrow 0$ this reduces to the cross entropy and for $q = 1$ it reduces to the mean absolute error. As shown in Figure 1, this loss (or a slightly adapted version, see paper, respectively) may obtain better performance on noisy labels. To this end, the label noise is assumed to be uniform, meaning that $p(\tilde{y} = k|y = j, x)= 1 - \eta$ where $\tilde{y}$ is the perturbed label.

https://i.imgur.com/HRQ84Zv.jpg
Figure 1: Performance of the proposed loss for different $q$ and noise rate $\eta$ on Cifar-10. A ResNet-34 is used.

[1] Aritra Gosh, Himanshu Kumar, PS Sastry. Robust loss functions under label noise for deep neural networks. AAAI, 2017.

Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/).

Probabilistic latent semantic indexing (PLSI) is an approach for document retrieval by modeling the joint probability model of words and documents as a mixture of independent multinomial distribution conditioned by latent semantic classes. The model is based on two independence assumption. First, the observed words and documents are assumed to be generated independently. Second, conditioned on the latent class, words are generated independently of the specific document identity. Given that the number of classes is smaller than the number of documents, each class acts as a bottleneck variable in predicting the distribution of words conditioned on documents.

Technical details

Given a word w and a document d, their joint probability distribution is model as follows.

$$P(d,w) = P(d)P(w|d), where$$

$$P(w|d) = \displaystyle\sum\_{z\in Z} P(w|z)P(z|d)$$

where $z$ denotes a latent class. 

Following the likelihood principle, one determines the distributions in (1) and (2) by maximization of the log-likelihood function

$$\mathcal{L} = \displaystyle\sum\_{d \in D} \displaystyle\sum\_{w \in W} n(d,w) log P(d,w)$$

The maximization is done by the Expectation Maximization (EM) algorithm.

Results

![](http://1.bp.blogspot.com/-eSKjS0950ac/VUHFJ2Vv7fI/AAAAAAAAA4U/bMGoVNh5_O0/s1600/result.png)

_Objective:_ Fondamental analysis of random networks using mean-field theory. Introduces two scales controlling network behavior.

## Results:

Guide to choose hyper-parameters for random networks to be nearly critical (in between order and chaos). This in turn implies that information can propagate forward and backward and thus the network is trainable (not vanishing or exploding gradient).

Basically for any given number of layers and initialization covariances for weights and biases, tells you if the network will be trainable or not, kind of an architecture validation tool.

**To be noted:** any amount of dropout removes the critical point and therefore imply an upper bound on trainable network depth.

## Caveats:

*   Consider only bounded activation units: no relu, etc.
*   Applies directly only to fully connected feed-forward networks: no convnet, etc.

#### Explainability-Accuracy trade-off

Many practical applications of machine learning systems call for the ability to explain why certain predictions are made. Consider a fraud detection system: it is not very useful for a user to see a list of possible fraud attempts without any explanation why the system thought the attempt was fraud. You want to say something like 'the system thinks it's fraud because the credit card was used to make several transactions that are smaller than usual'. But such explanations are not always compatible with our machine learning model. Or are they?

When choosing a machine learning model we usually think in terms of two choices:

- accurate but black-box: The best classification accuracy is typically achieved by black-box models such as Gaussian processes, neural networks or random forests, or complicated ensembles of all of these. Just look at the kaggle leaderboards. These are called black-box and are often criticised because their inner workings are really hard to understand. They don't, in general, provide a clear explanation of the reasons they made a certain prediction, they just spit out a probability.

- white-box but weak: On the other end of the spectrum, models whose predictions are easy to understand and communicate are usually very impoverished in their predictive capacity (linear regression, a single decision tree) or are inflexible and computationally cumbersome (explicit graphical models).

So which ones should we use: accurate black-box models, or less accurate but easy-to-explain white-box models?

The paper basically tells us that this is a false tradeoff. To summarise my take-home from this poster in one sentence:

`Explainability is not a property of the model`

Ryan presents a nice way to separate concerns of predictive power and explanation generation. He does this by introducing a formal framework in which simple, human-readable explanations can be generated for any black-box classifier, without assuming anything about the internal workings of the classifier.

If you think about it, it makes sense. If you watch someone playing chess, you can probably post-rationalise and give a reason why the person might think it's a good move. But you probably don't have an idea about the algorithm the person was executing in his brain.

Now we have a way to explain why decisions were made by complex systems, even if that explanation is not an exact explanation of what the classifier algorithm actually did. This is super-important in applications such as face recognitions where the only models that seem to work today are large black-box models. As (buzzword alert) AI-assisted decision making is becoming commonplace, the ability to generate simple explanations for black-box systems is going to be super important, and I think Ryan has made some very good observations in this paper.

I recommend everyone to take a look, I'm definitely going to see the world a bit differently after reading this.

TLDR; The authors train a DQN on text-based games. The main difference is that their Q-Value functions embeds the state (textual context) and action (text-based choice) separately and then takes the dot product between them. The authors call this a Deep Reinforcement Learning Relevance network. Basically, just a different Q function implementation. Empirically, the authors show that their network can learn to solve "Saving John" and "Machine of Death" text games.