Multiple-Instance Support Vector Machines in Python

sAwMIL (Sparse Aware Multiple-Instance Learning) is an open-source Python library providing a collection of Support Vector Machine (SVM) classifiers for multiple-instance learning (MIL). It builds upon ideas from the earlier misvm package, adapting it for the latest Python version, as well as introducing new models.

In Single-Instance Learning (SIL), the dataset consists of pairs of an instance and a label:

$$ \langle \mathbf{x}_i, y_i \rangle \text{ , where } \mathbf{x}_i \in \mathbb{R}^{d} \text{ and } y_i \in \mathcal{Y}. $$

In binary settings, the label is $y \in {0,1}$. To solve this problem, we can use a standard SVM model.

In Multiple-Instance Learning (MIL), the dataset consists of bags of instances paired with a single bag-level label:

$$ \langle \mathbf{X}_i, y_i \rangle \text{ , where } \mathbf{X}_i = { \mathbf{x}_{1}, \mathbf{x}_{2}, ..., \mathbf{x}_{n_i} }, \mathbf{x}_j \in \mathbb{R}^{d} \text{ and } y_i \in \mathcal{Y}. $$

To solve this problem, we can use NSK or sMIL models.

In some cases, each bag, along with the instances and a label, could contain a intra-bag mask that specifies which items are likely to contain the signal related to $y$. In that case, we have a triplet of $\langle \mathbf{X}_i, \mathbf{M}_i, y_i \rangle$, where

$$ \mathbf{M}_i = {m_1, m_1,... m_{n_i}}, \text{ where } m_j \in {0,1}. $$

To solve this problem, one can use the sAwMIL model.

Installation

sawmil supports three QP backends:

• Gurobi
• OSQP
• DAQP

By default, the base package installs without any solver; pick one (or both) via extras.

Base package (no solver)

pip install sawmil
# it installs numpy>=1.22 and scikit-learn>=1.7.0

Option 1: Gurobi backend

Gurobi is commercial software. You’ll need a valid license (academic or commercial), refer to the official website.

pip install "sawmil[gurobi]"
# in additionl to the base packages, it install gurobi>12.0.3

Option 2: OSQP backend

pip install "sawmil[osqp]"
# in additionl to the base packages, it installs osqp>=1.0.4 and scipy>=1.16.1

Option 3: DAQP backend

pip install "sawmil[daqp]"
# in additionl to the base packages, it installs daqp>=0.5 and scipy>=1.16.1

Option 4 — All supported solvers

pip install "sawmil[full]"

Picking the solver in code

from sawmil import SVM, RBF

k = RBF(gamma = 0.1)
# solver= "osqp" (default is "gurobi")
# SVM is for single-instances 
clf = SVM(C=1.0, 
          kernel=k, 
          solver="osqp").fit(X, y)

Quick start

1. Generate Dummy Data

from sawmil.data import generate_dummy_bags
import numpy as np
rng = np.random.default_rng(0)

ds = generate_dummy_bags(
    n_pos=300, n_neg=100, inst_per_bag=(5, 15), d=2,
    pos_centers=((+2,+1), (+4,+3)),
    neg_centers=((-1.5,-1.0), (-3.0,+0.5)),
    pos_scales=((2.0, 0.6), (1.2, 0.8)),
    neg_scales=((1.5, 0.5), (2.5, 0.9)),
    pos_intra_rate=(0.25, 0.85),
    ensure_pos_in_every_pos_bag=True,
    neg_pos_noise_rate=(0.00, 0.05),
    pos_neg_noise_rate=(0.00, 0.20),
    outlier_rate=0.1,
    outlier_scale=8.0,
    random_state=42,
)

2. Fit NSK with RBF Kernel

Load a kernel:

from sawmil.kernels import get_kernel, RBF
k1 = get_kernel("rbf", gamma=0.1)
k2 = RBF(gamma=0.1)
# k1 == k2

Fit NSK Model:

from sawmil.nsk import NSK

clf = NSK(C=1, kernel=k, 
          # bag kernel settings
          normalizer='average',
          # solver params
          scale_C=True, 
          tol=1e-8, 
          verbose=False).fit(ds, None)
y = ds.y
print("Train acc:", clf.score(ds, y))

3. Fit sMIL Model with Linear Kernel

from sawmil.smil import sMIL

k = get_kernel("linear") # base (single-instance kernel)
clf = sMIL(C=0.1, 
           kernel=k, 
           scale_C=True, 
           tol=1e-8, 
           verbose=False).fit(ds, None)

See more examples in the example.ipynb notebook.

4. Fit sAwMIL with Combined Kernels

from sawmil.kernels import Product, Polynomial, Linear, RBF, Sum, Scale
from sawmil.sawmil import sAwMIL

k = Sum(Linear(), 
        Scale(0.5, 
              Product(Polynomial(degree=2), RBF(gamma=1.0))))

clf = sAwMIL(C=0.1, 
             kernel=k,
             solver="gurobi", 
             eta=0.95) # here eta is high, since all items in the bag are relevant
clf.fit(ds)
print("Train acc:", clf.score(ds, ds.y))

Citation

If you use sawmil package in academic work, please cite:

Savcisens, G. & Eliassi-Rad, T. sAwMIL: Python package for Sparse Multiple-Instance Learning (2025).

@software{savcisens2025sawmil,
  author = {Savcisens, Germans and Eliassi-Rad, Tina},
  title = {sAwMIL: Python package for Sparse Multiple-Instance Learning},
  year = {2025},
  doi = {10.5281/zenodo.16990499},
  url = {https://github.com/carlomarxdk/sawmil}
}

If you want to reference a specific version of the package, find the correct DOI here.