`skscope`: Fast Sparse-Constraint Optimization

What is `skscope`?

skscope aims to make sparsity-constrained optimization (SCO) accessible to everyone because SCO holds immense potential across various domains, including machine learning, statistics, and signal processing. By providing a user-friendly interface, skscope empowers individuals from diverse backgrounds to harness the power of SCO and unlock its broad range of applications (see examples exhibited below).

Installation

The recommended option for most users:

bash
pip install skscope

For Linux or Mac users, an alternative is

bash
conda install skscope

If you want to work with the latest development version, the further installation instructions help you install from source.

Quick examples

Here's a quick example showcasing how you can use three simple steps to perform feature selection via the skscope:

python
from skscope import ScopeSolver
from sklearn.datasets import make_regression
import jax.numpy as jnp

## generate data
x, y, coef = make_regression(n_features=10, n_informative=3, coef=True)

## 1. define loss function
def ols_loss(para):
    return jnp.sum(jnp.square(y - x @ para))

## 2. initialize the solver where 10 parameters in total and three of which are sparse
solver = ScopeSolver(10, 3) 

## 3. use the solver to optimized the objective
params = solver.solve(ols_loss)

Below's another example illustrates that you can modify the objective function to address another totally different problem.

python
import numpy as np
import jax.numpy as jnp
import matplotlib.pyplot as plt
from skscope import ScopeSolver

## generate data
np.random.seed(2023)
x = np.cumsum(np.random.randn(500)) # random walk with normal increment

## 1. define loss function
def tf_objective(params):
    return jnp.sum(jnp.square(x - jnp.cumsum(params)))  

## 2. initialize the solver where 10 parameters in total and three of which are sparse
solver = ScopeSolver(len(x), 10)

## 3. use the solver to optimized the objective
params = solver.solve(tf_objective)

tf_x = jnp.cumsum(params)
plt.plot(x, label='observation', linewidth=0.8)
plt.plot(tf_x, label='filtering trend')
plt.legend(); plt.show()

The above Figure shows that the solution of ScopeSolver now captures the main trend of the observed random work. Again, 4 lines of code help us attain the solution.

Example gallery

Since skscope can easily be applied to diverse objective functions, we can definitely leverage it to develop various machine learning methods that is driven by SCO. In our example gallery, we supply 25 comprehensive statistical/machine learning examples to illustrate the versatility of skscope.

Why `skscope` is versatile?

The high versatility of skscope in effectively addressing SCO problems are derived from two key factors: theoretical concepts and computational implementation. In terms of theoretical concepts, there have been remarkable advancements in SCO in recent years, offering a range of efficient iterative methods for solving SCO. Some of these algorithms exhibit elegance by only relying on the current parameters and gradients for the iteration process. On the other hand, significant progress has been made in automatic differentiation, a fundamental component of deep learning algorithms that plays a vital role in computing gradients. By ingeniously combining these two important advancements, skscope emerges as the pioneering tool capable of handling diverse sparse optimization tasks.

With skscope, the creation of new machine learning methods becomes effortless, leading to the advancement of the "sparsity idea" in machine learning. This, in turn, facilitates the availability of a broader spectrum of machine learning algorithms for tackling real-world problems.

Software features

Support multiple state-of-the-art SCO solvers. Now, skscope has supported these algorithms: SCOPE, HTP, Grasp, IHT, OMP, and FoBa.
User-friendly API
- zero-knowledge of SCO solvers: the state-of-the-art solvers in skscope has intuitive and highly unified APIs.
- extensive documentation: skscope is fully documented and accompanied by example gallery and reproduction scripts.
Solving SCO and its generalization:
- SCO: $\arg\min\limits_{\theta \in R^p} f(\theta) \text{ s.t. } ||\theta||_0 \leq s$;
- SCO for group-structure parameters: $\arg\min\limits_{\theta \in R^p} f(\theta) \text{ s.t. } I(||\theta_{G_i}||2 \neq 0) \leq s$ where ${G_i}{i=1}^q$ is a non-overlapping partition for ${1, \ldots, p}$;
- SCO when pre-selecting parameters in set $\mathcal{P}$: $\arg\min\limits_{\theta \in R^p} f(\theta) \text{ s.t. } ||\theta_{\mathcal{P}^c}||_0 \leq s$.
Data science toolkit
- Information criterion and cross-validation for selecting $s$
- Portable interface for developing new machine-learning methods
Just-in-time-compilation compatibility

Benchmark

Support recovery accuracy

Methods	Linear regression	Logistic regression	Trend filtering	Multi-task learning	Ising model	Nonlinear feature selection
`OMPSolver`	1.00(0.01)	0.91(0.05)	0.70(0.18)	1.00(0.00)	0.98(0.03)	0.77(0.09)
`IHTSolver`	0.79(0.04)	0.97(0.03)	0.08(0.10)	0.97(0.02)	0.96(0.05)	0.78(0.09)
`HTPSolver`	1.00(0.00)	0.84(0.05)	0.41(0.22)	1.00(0.00)	0.97(0.03)	0.78(0.09)
`GraspSolver`	1.00(0.00)	0.90(0.08)	0.58(0.23)	1.00(0.00)	0.99(0.01)	0.78(0.08)
`FoBaSolver`	1.00(0.00)	0.92(0.06)	0.87(0.13)	1.00(0.00)	1.00(0.01)	0.77(0.09)
`ScopeSolver`	1.00(0.00)	0.94(0.04)	0.79(0.19)	1.00(0.00)	1.00(0.01)	0.77(0.09)
`cvxpy`	0.83(0.17)	0.83(0.05)	0.19(0.22)	1.00(0.00)	0.94(0.04)	0.74(0.09)

All solvers (except IHTSolver) in skscope consistently outperformed cvxpy in terms of accuracy for the selection of the support set.

Runtime (measured in seconds):

Methods	Linear regression	Logistic regression	Trend filtering	Multi-task learning	Ising model	Nonlinear feature selection
`OMPSolver`	0.62(0.11)	0.80(0.11)	0.03(0.00)	2.70(0.26)	1.39(0.13)	13.24(3.91)
`IHTSolver`	0.23(0.05)	0.18(0.12)	0.30(0.06)	0.80(0.11)	0.98(0.08)	1.67(0.50)
`HTPSolver`	0.50(0.14)	0.94(0.44)	0.03(0.01)	14.18(5.13)	3.41(1.22)	12.97(6.23)
`GraspSolver`	0.18(0.06)	2.55(0.86)	0.08(0.03)	0.54(0.28)	0.53(0.22)	3.06(0.75)
`FoBaSolver`	3.71(0.50)	3.28(0.39)	0.13(0.02)	6.22(0.61)	11.10(1.04)	57.42(12.95)
`ScopeSolver`	0.30(0.08)	1.20(2.14)	0.09(0.01)	1.14(0.89)	1.17(0.25)	7.78(2.23)
`cvxpy`	14.59(5.60)	69.45(53.47)	0.47(0.16)	39.36(155.70)	32.26(17.88)	534.49(337.72)

skscope demonstrated significant computational advantages over cvxpy, exhibiting speedups ranging from approximately 3-500 times.

Software architecture

Citation

If you use skscope or reference our tutorials in a presentation or publication, we would appreciate citations of our library.

The corresponding BibteX entry:

@article{JMLR:v25:23-1574,
  author  = {Zezhi Wang and Junxian Zhu and Xueqin Wang and Jin Zhu and Huiyang Pen and Peng Chen and Anran Wang and Xiaoke Zhang},
  title   = {skscope: Fast Sparsity-Constrained Optimization in Python},
  journal = {Journal of Machine Learning Research},
  year    = {2024},
  volume  = {25},
  number  = {290},
  pages   = {1--9},
  url     = {http://jmlr.org/papers/v25/23-1574.html}
}