strat_models

strat_models is a Python package for fitting Laplacian regularized stratified models.

The implementation is based on our paper A distributed method for fitting Laplacian regularized stratified models.

Installation

To install pytorch, follow instructions from pytorch.org, e.g. (python 3.7 pip installation): pip install https://download.pytorch.org/whl/cpu/torch-1.0.1.post2-cp37-cp37m-linux_x86_64.whl

To install the latest version, run: pip install git+https://github.com/cvxgrp/strat_models.git

Usage

To fit a stratified model, one needs to specify a base model, a graph, and data.

Base model

To specify a base model, one needs to specify a local loss function and a local regularization function. Currently, we support fitting with the following local loss functions: * Sum of squares loss * Logistic loss * Bernoulli negative log-likelihood * Poisson negative log-likelihood * Multivariate Gaussian negative log-likelihood (zero mean) * Multivariate Gaussian negative log-likelihood (non-zero mean)

We also support fitting with the following local regularization functions: * None * Sum of squares * L1 * L2 * Elastic net * Negative logarithm * Non-negative indicator function * Box indicator function

For example, here is how to specify a base model with a logistic regression local loss and sum of squares local regularization with parameter 1: bm = strat_models.BaseModel(loss=strat_models.logistic_loss(intercept=True), reg=strat_models.sum_squares_reg(lambd=1))

Graph

The graphs must be made using networkx Graphs. You can look more into how to build a networkx Graph here.

Data

Data must be specified as a dictionary with keys X, Y, and Z (X may be omitted if fitting a distribution.) X and Y must be Python lists with entries being the inputs/outputs, respectively. Z must be a Python list with entries being tuples of the same form as the specified networkx Graph.

Here is an example of an appropriate data dictionary with 500 samples consisting of 100 unique categorical parameter values: ``` K = 100 n = 10 num_samples = 500

X = np.random.randn(numsamples, n) Z = np.random.randint(K, size=numsamples) Y = np.random.randn(num_samples, 1)

data = dict(X=X, Y=Y, Z=Z) ```

Stratified model

A stratified model is specified by a base model and a graph. For example, here is how to specify a stratified model with a base model bm and a graph G: sm = strat_models.StratifiedModel(bm, graph=G)

For example, we fit a ridge regression model with local regularization, stratified based on time and location:

``` import strat_models import networkx as nx

G is the cartesian product of a cycle graph and a path graph

Gtime = nx.cyclegraph(10) Glocation = nx.pathgraph(20) G = stratmodels.cartesianproduct([Gtime, Glocation])

Get the data

X, Y, Z = getdata() Xtest, Ytest, Ztest = gettest_data()

data = dict(X=X, Y=Y, Z=Z)

Construct the model

bm = stratmodels.BaseModel(loss=stratmodels.sumsquaresloss(intercept=True), reg=stratmodels.sumsquares_reg(lambd=1))

sm = strat_models.StratifiedModel(bm, graph=G)

sm.fit(data) ```

Examples

First, install the requirements in requirements.txt: pip install -r requirements.txt

Next, navigate to the examples folder. Unfortunately, we cannot include the data to run the examples in this repository. At the top of each script are instructions on how to get the data to be able to run that script. Once downloaded, place the data in a folder called data in the examples folder, and then run the script; for example: python house.py

Citing strat_models

If you use strat_models, please cite the following papers:

``` @article{strat_models, author = {Jonathan Tuck and Shane Barratt and Stephen Boyd}, title = {A Distributed Method for Fitting {L}aplacian Regularized Stratified Models}, journal = {Journal of Machine Learning Research}, year = {2021}, note = {To appear} }

@article{eigenstratmodels, author = {Jonathan Tuck and Stephen Boyd}, title = {Eigen-stratified models}, journal = {Optimization and Engineering}, year = {2021}, }

@article{covstratmodels, author = {Jonathan Tuck and Stephen Boyd}, title = {Fitting {L}aplacian Regularized Stratified {G}aussian Models}, journal = {Optimization and Engineering}, year = {2021}, note = {To appear} }

@article{mmdistlapl, author = {Jonathan Tuck and David Hallac and Stephen Boyd}, title = {Distributed Majorization-Minimization for {L}aplacian Regularized Problems}, journal = {IEEE/CAA Journal of Automatica Sinica}, year = {2019}, } ```