bess Python Package

# bess: An python Package for Best Subset Selection

## Introduction

One of the main tasks of statistical modeling is to exploit the association between a response variable and multiple predictors. Linear model (LM), as a simple parametric regression model, is often used to capture linear dependence between response and predictors. Generalized linear model (GLM) can be considered as the extensions of linear model, depending on the types of responses. Parameter estimation in these models can be computationally intensive when the number of predictors is large. Meanwhile, Occam's razor is widely accepted as a heuristic rule for statistical modeling, which balances goodness of fit and model complexity. This rule leads to a relative small subset of important predictors.

bess package provides solutions for best subset selection problem for sparse LM, and GLM models.

We consider a primal-dual active set (PDAS) approach to exactly solve the best subset selection problem for sparse LM and GLM models. The PDAS algorithm for linear least squares problems was first introduced by Ito and Kunisch (2013) and later discussed by Jiao, Jin, and Lu (2015) and Huang, Jiao, Liu, and Lu (2017). It utilizes an active set updating strategy and fits the sub-models through use of complementary primal and dual variables. We generalize the PDAS algorithm for general convex loss functions with the best subset constraint, and further extend it to support both sequential and golden section search strategies for optimal k determination.

## Install

Python Version

• python >= 3.5

Modules needed

• numpy

The package has been publish in PyPI. You can easy install by:

```\$ pip install bess
```

## Example

```from bess.linear import PdasLm, PdasLogistic, PdasPoisson
import numpy as np
np.random.seed(12345)

### PdasLm sample
x = np.random.normal(0, 1, 100 * 150).reshape((100, 150))
beta = np.hstack((np.array([1, 1, -1, -1, -1]), np.zeros(145)))
noise = np.random.normal(0, 1, 100)
y = np.matmul(x, beta) + noise      # test_x
model = PdasLm(path_type = "seq", sequence = )
model.fit(X = x, y = y)
print(np.nonzero(model.beta))
print(model.beta[0:5])

### PdasLogistic sample
np.random.seed(12345)
x = np.random.normal(0, 1, 100 * 150).reshape((100, 150))
beta = np.hstack((np.array([1, 1, -1, -1, -1]), np.zeros(145)))
xbeta = np.matmul(x, beta)
p = np.exp(xbeta)/(1+np.exp(xbeta))
y = np.random.binomial(1, p)
model = PdasLogistic(path_type="seq", sequence=)
model.fit(X=x, y=y)
print(np.nonzero(model.beta))
print(model.beta[0:5])

### PdasPoisson sample
np.random.seed(12345)
x = np.random.normal(0, 1, 100 * 150).reshape((100, 150))
beta = np.hstack((np.array([1, 1, -1, -1, -1]), np.zeros(145)))
lam = np.exp(np.matmul(x, beta))
y = np.random.poisson(lam=lam)
model = PdasPoisson(path_type="seq", sequence=)
model.fit(x, y)
print(np.nonzero(model.beta))
```

## Bug report

Connect to @Jiang-Kangkang, or send an email to Jiang Kangkang(jiangkk3@mail2.sysu.edu.cn)

## Project details

This version 0.0.8 0.0.7 0.0.6 0.0.5 0.0.4 0.0.3 0.0.2