Implementation:Online ml River Facto FwFM

Knowledge Sources	Online_ml_River
Domains	Online_Learning, Factorization_Machines, Click_Through_Rate_Prediction
Last Updated	2026-02-08 16:00 GMT

Overview

Field-weighted Factorization Machines (FwFM) extend standard FM by learning interaction strength weights for each pair of feature fields, allowing the model to emphasize or de-emphasize specific field interactions.

Description

FwFM augments Factorization Machines with learnable field-pair weights that modulate the strength of interactions between different fields. Each field pair has an associated weight that is learned alongside the latent factors and feature weights. The model computes interactions as the dot product of latent vectors multiplied by the learned field-pair weight. This allows FwFM to automatically discover which field interactions are most important for the prediction task. Field names are inferred from feature names by splitting at the first underscore. The model uses three optimizers: one for feature weights, one for latent factors, and one for interaction weights.

Usage

Use FwFM for CTR prediction and display advertising where different field combinations have varying importance. It is particularly valuable when you want the model to automatically learn which field interactions matter most rather than manually engineering field combinations. FwFM works best with datasets that have clear field structure (user features, item features, context features, etc.) where some field pairs are naturally more predictive than others.

Code Reference

Source Location

Repository: Online_ml_River
File: river/facto/fwfm.py

Signature

class FwFMRegressor(
    n_factors=10,
    weight_optimizer: optim.base.Optimizer | None = None,
    latent_optimizer: optim.base.Optimizer | None = None,
    int_weight_optimizer: optim.base.Optimizer | None = None,
    loss: optim.losses.RegressionLoss | None = None,
    sample_normalization=False,
    l1_weight=0.0,
    l2_weight=0.0,
    l1_latent=0.0,
    l2_latent=0.0,
    intercept=0.0,
    intercept_lr: optim.base.Scheduler | float = 0.01,
    weight_initializer: optim.initializers.Initializer | None = None,
    latent_initializer: optim.initializers.Initializer | None = None,
    clip_gradient=1e12,
    seed: int | None = None,
)

class FwFMClassifier(
    n_factors=10,
    weight_optimizer: optim.base.Optimizer | None = None,
    latent_optimizer: optim.base.Optimizer | None = None,
    int_weight_optimizer: optim.base.Optimizer | None = None,
    loss: optim.losses.BinaryLoss | None = None,
    sample_normalization=False,
    l1_weight=0.0,
    l2_weight=0.0,
    l1_latent=0.0,
    l2_latent=0.0,
    intercept=0.0,
    intercept_lr: optim.base.Scheduler | float = 0.01,
    weight_initializer: optim.initializers.Initializer | None = None,
    latent_initializer: optim.initializers.Initializer | None = None,
    clip_gradient=1e12,
    seed: int | None = None,
)

Import

from river import facto

I/O Contract

Input
Parameter	Type	Description
x	dict	Feature dictionary with field prefixes in feature names
y	float/bool	Target value for regression or classification

Output
Method	Return Type	Description
predict_one(x)	float/bool	Predicted value or class label
predict_proba_one(x)	dict	Class probabilities (classifier only)
learn_one(x, y)	None	Updates model with sample

Usage Examples

from river import facto

dataset = (
    ({'user': 'Alice', 'item': 'Superman'}, 8),
    ({'user': 'Alice', 'item': 'Terminator'}, 9),
    ({'user': 'Alice', 'item': 'Star Wars'}, 8),
    ({'user': 'Alice', 'item': 'Notting Hill'}, 2),
    ({'user': 'Bob', 'item': 'Superman'}, 8),
)

model = facto.FwFMRegressor(
    n_factors=10,
    intercept=5,
    seed=42,
)

for x, y in dataset:
    model.learn_one(x, y)

prediction = model.predict_one({'Bob': 1, 'Harry Potter': 1})
print(f"Prediction: {prediction}")  # 5.236501

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