Ernst

Since english isn't my native language, maybe I have expressed myself unclear. When you are doing the pools you want to have as many right as possible. I have probably stated my first question the wrong way. Whichever of the 81 possible results for 4 matches, I will always have at least 3 matches right with e.g. the nine combinations: 1X212X1X2 1X2X1221X 1X22X1X21 XXX222111 That doesn't take long time to verify. If my first question had concerned 8 soccer matches and there would have been 4 possible outcomes(very strange) but e.g. 1 = home win with more than 3 goals, 2=any other home win, 3=draw, 4=away win. Then the total number of possible combinatiions would have been 4^8 = 65536. It seems unlikely that I must choose 65513 of those to be guaranteed to have 7 right, but maybe... Maybe it's possible to use applied integer programming to solve my problem. I don't know enough. Forget my first question and try to regard my problem as soccer matches in this strange way. Do you understand me now?

I was in a hurry when I wrote, so I missed the vector (1, 1, 1 ,1 ,1 ,1 ,1 , 3). I know that this is not a TSP. Since roads and cities were involved I called it "a kind of TSP". Compare my question to trying to do the pools on 4 soccer matches. Home win: 1, draw: X, away win: 2. Number of possible results: 3 ^4 = 81 You can get away with only 9 of the 81 possible results and still have 3 out of 4 right. That's a reduction with 88.89 %. E.g. 1X212X1X2 1X2X1221X 1X22X1X21 XXX222111 Now I think you understand my question. I doubt that I have to chose as many as 65513 out of 65536 to "have" 7 "right". A reduction with only 0.035 %.

There are 9 cities. The ciities ar ordered from 1 to 9 and they are always visited in order from 1 to 9. From city n to city n+1 there are 4 routes, let's call them 1, 2, 3 and 4 . The distances doesn't matter. There are 4^8 possible routes from city 1 to city 9. Is it possible to find out the minimum number of ways to go from city 1 to city 9, such that the route would differ at one and only one segment from the one considered to be the right route? In other words: Possible vectors: (1,1,1,1,1,1,1,1) (1,1,1,1,1,1,1,2) (1,1,1,1,1,1,1,4) (1,1,1,1,1,1,2,1) (1,1,1,1,1,1,2,2) . . . (4,4,4,4,4,4,4,4) Person A chooses any of those. What is the minimum number of vectors person B must choose, to be sure that there is a difference in one and only one place(at most) compared to person A:s vector?

You can regard the 9 sets as 9 horse races and the 10 individuals as 10 different horses, with start number from 1 to 10. You are supposed to find the 9 winning start numbers and there is 10 ^ 9 possible combinations. The data are historical data and I want to predict the outcome when I get the next 9 races with 10 horses, i.e. 9 sets with 5(five) columns of data on each of the 10 horses in each race. There are only numbers, so no real identity on the horses. Column 1: Start numbers Columns 2 - 5: Ranking of the 10 horses in each race , rank 1 would be the best and 10 the worst, based on certain given data concerning each horse. Column 6: Winner = 1, loosers = 0. Then I think you understand that I could do logistic classification on the historical data and use that model to predict the winners(1) and losers(0). I regard that as "horisontal modeling". But I have plenty of data that strongly predicts that for the start numbers; column 1, very often 4 - 7 of the winning start numbers, out of 9, comes from the interval [ 1, 3]. I regard that as "vertical knowledge". I hope this makes it more clear what I want. I don't think a logistic classification could give a model that could predict, with any accuracy, which one of the 10 ^ 9 possible outcomes would be the right one. The "vertical knowledge" could maybe narrow the number of combinations that could be of interest. I would be happy if I had 7 of the races correct and if the model could pick out the 5 000 000 ( 0.5 % )best combinations to (randomly) choose among, since I of course can't afford to pay for 5 000 000 combinations. Best regards Ernst

Recently I have been trying to understand machine learning. I have a problem that machine learning maybe can solve. In principle this is my problem( the number of individuals in the real case is more than 10 in each set ) Everyday I get 9 data sets that look like this: 1 4 9 3 2 0 2 1 4 6 8 1 3 2 1 4 3 0 4 10 3 1 5 0 5 3 2 5 1 0 6 5 6 8 7 0 . . 9 . . . . 0 10 . . . . 0 The first column is always identical and let's call them identities. In the 9 data sets I want to get a solution that will predict the postive outcome(1) in column 6. So in this single data set, row 2 is of interest. Column 2 to 5 could be regarded as ranks. 9 sets give 10 ^ 9 possible combinations and only one is correct. 1 / 10 ^ 9 is a small number. I could make a logistic classification solution. I think that would give a poor solution. On the other hand there are very strong indications that for each combination of the 9 data sets, it nearly always is 4-7 out of the 9, among the values ​​1 to 3 in the first column, so a typical result would be the following numbers in column 1, with 1:s in column 6, for the combination of 9 sets: (2, 7, 1, 3, 2, 6, 1, 5, 3), i.e. 6 individuals in the interval [1- 3]. If I regard the logistic classification, which I don't think implicitly will capture "the 4-7-knowledge", as horisontal modeling, how could I get "the 4-7-knowledge", which I regard as vertical modeling, into the complete model? Best regards Ernst