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    A distributional view of high dimensional optimization

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    This PhD Thesis presents a distributional view of optimization. I motivate this view with an investigation of the failure point of classical worst-case optimization. After a review of Bayesian optimization I outline how a distributional view may explain predictable progress of optimization in high dimension and provide insights into optimal step size control of gradient descent. In this process we touch on mathematical tools to deal with random input to random functions and a characterization of non-stationary isotropic covariance kernels. Finally, I outline how assumptions about the data can lead to random objective functions in machine learning and analyze its landscape

    Assortment and price optimization under heterogeneous demand

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    Improving alignment and controllability in GANs and diffusion models

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    Visual generative modeling is a transformative area that aims to synthesize diverse, realistic-looking visual content, e.g., images and videos. These models are widely applied in various domains, ranging from creative art design and the visual effects industry to data augmentation for downstream computer vision tasks. Over the past decade, this field has made tremendous progress, with significant advancements evolving from Generative Adversarial Networks (GANs) to diffusion models. Despite achieving higher fidelity and improved training stability, it remains challenging to control the synthesis process and generate content precisely as desired. To this end, this thesis presents several new techniques aimed at improving alignment and controllability in GANs and diffusion models across various tasks, such as GAN inversion, layout-to-image, text-to-image, and text-to-video generation. Further, these enhancements make the models more effective in a wide range of real-world applications

    Metropolis-adjusted interacting particle sampling

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    No place like home: Charging infrastructure and the environmental advantage of plug-in hybrid electric vehicles

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    Many European companies face the challenge of lowering CO2 emissions from their company car fleets. A promising lever is to increase the notoriously low electric usage of Plug-in Hybrid Electric Vehicles (PHEVs). This paper examines whether home charging infrastructure can help achieve these goals. We leverage quasi-experimental variation in the delivery and installation of home chargers to quantify the impact of this technology on energy use and CO2 emissions of PHEV company cars held by 856 employees of a large German company. Since fuel and electricity expenditures for these cars are covered by the employer, home charging mainly changes the non-monetary costs to an employee. We find that access to home charging increases electricity consumption by 317.9 ((±23.3) kWh per quarter and decreases fuel consumption by 97.97 ((±36.5) liters, reducing CO2 emissions by 38%. Moreover, access to home charging increases the employee's propensity to choose a Battery Electric Vehicle (BEV) upon renewal of the lease by 28.4 ((±25.6) percentage points. We use these estimates to compute the private levelized abatement costs of home chargers for a range of scenarios characterizing the diffusion of BEVs and the effect of the program on vehicle choice. With current tax-inclusive energy prices, home chargers break even for the company within eight to 16 years

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