Research

We introduce the framework of slowly varying regression under sparsity, which allows sparse regression models to vary slowly and sparsely. We formulate the problem of parameter estimation as a mixed integer optimization problem and demonstrate that it can be reformulated exactly as a binary convex optimization problem through a novel exact relaxation. The relaxation utilizes a new equality on Moore-Penrose inverses that convexifies the non-convex objective function while coinciding with the original objective on all feasible binary points. This allows us to solve the problem significantly more efficiently and to provable optimality using a cutting plane-type algorithm. We develop a highly optimized implementation of such an algorithm, which substantially improves upon the asymptotic computational complexity of a straightforward implementation. We further develop a fast heuristic method that is guaranteed to produce a feasible solution and, as we empirically illustrate, generates high-quality warm-start solutions for the binary optimization problem. We show, on both synthetic and real-world datasets, that the resulting algorithm outperforms competing formulations in comparable times across a variety of metrics including estimation accuracy, predictive power, and computational time, and is highly scalable, enabling us to train models with 10,000s of parameters. We make our implementation available open-source at https://github.com/vvdigalakis/SSVRegression.git.

Owing to their inherently interpretable structure, decision trees are commonly used in applications where interpretability is essential. Recent work has focused on improving various aspects of decision trees, including their predictive power and robustness; however, their instability, albeit well-documented, has been addressed to a lesser extent. In this paper, we take a step towards the stabilization of decision tree models through the lens of real-world health care applications due to the relevance of stability and interpretability in this space. We introduce a new distance metric for decision trees and use it to determine a tree's level of stability. We propose a novel methodology to train stable decision trees and investigate the existence of trade-offs that are inherent to decision tree models — including between stability, predictive power, and interpretability. We demonstrate the value of the proposed methodology through an extensive quantitative and qualitative analysis of six case studies from real-world health care applications, and we show that, on average, with a small 4.6% decrease in predictive power, we gain a significant 38% improvement in the model's stability.

We present our collaboration with the OCP Group, one of the world's largest producers of phosphate and phosphate-based products, in support of a green initiative designed to reduce OCP's carbon emissions significantly. We study the problem of decarbonizing OCP's electricity supply by installing a mixture of solar panels and batteries to minimize its time-discounted investment cost plus the cost of satisfying its remaining demand via the Moroccan national grid. OCP is currently designing its renewable investment strategy, using insights gleaned from our optimization model, and has pledged to invest 130 billion MAD (12.3 billion USD) in a green initiative by 2027, a subset of which involves decarbonization.

We immunize our model against deviations between forecast and realized solar generation output via a combination of robust and distributionally robust optimization. To account for variability in daily solar generation, we propose a data-driven robust optimization approach that prevents excessive conservatism by averaging across uncertainty sets. To protect against variability in seasonal weather patterns induced by climate change, we invoke distributionally robust optimization techniques. Under a ten billion MAD (approx. one billion USD) investment by OCP, the proposed methodology reduces the carbon emissions which arise from OCP's energy needs by more than 70% while generating a net present value (NPV) of five billion MAD over a twenty-year planning horizon. Moreover, a twenty billion MAD investment induces a 90% reduction in carbon emissions and generates an NPV of around two billion MAD.

To fulfill the Paris climate agreement, rapidly decarbonizing the global economy in a financially sustainable fashion is imperative. Accordingly, this work develops a robust optimization methodology that enables OCP to decarbonize at a profit by purchasing solar panels and batteries. Moreover, the methodology could be applied to decarbonize other industrial consumers. Indeed, our approach suggests that decarbonization's profitability depends on solar capacity factors, energy prices, and borrowing costs.

We address the questions of where to locate COVID-19 mass vaccination sites and how to distribute vaccines in the US using a data-driven approach.

The outbreak of COVID-19 led to a record-breaking race to develop a vaccine. However, the limited vaccine capacity creates another massive challenge: how to distribute vaccines to mitigate the near-end impact of the pandemic? In the United States in particular, the new Biden administration is launching mass vaccination sites across the country, raising the obvious question of where to locate these clinics to maximize the effectiveness of the vaccination campaign. This paper tackles this question with a novel data-driven approach to optimize COVID-19 vaccine distribution. We first augment a state-of-the-art epidemiological model, called DELPHI, to capture the effects of vaccinations and the variability in mortality rates across age groups. We then integrate this predictive model into a prescriptive model to optimize the location of vaccination sites and subsequent vaccine allocation. The model is formulated as a bilinear, nonconvex optimization model. To solve it, we propose a coordinate descent algorithm that iterates between optimizing vaccine distribution and simulating the dynamics of the pandemic. As compared to benchmarks based on demographic and epidemiological information, the proposed optimization approach increases the effectiveness of the vaccination campaign by an estimated 20%, saving an extra 4000 extra lives in the United States over a 3-month period. The proposed solution achieves critical fairness objectives—by reducing the death toll of the pandemic in several states without hurting others—and is highly robust to uncertainties and forecast errors—by achieving similar benefits under a vast range of perturbations.

We design analytics-based tools to combat the COVID-19 pandemic.

The COVID-19 pandemic has created unprecedented challenges worldwide. Strained healthcare providers make difficult decisions on patient triage, treatment and care management on a daily basis. Policy makers have imposed social distancing measures to slow the disease, at a steep economic price. We design analytical tools to support these decisions and combat the pandemic. Specifically, we propose a comprehensive data-driven approach to understand the clinical characteristics of COVID-19, predict its mortality, forecast its evolution, and ultimately alleviate its impact. By leveraging cohort-level clinical data, patient-level hospital data, and census-level epidemiological data, we develop an integrated four-step approach, combining descriptive, predictive and prescriptive analytics. First, we aggregate hundreds of clinical studies into the most comprehensive database on COVID-19 to paint a new macroscopic picture of the disease. Second, we build personalized calculators to predict the risk of infection and mortality as a function of demographics, symptoms, comorbidities, and lab values. Third, we develop a novel epidemiological model to project the pandemic’s spread and inform social distancing policies. Fourth, we propose an optimization model to re-allocate ventilators and alleviate shortages. Our results have been used at the clinical level by several hospitals to triage patients, guide care management, plan ICU capacity, and re-distribute ventilators. At the policy level, they are currently supporting safe back-to-work policies at a major institution and vaccine trial location planning at Janssen Pharmaceuticals, and have been integrated into the US Center for Disease Control’s pandemic forecast.