The paper starts with the BNN with latent variable and proposes an entropy-based and a variance-based measure of prediction uncertainty. For each uncertainty measure, the authors propose a decomposition of the aleatoric term and epistemic term. A simple regression toy experiment proves this decomposition and its measure of uncertainty. Then the author tries to improve the regression toy experiment performance by using this uncertainty measure into an active learning scheme. For each batch, they would actively sample which data to label. The result shows that using epistemic uncertainty alone outperforms using total certainty, which both outperforms simple gaussian process. The result is understandable since epistemic is directly related to model weight uncertainty, and sampling from high aleatoric uncertain area does help supervised learning.

Then the authors talk about how to extend the model based RL by adding a risk term which consider both aleatoric term and epistemic term, and its related to model-bias and noise aversion. The experiments on Industrial Benchmark shows the method is able prevent overfitting the learned model and better transfer to real world, but the method seems to be pretty sensitive to $\beta$ and $\gamma$. 

Paper overviews importance of Causality in AI and highlights important aspects of it. Current state of AI deals with only association/curve fitting of data without need of a model. But this is far from human-like intelligence who have a mental representation that is manipulated from time-to-time using data and queried with What If? questions. To incorporate this, one needs to add two more layers on top of curve fitting module which are interventions(What if I do this?) and counterfactuals(What if I had done this?). Interventions are represented by P(y|do(x)) where do(x) is action 'x' performed leading to change in behavior of certain variables, thereby making previous data useless for its estimation. Counterfactuals are represented by P(y(x)|x',y') where x',y' are observed and goal is to determine probability of y given x. Pearl suggests use of Structural Causal Models(SCM) for interventions and counterfactuals. SCM takes a query(association, intervention or counterfactual) and graphical model(based on assumptions) to build a estimand(mathematical recipe). Estimand takes data and produces an estimate(answer) with confidence. Assumptions are fine tuned based on data. There are lot of advantages provided by Causal Models - (1)Graphical models make it easier to read the assumptions, thereby providing transparency. It also makes it easier to verify all dependencies encoded in data with the help of d-separation, thereby providing testability (2)Causal models help in mediation analysis that identify mechanisms that change cause to effect for explainability (3)Current transfer learning approaches are tried at association level but it cannot identify mechanisms that are affected by changes (4)Causality provides tools to recover causal relationships when data has missing attributes unlike statistical analysis that provide tools only when values are missing at random i.e. independent of other variables.

DRL has lot of disadvantages like large data requirement, slow learning, difficult interpretation, difficult transfer, no causality, analogical reasoning done at a statistical level not at a abstract level etc. This can be overcome by adding a symbolic front end on top of DL layer before feeding it to RL agent. Symbolic front end gives advantage of smaller state space generalization, flexible predicate length and easier combination of predicate expressions. DL avoids manual creation of features unlike symbolic reasoning. Hence DL along with symbolic reasoning might be the way to progress for AGI. State space reduction in symbolic reasoning is carried out by using object interactions(object positions and object types) for state representation. Although certain assumptions are made in the process such as objects of same type behave similarly etc, one can better understand causal relations in terms of actions, object interactions and reward by using symbolic reasoning. 

Broadly, pipeline consists of (1)CNN layer - Raw pixels to representation (2)Salient pixel identification - Pixels that have activations in CNN above a certain threshold (3)Identify objects of similar kind by using activation spectra of salient pixels (4)Identify similar objects in consecutive time steps to track object motion using spatial closeness(as objects can move only by a small distance in consecutive frames) and similar neighbors(different type of objects can be placed close to each other and spatial closeness alone cannot identify similar objects) (4)Building symbolic interactions by using relative object positions for all pairs of objects located within a certain maximal distance. Relative object position is necessary to capture object dynamics. Maximal distance threshold is required to make the learning quicker eventhough it may reach a locally optimal policy (4)RL agent uses object interactions as states in Q-Learning update. Instead of using all object interactions in a frame as one state, number of states are further reduced by considering interactions between two types to be independent of other types and doing a Q-Learning update separately for each type pair. Intuitive explanation for doing so is to look at a frame as a set of independent object type interactions. Action choice at a state is then the one that maximizes sum of Q values across all type pairs. 

Results claim that using DRL with symbolic reasoning, transfer in policies can be observed by first training on evenly spaced grid world and using it for randomly spaced grid world with a performance close to 70% contrary to DQN that achieves 50% even after training for 1000 epochs with epoch length of 100. 

There are 2 implementations for the paper:

 1. [Reference Implementation of Deep Linear Discriminant Analysis (DeepLDA)](https://github.com/CPJKU/deep_lda).
 2. [VahidooX/DeepLDA](https://github.com/VahidooX/DeepLDA).

[It seems something is wrong with the cost function implemented](https://github.com/VahidooX/DeepLDA/issues/1#issuecomment-392261355).
Also, while they derive the Gradient they didn't verify it and in the implementation use Theano's Auto Grad (While other Auto Grad can't work it out).

Main Purpose:
* The main goal of the proposed method is to exploit a global perception
mechanism, known as figure-ground segregation and Boolean Map Theory of
visual attention to compute saliency map.

Drawbacks of previous works:
* Most of the previous works do not exploit the topological structures of an image to
saliency calculation. Thus this paper aims to exploit the topological structure of a
scene in saliency calculation.

Main Idea:
* Relying on Boolean Map Theory of visual attention, an observer’s momentary
conscious awareness of a scene can be represented by a Boolean map. Given an
input image, a set of Boolean maps can be generated by randomly thresholding its
feature channels, e.g. color channel. When the set of Boolean maps is generated,
some concepts from figure-ground segregation, introduced by Gestalt
psychological studies, can be utilized to create a saliency map. As Gestalt
psychological studies suggest, figures are more likely to be attended than to
background elements. But how the figures are characterized? There is some factors
that are likely to influence figure-ground segregation such as size, surroundedness,
symmetry and etc. The proposed method uses the surroundedness factor to form a
saliency map. This factor implies that figures tends to be surrounded, that is,
they’re likely to have a closed outer contour. Therefore, this factor can be
evaluated over Boolean maps and each region which has the closed outer contour,
not connected to the image borders, gets higher attention value. So each Boolean
map result in an attention map. Then, attentions maps are summed up lineally to
form a saliency map.
In brief, the contribution of the proposed method is twofold: 1) It uses Boolean
maps to characterizes an image. 2) It exploits the figure-ground segregation
concepts to form a saliency map.

Implementation Details:
* Given an input image, a set of Boolean maps are generated by thresholding the
color channels (Lab) with uniformly selected thresholds from 0 to 255. Then, each
Boolean map is evaluated by surroundedness. Those regions which are surrounded
(closed outer contour) get value 1 and others 0. These maps are called attention
maps. After some normalization steps, the attention maps (per Boolean map) are
summed up linearly to form a mean attention map. Again, some normalization and
post-processing steps are applied and the final saliency map is obtained.

* Conclusion
In this work, a novel Boolean Map based Saliency model is proposed to leverage
the surroundedness cue that helps in figure-ground segregation. The model
borrows the concept of Boolean map from the Boolean Map Theory of visual
attention and characterizes an image by a set of Boolean maps. This representation
leads to an efficient algorithm for saliency detection. BMS is the only model that
consistently achieves state-of-the-art performance on five benchmark eye tracking
datasets, and it is also shown to be useful in salient object detection.