Timeline for Are models using satellite image inputs well-posed?
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Nov 16, 2021 at 11:53 | vote | accept | Avatrin | ||
| S Oct 1, 2021 at 11:12 | history | bounty ended | Avatrin | ||
| S Oct 1, 2021 at 11:12 | history | notice removed | Avatrin | ||
| Sep 25, 2021 at 16:14 | comment | added | Avatrin | Let us continue this discussion in chat. | |
| Sep 25, 2021 at 15:15 | comment | added | Avatrin | @SextusEmpiricus No, it's a regression task for an image and a geographic coordinate ( f(x,t) = amount of pollution at said coordinate at a given time). The input LUR uses is an image of the area around said coordinate. The only reason I used the time example was to show that maps are discontinuous since the last criterion for well-posedness is that output change continuously with inputs. Hadamards original formulation is for differential equations, but there are generalizations for, e.g., Bayesian inverse problems... Also, have you ever seen a map or satellite image? | |
| Sep 25, 2021 at 15:01 | comment | added | Sextus Empiricus | So, the following analogy is how I try to interpret your question by imagining what this land use regression task is supposed to mean (I am not sure what the machine learning algorithm is supposed to do). Say you have an image classification that interprets images of size 80 by 80. It will tell you for instance a probability for whether a street is in the image or not. Now you apply this classification on a set of images that are created along along a path. Then you get a function of the probability along the path. But why should this bother the classification? Is my interpretation wrong? | |
| Sep 25, 2021 at 14:28 | comment | added | Sextus Empiricus | " I never said one that discreteness is the issue. Where did you get that from?" I interpreted discontinuity as discreteness or categorical data. Either the 80 by 80 meters contains a street or it does not. Then you turn this into a function of time or space coordinates. But the image of the function is a discrete or categorical variable. | |
| Sep 25, 2021 at 14:27 | comment | added | Sextus Empiricus | "That is, if I continuously move across the globe, the output should change continuously as well. " Why should the output change continuosly? Is this some criterion for landuse regression? For an average statistics user this doesn't sound obvious. | |
| Sep 25, 2021 at 14:25 | comment | added | Avatrin | @SextusEmpiricus I never said one that discreteness is the issue. Where did you get that from? I wrote continuity, so clearly I am thinking of the underlying uncountably infinite set. | |
| Sep 25, 2021 at 14:17 | comment | added | Sextus Empiricus | Maybe my issue with this question is that I haven't heard of Hadamard's criterions before. I could also not find any articles that use it or at least a search for Hadamard's criterion on JSTOR and Google scholar only gave unrelated results. What I don't see is how you believe that discrete input is problatic. This is ubiquitous in machine learning. E.g. any image recognition algorithm will be trained with images that either do or don't contain a cat in the image. Continuous cat's live only in thoughtproblems in quantum mechanics. | |
| Sep 25, 2021 at 13:36 | answer | added | shimao | timeline score: 2 | |
| Sep 25, 2021 at 9:54 | history | edited | Avatrin | CC BY-SA 4.0 |
added 175 characters in body
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| Sep 25, 2021 at 9:45 | comment | added | Avatrin | @SextusEmpiricus The point here is not the task or how it's presented; It's Hadamards third criterion for well-posedness; That is, if I continuously move across the globe, the output should change continuously as well. It doesn't really matter much what the task here is; Any sudden discontinuity in the input space, here it is the globe as seen from above, seems to contradict that property. I'll try rephrasing the question. It may be a tad misleading. | |
| Sep 25, 2021 at 8:43 | comment | added | Sextus Empiricus | "If I start scanning over a street..." I have the idea now that you have a series of nearby images in which some have the street en some have not. But I am not sure what the problem is with this. How does the mechanism of the machine-learning work? What is it doing? And what is the deal with the time, can I imagine that an airplane or satellite is scanning along some path making repeatedly video/picture frames of 80 by 80 meters? So the time is effectively a coordinate in space? Or are you scanning the same place and observe changes in time? | |
| S Sep 25, 2021 at 7:44 | history | bounty started | Avatrin | ||
| S Sep 25, 2021 at 7:44 | history | notice added | Avatrin | Draw attention | |
| Sep 24, 2021 at 12:57 | history | edited | Avatrin | CC BY-SA 4.0 |
added 8 characters in body
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| Sep 24, 2021 at 12:49 | history | edited | Avatrin | CC BY-SA 4.0 |
generalizing the question a bit... and correcting a statement in the text
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| Sep 22, 2021 at 13:23 | history | asked | Avatrin | CC BY-SA 4.0 |