## Projects## List of Projects## Quantum Computing: Practical Synthesis of Quantum Signal Processing Circuits
The ## Diversity in Matching Markets
How should a firm allocate its limited interviewing resources to select the optimal cohort of new employees from a large set of job applicants? How should that firm allocate cheap but noisy resume screenings and expensive but in-depth in-person interviews? We view this problem through the lens of combinatorial pure exploration (CPE) in the multi-armed bandit setting, where a central learning agent performs costly exploration of a set of arms before selecting a final subset with some combinatorial structure. In our case, that combinatorial structure will incorporate elements of diversity, where including multiple elements of the same type in the final set results in diminishing marginal gain. We will apply our algorithms to real data from university admissions and the hiring processes from major tech firms. ## Using Generative Adversarial Networks to Generate Fake but Believable Images
Learning a probability model from data is a fundamental problem in machine learning and statistics. A classical approach to this problem is to fit (approximately) an explicit probability model to the training data via a maximum likelihood estimation. Building off the success of deep learning, however, there has been another approach to this problem using Generative Adversarial Networks (GANs). GANs view to this problem as a game between two sets of functions: a generator whose goal is to generate fake samples that are close to the real data training samples and a discriminator whose goal is to distinguish between the real and fake samples. In this project, we aim to train some of the state-of-the-art GAN architectures on image datasets and produce fake but believable images. ## Unsupervised Machine Learning in High Dimensions
Learning expressive and yet concise representation of complex high-dimensional data is the key for successful unsupervised learning, where no labeled information is provided. Although the data lies in a complex high-dimensional space, there is oftentimes an underlying low-dimensional structure that concisely describes the data generating process. Therefore the problem is to uncover the hidden structure. We will use linear latent variable models and spectral methods such as matrix/tensor decomposition on this problem. We will learn these techniques as needed. ## Muffin Mathematics: Nobody Wants a Small Piece
You have 5 muffins to distribute to 3 students. Every students gets 5 General Problem: You have m muffins to distribute to s students. Every students gets 5/3. Find the way to do this that maximizes the min piece. Prove its the best you can do! There are many techniques known for this problem, though very little has been proven. This project has several aspects: 1) write a package that uses known and new techniques that will, given m,s, output the best way to allocate them AND a proof that its the best. 2) PROVE theorems about our techniques. 3) Use ML techniques to generate more results. WARNING: Bill Gasarch is REALLY INTO this and is the worlds leading authority on this problem. Here is the proof: ## Cryptanalysis for Lattice-Based Cryptography
Next-generation cryptosystems may be based on newer assumptions related to the hardness of solving certain problems on lattices. This project will explore implementations of known algorithms from the literature for solving these problems in an effort to understand their concrete hardness. |