29 research outputs found
Scalable Holistic Linear Regression
We propose a new scalable algorithm for holistic linear regression building
on Bertsimas & King (2016). Specifically, we develop new theory to model
significance and multicollinearity as lazy constraints rather than checking the
conditions iteratively. The resulting algorithm scales with the number of
samples in the 10,000s, compared to the low 100s in the previous framework.
Computational results on real and synthetic datasets show it greatly improves
from previous algorithms in accuracy, false detection rate, computational time
and scalability.Comment: Accepted by Operation Research Letter
Stochastic Cutting Planes for Data-Driven Optimization
We introduce a stochastic version of the cutting-plane method for a large
class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We
show that under very weak assumptions the stochastic algorithm is able to
converge to an -optimal solution with high probability. Numerical
experiments on several problems show that stochastic cutting planes is able to
deliver a multiple order-of-magnitude speedup compared to the standard
cutting-plane method. We further experimentally explore the lower limits of
sampling for stochastic cutting planes and show that for many problems, a
sampling size of appears to be sufficient for high quality
solutions
Distributionally Robust Causal Inference with Observational Data
We consider the estimation of average treatment effects in observational
studies without the standard assumption of unconfoundedness. We propose a new
framework of robust causal inference under the general observational study
setting with the possible existence of unobserved confounders. Our approach is
based on the method of distributionally robust optimization and proceeds in two
steps. We first specify the maximal degree to which the distribution of
unobserved potential outcomes may deviate from that of obsered outcomes. We
then derive sharp bounds on the average treatment effects under this
assumption. Our framework encompasses the popular marginal sensitivity model as
a special case and can be extended to the difference-in-difference and
regression discontinuity designs as well as instrumental variables. Through
simulation and empirical studies, we demonstrate the applicability of the
proposed methodology to real-world settings
Branch-and-Price for Prescriptive Contagion Analytics
Predictive contagion models are ubiquitous in epidemiology, social sciences,
engineering, and management. This paper formulates a prescriptive contagion
analytics model where a decision-maker allocates shared resources across
multiple segments of a population, each governed by continuous-time dynamics.
We define four real-world problems under this umbrella: vaccine distribution,
vaccination centers deployment, content promotion, and congestion mitigation.
These problems feature a large-scale mixed-integer non-convex optimization
structure with constraints governed by ordinary differential equations,
combining the challenges of discrete optimization, non-linear optimization, and
continuous-time system dynamics. This paper develops a branch-and-price
methodology for prescriptive contagion analytics based on: (i) a set
partitioning reformulation; (ii) a column generation decomposition; (iii) a
state-clustering algorithm for discrete-decision continuous-state dynamic
programming; and (iv) a tri-partite branching scheme to circumvent
non-linearities. Extensive experiments show that the algorithm scales to very
large and otherwise-intractable instances, outperforming state-of-the-art
benchmarks. Our methodology provides practical benefits in contagion systems;
in particular, it can increase the effectiveness of a vaccination campaign by
an estimated 12-70%, resulting in 7,000 to 12,000 extra saved lives over a
three-month horizon mirroring the COVID-19 pandemic. We provide an open-source
implementation of the methodology in an online repository to enable
replication
Holistic Deep Learning
There is much interest in deep learning to solve challenges in applying
neural network models in real-world environments. In particular, three areas
have received considerable attention: adversarial robustness, parameter
sparsity, and output stability. Despite numerous attempts to solve these
problems independently, little work simultaneously addresses the challenges. In
this paper, we address the problem of constructing holistic deep learning
models by proposing a novel formulation that solves these issues in
combination. Real-world experiments on both tabular and MNIST datasets show
that our formulation can simultaneously improve the accuracy, robustness,
stability, and sparsity over traditional deep learning models among many
others.Comment: In preparation for Machine Learnin