HAL-X: Scalable hierarchical clustering for rapid and tunable single-cell analysis.

Data clustering plays a significant role in biomedical sciences, particularly in single-cell data analysis. Researchers use clustering algorithms to group individual cells into populations that can be evaluated across different levels of disease progression, drug response, and other clinical statuses. In many cases, multiple sets of clusters must be generated to assess varying levels of cluster specificity. For example, there are many subtypes of leukocytes (e.g. T cells), whose individual preponderance and phenotype must be assessed for statistical/functional significance. In this report, we introduce a novel hierarchical density clustering algorithm (HAL-x) that uses supervised linkage methods to build a cluster hierarchy on raw single-cell data. With this new approach, HAL-x can quickly predict multiple sets of labels for immense datasets, achieving a considerable improvement in computational efficiency on large datasets compared to existing methods. We also show that cell clusters generated by HAL-x yield near-perfect F1-scores when classifying different clinical statuses based on single-cell profiles. Our hierarchical density clustering algorithm achieves high accuracy in single cell classification in a scalable, tunable and rapid manner.

A high-bias, low-variance introduction to Machine Learning for physicists.

Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute.

Glassy Phase of Optimal Quantum Control.

We study the problem of preparing a quantum many-body system from an initial to a target state by optimizing the fidelity over the family of bang-bang protocols. We present compelling numerical evidence for a universal spin-glasslike transition controlled by the protocol time duration. The glassy critical point is marked by a proliferation of protocols with close-to-optimal fidelity and with a true optimum that appears exponentially difficult to locate. Using a machine learning (ML) inspired framework based on the manifold learning algorithm t-distributed stochastic neighbor embedding, we are able to visualize the geometry of the high-dimensional control landscape in an effective low-dimensional representation. Across the transition, the control landscape features an exponential number of clusters separated by extensive barriers, which bears a strong resemblance with replica symmetry breaking in spin glasses and random satisfiability problems. We further show that the quantum control landscape maps onto a disorder-free classical Ising model with frustrated nonlocal, multibody interactions. Our work highlights an intricate but unexpected connection between optimal quantum control and spin glass physics, and shows how tools from ML can be used to visualize and understand glassy optimization landscapes.