State of Astro-informatics

I had a glance through "Realizing the potential of astrostatistics and astroinformatics" by Eadie et al. (2019). While I do not feel qualified or informed to comment on the suggestions, I can summarize them quickly. There are three problems:

1. Education: Most astronomers are not trained in code development resulting in maybe good but fragile code. Similarly, most computer scientists don't have the astronomy background or connections. 
2. Funding: Grants for methodology improvement are scarce. I wonder if these things can be funded from the computer science side of things in collaborations. 
3. Quality: Astro-informatics lacks support of state-of-the-art methodology as it stands. 

I was much more interested in the final section about potential themes in research:

1. Nonlinear dimensionality reduction.
2. Sparsity.
3. Deep learning.

I find the last theme incredibly broad and am unclear exactly how they mean it. It seems they're most interested in hierarchical representations of data. I would also claim that anomaly detection/clustering is important for reducing the volume of data. 

Training an autoencoder with mostly noise

I am working on a project where we wish to use anomaly detection to find what image patches have structure and which don't. As an aside, I ran an experiment on MNIST. You have 500 images of fives. You have 5000 images that are pure noise. You train a deep convolutional autoencoder. What you end up with is the following reconstruction:

The top row are the inputs and the bottom row are the reconstructions. You find images of fives even when nothing is present.

Flood

I stumbled upon a game called Flood. It's a simple enough game. You start with a grid of random colors. Then, you change the color of contiguous region formed from the upper left corner until you have flooded the entire grid with one color. I wrote some code and have been tinkering around some. 

The most naive solver is a breadth first search. So, I did that. Below you see the solution length for a grid size of varying size with only three colors.

This search breaks down at large grid size because it's so slow. Some kind of heuristic approach would perform better, but can you prove it's within some epsilon of optimal? What is the expected optimal solution length? I think that should be proveable theoretically since you just have a uniform grid and can constrain the growth rate. I will likely return and do that. 

Goal of Anomaly Detection in Non-stationary Data

I was explaining anomaly detection in non-stationary data to someone and threw together this crude example figure. The blue points are nominal and represent 90% of the points. The red are anomalous and represent 10% of the points. In this example, the red data is stationary while the blue passes through it. Thus, it would be very difficult to differentiate the red and blue points when they overlap. However, even if we only had a few frames of this video, we would like to be able to realize there are two dynamics going on.

The code for this is:

The Value of a Peer-Reviewed Activity

This week, we have been talking about proof writing in the discrete mathematics course I'm teaching. Yesterday, I started class by having students answer how confident they are about their proof writing skills on a scale of 1 to 10, 1 being "clueless and not sure where to start", 5 being "Okay and ready for homework," and 10 being "I can do most any proof you throw at me with ease." I then had them individually complete three proofs in 15 minutes.

Many students struggled with Problem 2 because they are not comfortable with sequence notation. Some misunderstood Problem 3 and tried proving something completely different than intended. After 15 minutes, they traded papers (with anonymous codes instead of their names so there was no embarrassment) and reviewed each someone else's papers as we went over them in class. They wrote some lovely, encouraging comments to each other. For example, one student had no idea of what to do on the second problem so they left it blank and their reviewer wrote, "Bet you can do it now! :D." Others noted where the proof failed and wrote a comment that they too had that difficulty. It's refreshing to see such kindness. Finally, they took the same survey about their proof writing again and there were dramatic changes in confidence.

Many more students were confident in their abilities. I'm not sure who the one who reported 1 after the exercise is. I hope they come to office hours.

This is in no way a rigorous test, but students expressed they learned more from this exercise because it forced them to think about the material instead of just going through the proof together on the board. I imagine there is a psychological benefit of seeing how someone else is doing too and being kind to them in written comments. It was also suggested that I do a problem example in class without proving it before class so students could hear my raw thought process first hand. I'll have to think about that. I like being prepared, but I'm sure I could find some way to do that.

In-class assignment collection

I have been quite busy and not prioritized logging work here; it was fairly new so it never became a habit. I'm teaching a course in Discrete Mathematics right now, the first class I've ever been the instructor. It's exciting. I have many things to learn, but I believe it's going well.

One trick that someone suggested to me is to have students try and solve a problem, write down their solution, and then hand it in with their name on it. It serves two purposes: you get a record of attendance and also get to glance through the work and gauge student progress. I award 3 points of quiz credit regardless of whether they answered correctly as an incentive to attend class. It's a little thing I might never have thought of, but it seems very effective.

Atypicality Presentation Recap

Yesterday, I gave a presentation introducing the ideas of atypicality to the Monteleoni research group. These are the slides and handwritten notes. I plan to explore this idea further and write up better LaTeX notes, which I will then share as well. For now, the idea of atypicality centers around using two coders: one trained to perform best on typical data and one that is universal and not data specific. A sequence is atypical if its code length using the typical coder is longer than the universal coder, i.e. it is not favored by the typical coder indicating the information is somehow unique. 

An example of the usage of atypicality from their 2019 paper "Data Discovery and Anomaly Detection using Atypicality for Real-valued data."

I presented on Elyas Sabeti and Anders H⊘st-Madsen's 2016 paper titled "How interesting images are: An atypicality approach for social networks". I think there are lots of opportunities for development in the image space, e.g. using different representations of images maybe including deep learning, exploring what made those images interesting by training a supervised classifier on the resulting labels and exploring the learned features. I'm concerned that their atypicality could be keying on background features, a lot more investigation is needed to understand the details of this application. I also think the image application needs more rigorous validation. They could have tested against other kinds of images to see if they also were labeled as atypical. One idea that was suggested by a member of our group (Amit Rege) is using the atypicality idea in a down-stream application to speed up stochastic gradient descent by picking atypical examples to learn from. 

A list of atypicality papers, by Sabeti & H⊘st-Madsen:

• Information theory for atypical sequences (2013)
• Data discovery and anomaly detection using atypicality: theory (2017)
• Atypicality for vector gaussian models (2015)
• Atypicality for the class of exponential family (2016)
• Enhanced MDL with application to atypicality (2017)
• Atypicality for Heart Rate Variability using a pattern-tree weighting method (2017)
• Data Discovery and Anomaly Detection using Atypicality for Real-Valued Data (2019)