I am taking part in a classification challenge (classes are 0 and 1) where the inputs are encrypted (because these are expensive financial data). As the encryption is order-preserving I can only use the fact that e.g. $$ x_1 > x_2 $$ but not $$ d = x_1-x_2 $$

Besides trees, which ML algorithms give sound models under these circumstances.

EDIT: I assume that neural nets, SVM or logistic regression are not appropriate in this setting as they use linear transformations $b \cdot x$ which I can not apply as I don't have the "numerical structure" for this.

EDIT 2: I am given data of the following form: $$ (0.2,0.1,0.5,0); (0.1,0.2,0.3,1); (0.02,0.7,0.33,1) $$ and thousands of rows of them (and in my application more columns). In this example the first 3 entries are inputs and the 4th one is the target. All clumns consist of 1001 unique values in the range [0,1]. So I really think that only comparisons are possible.

I am sorry if my question was not formulated precisely enough ... I hope now the problem is clearer!

I am taking part in a classification challenge (classes are 0 and 1) where the inputs are encrypted (because these are expensive financial data). As the encryption is order-preserving I can only use the fact that e.g. $$ x_1 > x_2 $$ but not $$ d = x_1-x_2 $$

Besides trees, which machine learning algorithms give sound models under these circumstances?

EDIT: I assume that neural nets, SVM or logistic regression are not appropriate in this setting as they use linear transformations $b \cdot x$ which I can not apply as I don't have the "numerical structure" for this.

EDIT 2: I am given data of the following form: $$ (0.2,0.1,0.5,0); (0.1,0.2,0.3,1); (0.02,0.7,0.33,1) $$ and thousands of rows of them (and in my application more columns). In this example the first 3 entries are inputs and the 4th one is the target. All clumns consist of 1001 unique values in the range [0,1]. So I really think that only comparisons are possible.

I am sorry if my question was not formulated precisely enough ... I hope now the problem is clearer!

I am taking part in a classification challenge (classes are 0 and 1) where the inputs are encrypted (because these are expensive financial data). As the encryption is order-preserving I can only use the fact that e.g. $$ x_1 > x_2 $$ but not $$ d = x_1-x_2 $$

Besides trees, which ML algorithms give sound models under these circumstances.

EDIT: I assume that neural nets, SVM or logistic regression are not appropriate in this setting as they use linear transformations $b \cdot x$ which I can not apply as I don't have the "numerical structure" for this.

EDIT 2: I am given data of the following form: $$ (0.2,0.1,0.5,0); (0.1,0.2,0.3,1); (0.02,0.7,0.33,1) $$ and thousands of rows of them (and in my application more columns). In this example the first 3 entries are inputs and the 4th one is the target. All clumns consist of 1001 unique values in the range [0,1]. So I really think that only comparisons are possible.

I am taking part in a classification challenge (classes are 0 and 1) where the inputs are encrypted (because these are expensive financial data). As the encryption is order-preserving I can only use the fact that e.g. $$ x_1 > x_2 $$ but not $$ d = x_1-x_2 $$

Besides trees, which ML algorithms give sound models under these circumstances.

EDIT: I assume that neural nets, SVM or logistic regression are not appropriate in this setting as they use linear transformations $b \cdot x$ which I can not apply as I don't have the "numerical structure" for this.

EDIT 2: I am given data of the following form: $$ (0.2,0.1,0.5,0); (0.1,0.2,0.3,1); (0.02,0.7,0.33,1) $$ and thousands of rows of them (and in my application more columns). In this example the first 3 entries are inputs and the 4th one is the target. All clumns consist of 1001 unique values in the range [0,1]. So I really think that only comparisons are possible.

I am sorry if my question was not formulated precisely enough ... I hope now the problem is clearer!