Statistics and Models

Univariate Statistics

Statistic	OnlineStat
Mean	`Mean`
Variance	`Variance`
Quantiles	`Quantile`, `OrderStats`, and `P2Quantile`
Maximum/Minimum	`Extrema`
Skewness and kurtosis	`Moments`
Sum	`Sum`
Geometric Mean	`GeometricMean`

Plotting (See Data Visualization)

Info

Many OnlineStats have Plot recipes beyond what is listed here.

Plot	OnlineStat
Big Data Viz	`Partition`, `IndexedPartition`, `KIndexedPartition`
Mosaic Plot	`Mosaic`
HeatMap	`HeatMap`

Time Series

Statistic	OnlineStat
Difference	`Diff`
Lag	`Lag`
Autocorrelation/autocovariance	`AutoCov`
Tracked history	`Trace`, `StatLag`

Multivariate Analysis

Statistic/Model	OnlineStat
Covariance/correlation matrix	`CovMatrix`
Principal components analysis	`CovMatrix`, `CCIPCA`
K-means clustering	`KMeans`
Multiple univariate statistics	`Group`

Nonparametric Density Estimation

Statistic/Model	OnlineStat
Histograms/continuous density	`Hist`, `KHist`, and `ExpandingHist`
ASH density (semiparametric, similar to KDE)	`Ash`
Approximate order statistics	`OrderStats`
Count for each unique value	`CountMap`
Approximate CDF	`OrderStats`

Parametric Density Estimation

Distribution	OnlineStat
Beta	`FitBeta`
Cauchy	`FitCauchy`
Gamma	`FitGamma`
LogNormal	`FitLogNormal`
Normal	`FitNormal`
Multinomial	`FitMultinomial`
MvNormal	`FitMvNormal`

Machine/Statistical Learning

Model	OnlineStat
Linear (also ridge) regression	`LinReg`, `LinRegBuilder`
Decision Trees	`FastTree`
Random Forest	`FastForest`
Naive Bayes Classifier	`NBClassifier`
ML via Stochastic Approximation	`StatLearn`

Other

Statistic/Model	OnlineStat
Handling Missing Data	`FilterTransform`, `CountMissing`, `SkipMissing`
Statistical Bootstrap	`Bootstrap`
Approx. count of distinct elements	`HyperLogLog`
Approx. count of occurrences	`CountMinSketch`
Random sample	`ReservoirSample`
Moving Window	`MovingWindow`, `MovingTimeWindow`

Collection of Stats

Statistic/Model	OnlineStat
Univariate data stream	`Series`
Multivariate data streams	`Group`
Group by categorical variable	`GroupBy`

Stochastic Approximation with `StatLearn`

Regression and Classification Losses

Loss	Function
$L_{2}$ Loss (squared error)	`OnlineStats.l2regloss`
$L_{1}$ Loss (absolute error)	`OnlineStats.l1regloss`
Logistic Loss	`OnlineStats.logisticloss`
$L_{1}$ Hinge Loss	`OnlineStats.l1hingeloss`
Generalized distance weighted discrimination	`OnlineStats.DWDLoss`

Penalty/regularization functions

Penalty	Function
None	`zero`
LASSO ($L_{1}$ penalty)	`abs`
Ridge ($L_{2}$ penalty)	`abs2`
Elastic Net	`OnlineStats.ElasticNet`

Optimization Algorithms

Algorithm	Constructor
Stochastic Gradient Descent	`SGD`
RMSProp	`RMSPROP`
AdaGrad	`ADAGRAD`
AdaDelta	`ADADELTA`
ADAM	`ADAM`
ADAMax	`ADAMAX`
MSPI (Majorized Stochastic Proximal Iteration)	`MSPI`
Online Majorization-Minimization (MM) - averaged surrogate	`OMAS`
Online MM - Averaged Parameter	`OMAP`