I want to find atoms, within a pre-defined set of atoms, that are in all possible optimal solutions of an ASP problem.
I'll explain what i want to do. I have an optimization problem where multiple optimal answer sets can exist. An answer set consists of atoms that characterizes a solution, for example node(0), edge(1,2) , as well as some that are not relevant, like color(0).
I want to compute all optimal answer sets, only show atoms of the type node() and edge(), then find the specific relevant atoms (like node(0) and edge(1,0)) that exist in all optimal answer sets.
I know i can limit the output of certain atoms with the #show directive. I can also add the flags --opt-mode=optN to compute all optimal answer and limit the output to only those with --quiet=1.
As per guide, using --enum-mode cautious computes the intersection of all answer sets.
An example:
If i have two optimal answer sets:
Answer set 1: node(1) node(0) edge(1,0) edge(0,1) color(1)
Answer set 2: node(1) node(0) edge(1,0) color(0)
I want to the result node(1) node(0) edge(1,0)
I can run clingo with --opt-mode=optN --quiet=1 then manually search for all node() or edge() atoms that all answer sets have in common.
I can add #show node/1 #show edge/2 to my encoding then run clingo with --opt-mode=optN --quiet=1 --enum-mode cautious.
Are all those two options logically equivalent?
Is there a more efficient way of achieving what i want?
I'm unsure about the interplay between the #show directive and the --opt-mode, --quiet and --enum-mode flags. I have a problem where answer sets can be very large, so i would prefer using option 2 since it would use the least disk space.
Thank you in advance.
You are definitely on the right track. I'm unsure about the combination of options though, especially --quiet as it only prevents showing the non-optimal models, but they will still be counted as models for the --enum-mode=cautious thingy.
You should simply use the clingo python API to achieve your goal. First, compute one optimal solution. Then you do have the bound that you can give as an additional argument to the opt-mode and your approach should work.
https://potassco.org/clingo/python-api/current/clingo/
Related
I am implementing and analysing the Find-S Algorithm (which I understood quite well). However, for the testing part, I am not sure whether the order of the examples in the training set affect the output.
Is this known or still unproven?
The order of examples will not affect the output if the function which expands the hypothesis is associative -- that is, if f(f(h0),x1),x2) = f(f(h0,x2),x1) for all h0,x1,x2.
The order of instances will affect your output because when FIND-S try to maximally specific hypothesis, it looks attributes and their values. It is discussed in Tom Mitchell's Machine Learning Book under title of '2.4 FIND-S FINDING A MAXIMALLY SPECIFIC HYPOTHESIS'.
I'm not sure what exactly I'm trying to ask. I want to be able to make some code that can easily take an initial and final state and some rules, and determine paths/choices to get there.
So think, for example, in a game like Starcraft. To build a factory I need to have a barracks and a command center already built. So if I have nothing and I want a factory I might say ->Command Center->Barracks->Factory. Each thing takes time and resources, and that should be noted and considered in the path. If I want my factory at 5 minutes there are less options then if I want it at 10.
Also, the engine should be able to calculate available resources and utilize them effectively. Those three buildings might cost 600 total minerals but the engine should plan the Command Center when it would have 200 (or w/e it costs).
This would ultimately have requirements similar to 10 marines # 5 minutes, infantry weapons upgrade at 6:30, 30 marines at 10 minutes, Factory # 11, etc...
So, how do I go about doing something like this? My first thought was to use some procedural language and make all the decisions from the ground up. I could simulate the system and branching and making different choices. Ultimately, some choices are going quickly make it impossible to reach goals later (If I build 20 Supply Depots I'm prob not going to make that factory on time.)
So then I thought weren't functional languages designed for this? I tried to write some prolog but I've been having trouble with stuff like time and distance calculations. And I'm not sure the best way to return the "plan".
I was thinking I could write:
depends_on(factory, barracks)
depends_on(barracks, command_center)
builds_from(marine, barracks)
build_time(command_center, 60)
build_time(barracks, 45)
build_time(factory, 30)
minerals(command_center, 400)
...
build(X) :-
depends_on(X, Y),
build_time(X, T),
minerals(X, M),
...
Here's where I get confused. I'm not sure how to construct this function and a query to get anything even close to what I want. I would have to somehow account for rate at which minerals are gathered during the time spent building and other possible paths with extra gold. If I only want 1 marine in 10 minutes I would want the engine to generate lots of plans because there are lots of ways to end with 1 marine at 10 minutes (maybe cut it off after so many, not sure how you do that in prolog).
I'm looking for advice on how to continue down this path or advice about other options. I haven't been able to find anything more useful than towers of hanoi and ancestry examples for AI so even some good articles explaining how to use prolog to DO REAL THINGS would be amazing. And if I somehow can get these rules set up in a useful way how to I get the "plans" prolog came up with (ways to solve the query) other than writing to stdout like all the towers of hanoi examples do? Or is that the preferred way?
My other question is, my main code is in ruby (and potentially other languages) and the options to communicate with prolog are calling my prolog program from within ruby, accessing a virtual file system from within prolog, or some kind of database structure (unlikely). I'm using SWI-Prolog atm, would I be better off doing this procedurally in Ruby or would constructing this in a functional language like prolog or haskall be worth the extra effort integrating?
I'm sorry if this is unclear, I appreciate any attempt to help, and I'll re-word things that are unclear.
Your question is typical and very common for users of procedural languages who first try Prolog. It is very easy to solve: You need to think in terms of relations between successive states of your world. A state of your world consists for example of the time elapsed, the minerals available, the things you already built etc. Such a state can be easily represented with a Prolog term, and could look for example like time_minerals_buildings(10, 10000, [barracks,factory])). Given such a state, you need to describe what the state's possible successor states look like. For example:
state_successor(State0, State) :-
State0 = time_minerals_buildings(Time0, Minerals0, Buildings0),
Time is Time0 + 1,
can_build_new_building(Buildings0, Building),
building_minerals(Building, MB),
Minerals is Minerals0 - MB,
Minerals >= 0,
State = time_minerals_buildings(Time, Minerals, Building).
I am using the explicit naming convention (State0 -> State) to make clear that we are talking about successive states. You can of course also pull the unifications into the clause head. The example code is purely hypothetical and could look rather different in your final application. In this case, I am describing that the new state's elapsed time is the old state's time + 1, that the new amount of minerals decreases by the amount required to build Building, and that I have a predicate can_build_new_building(Bs, B), which is true when a new building B can be built assuming that the buildings given in Bs are already built. I assume it is a non-deterministic predicate in general, and will yield all possible answers (= new buildings that can be built) on backtracking, and I leave it as an exercise for you to define such a predicate.
Given such a predicate state_successor/2, which relates a state of the world to its direct possible successors, you can easily define a path of states that lead to a desired final state. In its simplest form, it will look similar to the following DCG that describes a list of successive states:
states(State0) -->
( { final_state(State0) } -> []
; [State0],
{ state_successor(State0, State1) },
states(State1)
).
You can then use for example iterative deepening to search for solutions:
?- initial_state(S0), length(Path, _), phrase(states(S0), Path).
Also, you can keep track of states you already considered and avoid re-exploring them etc.
The reason you get confused with the example code you posted is essentially that build/1 does not have enough arguments to describe what you want. You need at least two arguments: One is the current state of the world, and the other is a possible successor to this given state. Given such a relation, everything else you need can be described easily. I hope this answers your question.
Caveat: my Prolog is rusty and shallow, so this may be off base
Perhaps a 'difference engine' approach would be appropriate:
given a goal like 'build factory',
backwards-chaining relations would check for has-barracks and tell you first to build-barracks,
which would check for has-command-center and tell you to build-command-center,
and so on,
accumulating a plan (and costs) along the way
If this is practical, it may be more flexible than a state-based approach... or it may be the same thing wearing a different t-shirt!
Nominally a good problem to have, but I'm pretty sure it is because something funny is going on...
As context, I'm working on a problem in the facial expression/recognition space, so getting 100% accuracy seems incredibly implausible (not that it would be plausible in most applications...). I'm guessing there is either some consistent bias in the data set that it making it overly easy for an SVM to pull out the answer, =or=, more likely, I've done something wrong on the SVM side.
I'm looking for suggestions to help understand what is going on--is it me (=my usage of LibSVM)? Or is it the data?
The details:
About ~2500 labeled data vectors/instances (transformed video frames of individuals--<20 individual persons total), binary classification problem. ~900 features/instance. Unbalanced data set at about a 1:4 ratio.
Ran subset.py to separate the data into test (500 instances) and train (remaining).
Ran "svm-train -t 0 ". (Note: apparently no need for '-w1 1 -w-1 4'...)
Ran svm-predict on the test file. Accuracy=100%!
Things tried:
Checked about 10 times over that I'm not training & testing on the same data files, through some inadvertent command-line argument error
re-ran subset.py (even with -s 1) multiple times and did train/test only multiple different data sets (in case I randomly upon the most magical train/test pa
ran a simple diff-like check to confirm that the test file is not a subset of the training data
svm-scale on the data has no effect on accuracy (accuracy=100%). (Although the number of support vectors does drop from nSV=127, bSV=64 to nBSV=72, bSV=0.)
((weird)) using the default RBF kernel (vice linear -- i.e., removing '-t 0') results in accuracy going to garbage(?!)
(sanity check) running svm-predict using a model trained on a scaled data set against an unscaled data set results in accuracy = 80% (i.e., it always guesses the dominant class). This is strictly a sanity check to make sure that somehow svm-predict is nominally acting right on my machine.
Tentative conclusion?:
Something with the data is wacked--somehow, within the data set, there is a subtle, experimenter-driven effect that the SVM is picking up on.
(This doesn't, on first pass, explain why the RBF kernel gives garbage results, however.)
Would greatly appreciate any suggestions on a) how to fix my usage of LibSVM (if that is actually the problem) or b) determine what subtle experimenter-bias in the data LibSVM is picking up on.
Two other ideas:
Make sure you're not training and testing on the same data. This sounds kind of dumb, but in computer vision applications you should take care that: make sure you're not repeating data (say two frames of the same video fall on different folds), you're not training and testing on the same individual, etc. It is more subtle than it sounds.
Make sure you search for gamma and C parameters for the RBF kernel. There are good theoretical (asymptotic) results that justify that a linear classifier is just a degenerate RBF classifier. So you should just look for a good (C, gamma) pair.
Notwithstanding that the devil is in the details, here are three simple tests you could try:
Quickie (~2 minutes): Run the data through a decision tree algorithm. This is available in Matlab via classregtree, or you can load into R and use rpart. This could tell you if one or just a few features happen to give a perfect separation.
Not-so-quickie (~10-60 minutes, depending on your infrastructure): Iteratively split the features (i.e. from 900 to 2 sets of 450), train, and test. If one of the subsets gives you perfect classification, split it again. It would take fewer than 10 such splits to find out where the problem variables are. If it happens to "break" with many variables remaining (or even in the first split), select a different random subset of features, shave off fewer variables at a time, etc. It can't possibly need all 900 to split the data.
Deeper analysis (minutes to several hours): try permutations of labels. If you can permute all of them and still get perfect separation, you have some problem in your train/test setup. If you select increasingly larger subsets to permute (or, if going in the other direction, to leave static), you can see where you begin to lose separability. Alternatively, consider decreasing your training set size and if you get separability even with a very small training set, then something is weird.
Method #1 is fast & should be insightful. There are some other methods I could recommend, but #1 and #2 are easy and it would be odd if they don't give any insights.
I have two images of real world. (IMPORTANT)I approximately know transformation of one real world to another. Due to texture problem I don't get enough matches between two images. How can I bring transformation information into account to get more and correct matches by using SIFt.
Any idea will be helpful.
Have you tried other alternatives? Are you sure SIFT is the answer? First, OpenCV provides SIFT, among other tools. (At the moment, I can't speak highly enough of OpenCV).
If I were solving this problem, I would first try:
Downsample your two images to reduce the influence of "texture", i.e. cvPyrDown.
Perform some feature detection: edge detection, etc. OpenCV provides a Harris corner detector, among others. Google "cvGoodFeaturesToTrack" for some detail.
If you have good confidence in your transformations, take advantage of your a priori information and look for features in neighborhoods corresponding to the transformed locations.
If you still want to look at SIFT or SURF, OpenCV provides those capabilities, as well.
If you know the transform, then apply the transform and then apply SURF/SIFT to the transformed image. That's one standard way to extend the robustness of feature descriptors/matchers across large perspective changes.
There is another alternative:
In sift parameters, Contrast Threshold is set to 0.04. If you reduce it and set it to a lower value ( 0.02,0.01) SIFT would find more enough matches:
SIFT(int nfeatures=0, int nOctaveLayers=3, double contrastThreshold=0.04, double edgeThreshold=10, double sigma=1.6)
The first step I think is to try with the settings of the SIFT algorithm to find the best efficiency with respect to your problem.
One another way to use SIFT more effectively is adding the COLOR information to SIFT. So you can add the color information (RGB) of the points which are being used in the descriptor to it. For instance if your descriptor size is 10x128 then it shows that you are using 10 points in each descriptor. Now you can extract and add three column and make the size 10x(128+3) [R-G-B for each point]. In this way the SIFT algorithm will work more efficient. But remember, you need to apply weight to your descriptor and make the last three columns be stronger than the other 128 columns. Actually I do not know in your case how the images are. but this method helped me a lot. and you can see that this modification makes SIFT a stronger method than before.
A similar implementation can be find here.
I have a database of items. They are for cars and similar parts (eg cam/pistons) work better than others in different combinations (eg one product will work well with another, while another combination of 2 parts may not).
There are so many possible permutations, what solutions apply to this problem?
So far, I feel that these are possible approaches (Where I have question marks, something tells me these are solutions but I am not 100% confident they are).
Neural networks (?)
Collection-based approach (selection of parts in a collection for cam, and likewise for pistons in another collection, all work well with each other)
Business rules engine (?)
What are good ways to tackle this sort of problem?
Thanks
The answer largely depends on how do you calculate 'works better'?
1) Independent values
Assuming that 'works better' function f of x combination of items x=(a,b,c,d,...) and(!) that there are no regularities that can be used to decide if f(x') is bigger or smaller then f(x) knowing only x, f(x) and x' (which could allow to find the xmax faster) you will have to calculate f for all combinations at least once.
Once you calculate it for all combinations you can sort. If you will need to look up data in a partitioned way, using SQL/RDBMS might be a good approach (for example, finding top 5 best solutions but without such and such part).
For extra points after calculating all of the results and storing them you could analyze them statistically and try to establish patterns
2) Dependent values
If you can establish some regularities (and maybe you can) regarding the values the search for the max value can be simplified and speeded up.
For example if you know that function that you try to maximize is linear combination of all the parameters then you could look into linear programming
If it is not...