# Definitions

Overview of all definitions and vocabulary used to speak about scoring

Described below are the vast majority of definitions for functions and statistical tools used to publish scores. Read the open-sourced code at numerai-tools/scoring. Install the package with:

## Statistics

tie-broken rank

percentile rank a series

break ties based on id / index

tie-kept rank

percentile rank a series

for each set of ties set their ranks to the average of that set's tie-broken ranks

correlation

correlation coefficient between two series

spearman correlation

spearman correlation coefficient between live target and predictions

different than tie-broken-rank correlation b/c spearman ranking keeps ties by assigning mean rank

pearson correlation

pearson correlation coefficient between live target and predictions

different that other correlations b/c pearson does not use ranking

tie-broken-rank correlation

correlation between live target and tie-broken ranked predictions (w/ sorted index, no nans)

NOTE: This is a pearson correlation, but rank the predictions, so it behaves more like a spearman. It is impossible to achieve 1.0 correlation because targets still have ties but predictions do not.

variance normalize

given vector s, normalize its standard deviation to 1

power x / pow x

given vector s, exponentiate each value of s to some power x, ignoring sign

gaussianize

given vector s, make s unit norm by dividing standard deviation of s

neutralization

given vector s, find the orthogonal component s' WRT a matrix of neutralizers N:

s' = s -(N dot (N_inverse dot s))

orthogonalize

similar to neutralize, but is faster for 2 centered column vectors

given vectors u and v, find the component of v that is orthogonal to u:

v - (u ⦻ ( dot(transpose(v), u) / dot(transpose(u), u) )

numerai corr

given prediction vector s and target vector t find the correlation between s and t:

s` = tie-kept rank, then gaussianize, then pow 1.5 vector s

t` = pow 1.5 vector t

calculate the pearson correlation of s` and t`

feature neutral corr

given prediction vector s, matrix of features to neutralize F, and target vector t, find the correlation of s with t after neutralizing to F:

s` = tie-kept rank, then gaussianize s

s`` = neutralize s` to F, then variance normalize

calculate numerai corr of s`` and t

correlation contribution

given target vector t, meta model vector m, and prediction vector s, find how much s contributes to m’s correlation with t:

m` = tie-kept rank then gaussianize m

s` = tie-kept rank then gaussianize s

s`` = orthogonalize s` with respect to m

get the covariance of s`` and t

### Factors & Features

Factors

unencrypted (possibly cleaned/formatted/etc.) data from our data providers

signals not given to users, but are very well-known in finance

we always neutralize targets, portfolios, and the Meta Model to these

Features

encrypted stock market signals given to users for use as machine learning features

a dataset is made of several variations of a smaller set of features

we usually penalize exposure to these, but are not always 100% neutral

V3 Features

all features used in our v3 "supermassive" dataset

V4 Medium Safe Features

there are 5 feature variations in the v4 dataset

only 2 of those variations are included in this subset

### Targets

weekdays

Mon - Fri (20D = 20 Days = 4 weeks)

returns lag

number of days skipped before starting returns calculations

(2L = 2 Lag = skip 2 weekdays)

timeline XDYL

scores over X weekdays with Y days of returns lag

neutralizers

factors/features to which the target is neutral

bins=x

values for the target are binned into x distinct bins

uniformity = x, y, z, …

x% of values in outer 2 bins (e.g. 0 and 1)

y% of values in next inner 2 bins (e.g. 0.25 and 0.75)

z% of values in next inner bin(s) (e.g. 0.5)

…

target_[name]_20

timeline: 20D2L

bins=5, uniformity=10%, 40%, 50%

neutralizers: Common Factors and/or Features

target_[name]_60

timeline: 60D2L

bins=5, uniformity=10%, 40%, 50%

neutralizers: Common Factors and/or Features

### Meta Models

Stake-Weighted Meta Model (SWMM)

A stake-weighted average of Numerai submissions

The Numerai Hedge Fund uses this for trading

Benchmark Meta Model (BMM)

A stake-weighted average of Benchmark Models

### Scores

data lag

number of days it takes our vendors to process returns data

scores start returns lag + data lag days after a round closes (usually 2+2=4 days)

MMC - Meta Model Contribution

correlation contribution of a submission, SWMM, and target_cyrus_20

timeline: 20D2L (+ 2 days data lag)

CORR20v2 - Correlation 20D2L v2

numerai corr of a submission against target_cyrus_20

timeline: 20D2L (+ 2 days data lag)

CORJ60 - Correlation Jerome 60D2L

numerai corr of a submission against target_jerome_60

timeline: 60D2L (+ 2 days data lag)

BMC - Benchmark Model Contribution

correlation contribution of a submission, BMM, and target_cyrus_20

timeline: 20D2L (+ 2 days data lag)

FNCV3 - Feature Neutral Correlation V3

feature neutral corr of a submission, V3 Features, and target_nomi_20

timeline: 20D2L (+ 2 days data lag)

CWMM - Corr w/ Meta Model

s` = tie-kept rank, then gaussianize, then pow 1.5 a submission s

calculate pearson correlation between s` and SWMM

timeline: 4 days data lag / not dependant on returns

MCWNM - Max Corr w/ Numerai Models

Maximum pearson correlation of a submission with any other Tournament submission

only compared to other submissions made in the same round

timeline: 4 days data lag)/ not dependant on returns

APCWNM - Average Pairwise Corr w/ Numerai Models

Average pearson correlation of a submission with each other Tournament submission

only compared to other submissions made in the same round

timeline: 4 days data lag / not dependant on returns

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