xRFM - Recursive Feature Machines optimized for tabular data

xRFM is a scalable implementation of Recursive Feature Machines (RFMs) optimized for tabular data. This library provides both the core RFM algorithm and a tree-based extension (xRFM) that enables efficient processing of large datasets through recursive data splitting. For immediate use of xRFM with tuning and the correct preprocessing, you can also use XRFM_HPO_Regressor or XRFM_HPO_Classifier directly in PyTabKit (https://github.com/dholzmueller/pytabkit).

Installation

With GPU

If a GPU is available, it is highly recommended to use either the 'cu11' or 'cu12' extra requirement. These versions offer significantly accelerated Product and Lpq Laplace Kernels. With CUDA-11 use:

pip install xrfm[cu11]

or, with CUDA-12:

pip install xrfm[cu12]

General Installation

pip install xrfm

Development Installation

git clone https://github.com/dmbeaglehole/xRFM.git
cd xRFM
pip install -e .

Quick Start

Basic Usage

import torch
from xrfm import xRFM
from sklearn.model_selection import train_test_split

# Create synthetic data
def target_function(X):
    return torch.cat([
        (X[:, 0] > 0)[:, None], 
        (X[:, 1] < 0.5)[:, None]
    ], dim=1).float()

# Setup device and model
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
model = xRFM(device=device, tuning_metric='mse')

# Generate data
n_samples = 2000
n_features = 100
X = torch.randn(n_samples, n_features, device=device)
y = target_function(X)
X_trainval, X_test, y_trainval, y_test = train_test_split(X, y, test_size=0.2, random_state=0)
X_train, X_val, y_train, y_val = train_test_split(X_trainval, y_trainval, test_size=0.2, random_state=0)

model.fit(X_train, y_train, X_val, y_val)
y_pred_test = model.predict(X_test)

Custom Configuration

# Custom RFM parameters
rfm_params = {
    'model': {
        'kernel': 'l2',           # Kernel type
        'bandwidth': 5.0,         # Kernel bandwidth
        'exponent': 1.0,          # Kernel exponent
        'diag': False,            # Diagonal Mahalanobis matrix
        'bandwidth_mode': 'constant'
    },
    'fit': {
        'reg': 1e-3,              # Regularization parameter
        'iters': 5,               # Number of iterations
        'M_batch_size': 1000,     # Batch size for AGOP
        'verbose': True,          # Verbose output
        'early_stop_rfm': True    # Early stopping
    }
}

# Initialize model with custom parameters
model = xRFM(
    rfm_params=rfm_params,
    device=device,
    min_subset_size=10000,        # Minimum subset size for splitting
    tuning_metric='accuracy',     # Tuning metric
    split_method='top_vector_agop_on_subset'  # Splitting strategy
)

Recommended Preprocessing

• Standardize numerical columns using a scaler (e.g., StandardScaler).
• One-hot encode categorical columns and pass their metadata via categorical_info.
• Do not standardize one-hot categorical features. Use identity matrices for categorical_vectors.

Example (scikit-learn)

import numpy as np
import torch
from sklearn.preprocessing import StandardScaler, OneHotEncoder
from sklearn.model_selection import train_test_split

# Assume a pandas DataFrame `df` with:
# - numerical feature columns in `num_cols`
# - categorical feature columns in `cat_cols`
# - target column name in `target_col`

# Split
train_df, test_df = train_test_split(df, test_size=0.2, random_state=0)
train_df, val_df = train_test_split(train_df, test_size=0.2, random_state=0)

# Fit preprocessors on train only
scaler = StandardScaler()
ohe = OneHotEncoder(handle_unknown='ignore', sparse_output=False)

X_num_train = scaler.fit_transform(train_df[num_cols])
X_num_val = scaler.transform(val_df[num_cols])
X_num_test = scaler.transform(test_df[num_cols])

X_cat_train = ohe.fit_transform(train_df[cat_cols])
X_cat_val = ohe.transform(val_df[cat_cols])
X_cat_test = ohe.transform(test_df[cat_cols])

# Concatenate: numerical block first, then categorical block
X_train = np.hstack([X_num_train, X_cat_train]).astype(np.float32)
X_val = np.hstack([X_num_val, X_cat_val]).astype(np.float32)
X_test = np.hstack([X_num_test, X_cat_test]).astype(np.float32)

y_train = train_df[target_col].to_numpy().astype(np.float32)
y_val = val_df[target_col].to_numpy().astype(np.float32)
y_test = test_df[target_col].to_numpy().astype(np.float32)

# Build categorical_info (indices are relative to the concatenated X)
n_num = X_num_train.shape[1]
categorical_indices = []
categorical_vectors = []
start = n_num
for cats in ohe.categories_:
    cat_len = len(cats)
    idxs = torch.arange(start, start + cat_len, dtype=torch.long)
    categorical_indices.append(idxs)
    categorical_vectors.append(torch.eye(cat_len, dtype=torch.float32))  # identity; do not standardize
    start += cat_len

numerical_indices = torch.arange(0, n_num, dtype=torch.long)

categorical_info = dict(
    numerical_indices=numerical_indices,
    categorical_indices=categorical_indices,
    categorical_vectors=categorical_vectors,
)

# Train xRFM with categorical_info
from xrfm import xRFM
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

rfm_params = {
    'model': {
        'kernel': 'l2',
        'bandwidth': 10.0,
        'exponent': 1.0,
        'diag': False,
        'bandwidth_mode': 'constant',
    },
    'fit': {
        'reg': 1e-3,
        'iters': 3,
        'verbose': False,
        'early_stop_rfm': True,
    }
}

model = xRFM(
    rfm_params=rfm_params,
    device=device,
    tuning_metric='mse',
    categorical_info=categorical_info,
)

model.fit(X_train, y_train, X_val, y_val)
y_pred = model.predict(X_test)

Core Components

xRFM/
├── xrfm/
│   ├── xrfm.py              # Main xRFM class (tree-based)
│   ├── tree_utils.py        # Tree manipulation utilities
│   └── rfm_src/
│       ├── recursive_feature_machine.py  # Base RFM class
│       ├── kernels.py       # Kernel implementations
│       ├── eigenpro.py      # EigenPro optimization
│       ├── utils.py         # Utility functions
│       ├── svd.py           # SVD operations
│       └── gpu_utils.py     # GPU memory management
├── examples/                # Usage examples
└── setup.py                # Package configuration

File Structure

Core Files

File	Description
xrfm/xrfm.py	Main xRFM class implementing tree-based recursive splitting
xrfm/rfm_src/recursive_feature_machine.py	Base RFM class with core algorithm
xrfm/rfm_src/kernels.py	Kernel implementations (Laplace, Product Laplace, etc.)
xrfm/rfm_src/eigenpro.py	EigenPro optimization for large-scale training
xrfm/rfm_src/utils.py	Utility functions for matrix operations and metrics
xrfm/rfm_src/svd.py	SVD utilities for kernel computations
xrfm/rfm_src/gpu_utils.py	GPU memory management utilities
xrfm/tree_utils.py	Tree manipulation and parameter extraction utilities

API Reference

Main Classes

xRFM

Tree-based Recursive Feature Machine for scalable learning.

Key Methods:

• fit(X, y, X_val, y_val): Train the model
• predict(X): Make predictions
• predict_proba(X): Predict class probabilities
• score(X, y): Evaluate model performance

RFM

Base Recursive Feature Machine implementation.

Available Kernels

Kernel	String ID	Description
LaplaceKernel	'laplace', 'l2'	Standard Laplace kernel
KermacProductLaplaceKernel	'l1_kermac'	High-performance Product of Laplace kernels on GPU (requires install with [cu11] or [cu12])
KermacLpqLaplaceKernel	'lpq_kermac'	High-performance p-norm, q-exponent Laplace kernels on GPU (requires install with [cu11] or [cu12])
LightLaplaceKernel	'l2_high_dim', 'l2_light'	Memory-efficient Laplace kernel
ProductLaplaceKernel	'product_laplace', 'l1'	Product of Laplace kernels (not recommended, use Kermac if possible)
SumPowerLaplaceKernel	'sum_power_laplace', 'l1_power'	Sum of powered Laplace kernels

Splitting Methods

Method	Description
'top_vector_agop_on_subset'	Use top eigenvector of AGOP matrix
'random_agop_on_subset'	Use random eigenvector of AGOP matrix
'top_pc_agop_on_subset'	Use top principal component of data transformed with the AGOP
'random_pca'	Use vector sampled from Gaussian distribution with covariance $X^\top X$
'linear'	Use linear regression coefficients
'fixed_vector'	Use fixed projection vector

Tuning Metrics (and creating your own custom metrics)

xRFM chooses tuning candidates using the tuning_metric string on both tree splits and leaf RFMs. Built-in options are:

• mse, mae for regression error
• accuracy, brier, logloss, f1, auc for classification quality
• top_agop_vector_auc, top_agop_vector_pearson_r, top_agop_vectors_ols_auc for AGOP-aware diagnostics

To register a custom metric:

1. Create a new subclass of Metric in xrfm/rfm_src/metrics.py, fill in the metadata (name, display_name, should_maximize, task_types, required_quantities), and implement _compute(**kwargs) for the quantities you request.
2. Add the class to the all_metrics list inside Metric.from_name so the factory can return it by name.
3. Reference the new name in the tuning_metric argument when constructing xRFM or the standalone RFM.

Each metric receives tensors on the active device; convert to NumPy as needed. Return higher-is-better values when should_maximize = True, otherwise lower-is-better.