Multi-Integration of Labels Across Categories for Component Identification in Multi-trial Time Series (MILCCI), ICML 2026

Multi-axis Interpretable Latent Component and Condition Inference

MILCCI decomposes a 3D tensor Y (e.g., neurons × time × trials) into condition-varying spatial maps A and temporal traces Φ, with similarity regularization along multiple label axes.

Each trial carries a multi-axis label (e.g., stimulus identity × block number × trial order). MILCCI assigns a subset of ensembles to each axis and enforces that the spatial map A is shared across trials that agree on that axis, while allowing variation along other axes.

Citation

If you use MILCCI in your research, please cite:

@article{mudrik2026multi,
  title={Multi-Integration of Labels across Categories for Component Identification (MILCCI)},
  author={Mudrik, Noga and Chen, Yuxi and Mishne, Gal and Charles, Adam S},
  journal={ArXiv},
  pages={arXiv--2602},
  year={2026}
}

Mudrik, N., Chen, Y., Mishne, G., & Charles, A. S. (2026). Multi-Integration of Labels across Categories for Component Identification (MILCCI). ArXiv, arXiv-2602. Soon at ICML 2026.

Installation

pip install git+https://github.com/NogaMudrik/MILCCI.git

Requirements: Python ≥ 3.7, NumPy < 2.0, SciPy ≥ 1.7, scikit-learn ≥ 1.0.

Quick start

import milcci

# generate synthetic data
synth = milcci.generate_synthetic_data(
    N=50, T=100,
    n_ensembles_each=[2, 2],
    axis_values=[[0, 1, 2], [0, 1]],
    noise_std=0.2,
)

# run MILCCI
result = milcci.fit(
    data=synth['Y'],
    labels=synth['labels'],
    numbers2tuples=synth['numbers2tuples'],
    n_ensembles=4,
    n_ensembles_each=[2, 2],
    nu=[0.01] * 4,
    lambda_similarity=100,
    decor_A=2,
    num_repeats=15,
    split_A=True,
)

Usage

milcci.fit(data, labels, numbers2tuples, ...)

Main decomposition function. Returns a dict with:

Key	Shape	Description
Phi	(T, P, M)	Temporal traces
A	(N, P, K)	Spatial maps per unique condition
A_full	(N, P, M)	Spatial maps expanded to all trials
params	dict	Run parameters and metadata

Key parameters

Parameter	Description
n_ensembles	Total number of components
n_ensembles_each	Components per label axis (must sum to n_ensembles)
nu	Per-ensemble similarity strength
lambda_similarity	Global regularization weight
cont_axis_list	Which axes are continuous (e.g. trial number)
split_A	Infer separate A per axis-value (recommended)
style_infer_phi	'LS' or 'dynamic_prior' (LDS-regularized)

Running the demo

python examples/demo_synthetic.py

Or open examples/demo_notebook.ipynb in Jupyter for an interactive walkthrough.

Repository structure

MILCCI/
├── milcci/
│   ├── __init__.py         # public API
│   ├── core.py             # fit(), reconstruct()
│   ├── solvers.py          # least-squares / NNLS solvers
│   ├── phi_inference.py    # Phi update (LS + LDS prior)
│   ├── regularization.py   # basis patterns, nu matrices
│   ├── evaluation.py       # R^2, correlation metrics
│   ├── synthetic.py        # GP-based synthetic data generator
│   ├── plotting.py         # visualization functions
│   └── utils.py            # small utilities
├── examples/
│   ├── demo_synthetic.py
│   └── demo_notebook.ipynb
├── tests/
│   └── test_milcci.py
├── setup.py
├── LICENSE
├── .gitignore
└── README.md

License

MIT