scikit-learn interface

The following models are implemented in skwdro

Linear Models

Logistic Regression

LogisticRegression(rho, l2_reg, ...[, solver])

A Wasserstein Distributionally Robust logistic regression classifier.

Linear Regression

LinearRegression([rho, l2_reg, ...])

A Wasserstein Distributionally Robust linear regression.

Operations Research

NewsVendor

NewsVendor(rho, k, u, cost, l2_reg, ...)

A NewsVendor Wasserstein Distributionally Robust Estimator.

Portfolio Selection

Portfolio([rho, eta, alpha, C, d, ...])

A Wasserstein Distributionally Robust Mean-Risk Portfolio estimator.

Represents the Mean-Risk Portfolio model.

The stochastic optimisation problem associated with the optimal decision to be taken is

$\underset{\theta \in \Theta}{\inf} \mathbb{E}^{\mathbb{P}}(- \langle \theta, \xi \rangle) + \eta \mathbb{P}\text{-CVaR}_{\alpha}(- \langle \theta, \xi \rangle)$

where $\eta \geq 0$ and $\alpha \in (0,1]$ are the risk aversion parameters, and $\mathbb{P} \mathrm{-CVaR}_{\alpha}$ is the Conditional Value at Risk relative to the unknown probability distribution $\mathbb{P}$ and confidence level $\alpha$ . CVaR is a measure of risk used in financial mathematics. One of the most common definitions for a random variable X governed by a continuous probability distribution is as follows:

$\text{CVaR}_{\alpha}(X) = \mathbb{E}[X | \ X \geq \text{VaR}_{\alpha}(X)]$

where $\mathrm{VaR}_{\alpha}$ is the Value at Risk of order $\alpha$ , which corresponds exactly to the quantile of order $\alpha$ . The CVaR is therefore the average expected value for the portfolio following the returns on investments, given that this value is greater than the Value at Risk.