ROI formulas language¶

Syntax¶

ROI expression syntax is similar to Python, it has math and logial expressions, it can refer prediction, actual and feature values, it can call some builtin functions and constants.

All expressions are evaluated per one row of data (prediction, actual and corresponding feature values).
Filter expression drop all rows that don't match. Filter is optional.
Investment expression is calculated for each row of data then it's aggregated by days.
Same for revenue expression.
Then ROI is calculated as a (revenue - investment) / investment

Examples:

filter: P >= 0.20
investment: $100
revenue: (1 + A) * $100

or

filter: P = True
investment: $loan_amount
revenue: if(A = True, $loan_amount * ((1 + $interest_percent / 100) ** $period_years), $0)

Expressions can be nested with parentheses, the operators precedence same as in Python

Tuples¶

Tuples can be defined as a several values inside a parentheses separated by comma

(1, "one") (1 + 2, "something", f(1, 2))

If expression¶

ROI syntax has one flow control expression

if(P > 0.2, $1050, $0)

in this case if prediction value is greater than 0.2 if expression returns 1050, else 0

Top expression¶

This expression allows to filter rows by some aggregates

top 2 by P per $symbol - group all rows by $symbol and return top 2 by P rows per each group.

top 10 by P from (bottom 5 by $spread per $symbol) - first it finds 5 records with lowest $spread per each $symbol, then it returns top 10 by P from these records

Full syntax:

(((top | bottom) NUMBER by expression) | all) [with_expression] [per expression [having expression]] [where expression] [from (top_expression)]

top - sort in descending order
bottom - sort in ascending order
all - select all items
NUMBER - number of values to select
with_expression - allows to add additional fields to result e.g. all with agg_max(P) as max_p
by expression - define a value for sorting
per expression (optional) - define a grouping
having expression (optional) - define a filter to drop a group, if all rows do not match the expression then whole group is dropped
where expression (optional) - define addition filter
from (top_expression) (optional) - define nested top expression

Numbers¶

123 integer numbers
123.456 float numbers
-123.456 numbers can be negative
$50.99 numbers can start with dollar sign to express money

String literals¶

"some value"

Variables¶

P or prediction predicted value
A or actual actual value
$feature1 value of feature with name feature1, name should start with alphabetical char or underscore, name can contain digits

Builtin operators¶

Math operators:¶

+ addition
- subtraction and unary minus
* multiplication
/ divison
// floor division
% modulus
** exponentiation

Bitwise operators:¶

| or
& and
^ xor
~ unary not
<< zero fill left shift
>> signed right shift

Logical operators:¶

or logical or
and logical and
not logical unary not

Comparison operators:¶

== equal
!= not equal
> greater than
>= greater than or equal to
< less than
<= less than or equal

Builtin constants¶

None - None value
True - True value
False - False value

Builtin functions¶

abs(x : number) : number¶

Return the absolute value of a number

ceil(x : float) : integer¶

Return the ceiling of x, the smallest integer greater than or equal to x

cos(x : number) : float¶

Return the arc cosine of x, in radians. The result is between 0 and pi.

exp(x : number) : float¶

Return e raised to the power x, where e = 2.718281… is the base of natural logarithms.

floor(x : floor) : float¶

Return the floor of x, the largest integer less than or equal to x.

if(<boolean predicate>, <true expression>, <false expression>)¶

Evaludate predicate, if it's True returns result of true expression else result of false expression

len(s : string) : integer¶

Return the length (the number of chars) of an string.

log(x : number, [base : number]) : float¶

With one argument, return the natural logarithm of x (to base e).

With two arguments, return the logarithm of x to the given base, calculated as log(x)/log(base).

log10(x : number) : float¶

Return the base-10 logarithm of x. This is usually more accurate than log(x, 10).

log2(x : number) : float¶

Return the base-2 logarithm of x. This is usually more accurate than log(x, 2).

max(arg1 : number, arg2 : number, *args) : number¶

Return the largest of two or more arguments.

min(arg1 : number, arg2 : number, *args) : number¶

Return the smallest of two or more arguments.

randint(a : integer, b : integer) : integer¶

Return a random integer N such that a <= N <= b.

random() : float¶

Return the next random floating point number in the range [0.0, 1.0).

round(number : float [, ndigits : integer]) : integer¶

Return number rounded to ndigits precision after the decimal point. If ndigits is omitted or is None, it returns the nearest integer to its input.

sin(x : number) : number¶

Return the sine of x radians.

sqrt(x : number) : number¶

Return the square root of x.

tan(x : number) : number¶

Return the tangent of x radians.

Builtin agg functions¶

agg_max(expression) : number¶

Max value in the group

agg_min(expression) : number¶

Min value in the group