New approaches to binary classification using risk management and robust optimization
Abstract
In machine learning, performance metrics are often defined to be simple and intuitively appealing.
However, they often possess poor mathematical properties, particularly in an optimization context.
We use a new characterization of uncertainty called Buffered Probability of Exceedance to define performance metrics that are both intuitive and possess good mathematical properties,
particularly in an optimization context.
Importantly, these metrics can be optimized directly with convex and linear programming and share deep connections with existing algorithms like Support Vectors Machines.
In addition, we can naturally introduce regularization through a Robust Optimization framework that is flexible and provides interesting insight into current regularization methods.
Overall, this strategy allows us to develop efficient approaches for binary classification under a variety of performance criteria.
Speaker2
Alexander Mafusalov
Time
16:00 - 16:45
Title
Risk averse distribution approximation
Abstract
Entropy maximization with linear constraints (second order stochastic dominance constraints, first and second moment constraints)
is proposed to solve the sample distribution approximation problem.
Depending on the desired distribution domain, a solution can be a continuous density estimation or a discrete approximation.
A probability density of the optimal solution is proved to be a weighted maximum of Gaussian density functions.
The second moment convergence implies weak convergence of the solution to the sample distribution.
Cross-validation with likelihood maximization is used to validate the second moment proximity.
The method performance is tested in a simulation study when compared to the kernel density estimation method.
Extensions of the approach are discussed. Changes in entropy function allow achieving heavy-tailed approximations.
Changes in dominance constraints allow to approximate multidimensional distributions.
