API Reference 2 Original Algorithms

openmoa.regressors

API reference for OpenMOA's original regression algorithms. Both regressors are designed for streams with evolving feature spaces, extending their classification counterparts (FESL and OASF) to continuous target prediction.

Original Regressors

FESLRegressor OASFRegressor

Scope

algorithm coverage

§1 FESLRegressor

class FESLRegressor regression · src/openmoa/regressor/_fesl_regressor.py · Inheritance: Regressor

Full name: Feature Evolvable Streaming Learning — Regression

FESL regression handles feature-space transitions by maintaining two linear models, one per feature space (S1 and S2). During an overlap window straddling the transition point, it accumulates instances from both spaces and learns a mapping matrix M: S2 → S1 via Ridge Regression. After the transition, predictions are a weighted ensemble: ŷ = α1·w1·x1 + α2·w2·M·x2, where ensemble weights are updated based on per-model squared loss.

Constructor

signature

FESLRegressor(
    schema: Schema,
    s1_feature_indices: list[int],
    s2_feature_indices: list[int],
    overlap_size: int = 50,
    switch_point: int = 500,
    ensemble_method: str = "combination",
    learning_rate_scale: float = 1.0,
    random_seed: int = 1,
)

Parameter	Type	Default	Description
schema	Schema	required	Stream schema
s1_feature_indices	list[int]	required	Feature indices for the first (original) feature space S1
s2_feature_indices	list[int]	required	Feature indices for the second (new) feature space S2
overlap_size	int	50	Number of instances in the overlap buffer used to learn the mapping matrix M
switch_point	int	500	Instance index at which the feature space transition begins
ensemble_method	str	"combination"	`"combination"`: weighted ensemble of both models; `"selection"`: use the better-performing model only
learning_rate_scale	float	1.0	Scales the learning rate during weight updates
random_seed	int	1	RNG seed

Attributes

Attribute	Type	Description
w1	ndarray	Weight vector for feature space S1
w2	ndarray	Weight vector for feature space S2
M	ndarray	Mapping matrix from S2 to S1 (learned via Ridge Regression during overlap)
alpha1	float	Ensemble weight for model 1
alpha2	float	Ensemble weight for model 2
d1	int	Dimensionality of S1
d2	int	Dimensionality of S2
B	int	Overlap buffer size
T1	int	Switch point instance index
overlap_X1	list	Buffered S1 features during overlap period
overlap_X2	list	Buffered S2 features during overlap period

Methods

Method	Signature	Returns	Description
train	(instance: Instance) → None	None	Updates weight vectors via squared loss gradient; during overlap period accumulates buffer; when buffer full learns mapping matrix M and updates ensemble weights
predict	(instance: Instance) → float	float	`"combination"`: returns α1·w1·x1 + α2·w2·M·x2; `"selection"`: returns prediction from the better-performing model only

§2 OASFRegressor

class OASFRegressor regression sparse · src/openmoa/regressor/_oasf_regressor.py · Inheritance: Regressor

Full name: Online Active Sparse Feature Learning — Regression

OASF regression extends the classification ring-buffer architecture to continuous targets using a Passive-Aggressive ε-insensitive loss (PA-R). It adds CUR matrix decomposition regularization (eta) that constrains the weight matrix relative to the recent feature window X_cur, improving generalization under feature-space changes. The weight matrix W auto-expands for incremental feature streams and shrinks logically for decremental ones.

Constructor

signature

OASFRegressor(
    schema: Schema,
    lambda_param: float = 0.01,
    mu: float = 10.0,
    eta: float = 1.0,
    L: int = 100,
    d_max: int = 1000,
    random_seed: int = 1,
)

Parameter	Type	Default	Description
schema	Schema	required	Stream schema
lambda_param	float	0.01	L₁,₂ sparsity shrinkage threshold
mu	float	10.0	PA penalty parameter (controls update step size; regression default is larger than classification)
eta	float	1.0	CUR regularization coefficient — strength of feature-window constraint
L	int	100	Sliding window length (number of weight vector columns in ring buffer)
d_max	int	1000	Pre-allocated maximum feature dimension
random_seed	int	1	RNG seed

Attributes

Attribute	Type	Description
W	ndarray (d_max, L)	Ring buffer of weight vectors
X_cur	ndarray	Feature window used for CUR regularization
current_dim	int	Current feature dimensionality
lambda_param	float	L₁,₂ sparsity threshold
mu	float	PA penalty parameter
eta	float	CUR regularization coefficient
L	int	Sliding window size

Methods

Method	Signature	Returns	Description
train	(instance: Instance) → None	None	Selects incremental or decremental PA-R update based on feature-space change; applies L₁,₂ sparsity shrinkage; updates CUR feature window `X_cur`
predict	(instance: Instance) → float	float	Linear prediction using the latest weight column in the ring buffer

Comparison with OASFClassifier

Item	OASFClassifier	OASFRegressor
Loss function	Hinge loss (PA)	ε-insensitive loss (PA-R)
Default mu	1.0	10.0
Extra regularization	None	CUR matrix decomposition (eta)
Output	Class label (int)	Continuous value (float)

Algorithm Coverage

Of the 10 original OpenMOA algorithms, only 2 implement regression. The remaining 8 are classification-only.

FESLRegressor Regression ✓

OASFRegressor Regression ✓

RSOLClassifier Classification only

FOBOSClassifier Classification only

FTRLClassifier Classification only

OVFMClassifier Classification only

OSLMFClassifier Classification only

ORF3VClassifier Classification only

OLD3SClassifier Classification only

OWSSClassifier Classification only

CapyMOA regressors: OpenMOA also exposes CapyMOA regression algorithms (FIMTDD, ORTO, SOKNL, etc.) via the same Regressor interface. See the CapyMOA API Reference for their documentation.

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