Shallow shadows: Expectation estimation using low-depth random Clifford circuits

We provide practical and powerful schemes for learning many properties of an unknown n-qubit quantum state using a sparing number of copies of the state. Specifically, we present a depth-modulated randomized measurement scheme that interpolates between two known classical shadows schemes based on random Pauli measurements and random Clifford measurements. These can be seen within our scheme as the special cases of zero and infinite depth, respectively. We focus on the regime where depth scales logarithmically in n and provide evidence that this retains the desirable properties of both extremal schemes whilst, in contrast to the random Clifford scheme, also being experimentally feasible. We present methods for two key tasks; estimating expectation values of certain observables from generated classical shadows and, computing upper bounds on the depth-modulated shadow norm, thus providing rigorous guarantees on the accuracy of the output estimates. We consider observables that can be written as a linear combination of poly(n) Paulis and observables that can be written as a low bond dimension matrix product operator. For the former class of observables both tasks are solved efficiently in n. For the latter class, we do not guarantee efficiency but present a method that works in practice; by variationally computing a heralded approximate inverses of a tensor network that can then be used for efficiently executing both these tasks.Comment: 22 pages, 12 figures. Version 2: new MPS variational inversion algorithm and new numeric

Learning Discriminative Representations for Gigapixel Images

Digital images of tumor tissue are important diagnostic and prognostic tools for pathologists. Recent advancement in digital pathology has led to an abundance of digitized histopathology slides, called whole-slide images. Computational analysis of whole-slide images is a challenging task as they are generally gigapixel files, often one or more gigabytes in size. However, these computational methods provide a unique opportunity to improve the objectivity and accuracy of diagnostic interpretations in histopathology. Recently, deep learning has been successful in characterizing images for vision-based applications in multiple domains. But its applications are relatively less explored in the histopathology domain mostly due to the following two challenges. Firstly, there is difficulty in scaling deep learning methods for processing large gigapixel histopathology images. Secondly, there is a lack of diversified and labeled datasets due to privacy constraints as well as workflow and technical challenges in the healthcare sector. The main goal of this dissertation is to explore and develop deep models to learn discriminative representations of whole slide images while overcoming the existing challenges. A three-staged approach was considered in this research. In the first stage, a framework called Yottixel is proposed. It represents a whole-slide image as a set of multiple representative patches, called mosaic. The mosaic enables convenient processing and compact representation of an entire high-resolution whole-slide image. Yottixel allows faster retrieval of similar whole-slide images within large archives of digital histopathology images. Such retrieval technology enables pathologists to tap into the past diagnostic data on demand. Yottixel is validated on the largest public archive of whole-slide images (The Cancer Genomic Atlas), achieving promising results. Yottixel is an unsupervised method that limits its performance on specific tasks especially when the labeled (or partially labeled) dataset can be available. In the second stage, multi-instance learning (MIL) is used to enhance the cancer subtype prediction through weakly-supervised training. Three MIL methods have been proposed, each improving upon the previous one. The first one is based on memory-based models, the second uses attention-based models, and the third one uses graph neural networks. All three methods are incorporated in Yottixel to classify entire whole-slide images with no pixel-level annotations. Access to large-scale and diversified datasets is a primary driver of the advancement and adoption of machine learning technologies. However, healthcare has many restrictive rules around data sharing, limiting research and model development. In the final stage, a federated learning scheme called ProxyFL is developed that enables collaborative training of Yottixel among the multiple healthcare organizations without centralization of the sensitive medical data. The combined research in all the three stages of the Ph.D. has resulted in the development of a holistic and practical framework for learning discriminative and compact representations of whole-slide images in digital pathology

Generalization Through the Lens of Learning Dynamics

A machine learning (ML) system must learn not only to match the output of a target function on a training set, but also to generalize to novel situations in order to yield accurate predictions at deployment. In most practical applications, the user cannot exhaustively enumerate every possible input to the model; strong generalization performance is therefore crucial to the development of ML systems which are performant and reliable enough to be deployed in the real world. While generalization is well-understood theoretically in a number of hypothesis classes, the impressive generalization performance of deep neural networks has stymied theoreticians. In deep reinforcement learning (RL), our understanding of generalization is further complicated by the conflict between generalization and stability in widely-used RL algorithms. This thesis will provide insight into generalization by studying the learning dynamics of deep neural networks in both supervised and reinforcement learning tasks.Comment: PhD Thesi

Multimodal Image Fusion and Its Applications.

Image fusion integrates different modality images to provide comprehensive information of the image content, increasing interpretation capabilities and producing more reliable results. There are several advantages of combining multi-modal images, including improving geometric corrections, complementing data for improved classification, and enhancing features for analysis...etc. This thesis develops the image fusion idea in the context of two domains: material microscopy and biomedical imaging. The proposed methods include image modeling, image indexing, image segmentation, and image registration. The common theme behind all proposed methods is the use of complementary information from multi-modal images to achieve better registration, feature extraction, and detection performances. In material microscopy, we propose an anomaly-driven image fusion framework to perform the task of material microscopy image analysis and anomaly detection. This framework is based on a probabilistic model that enables us to index, process and characterize the data with systematic and well-developed statistical tools. In biomedical imaging, we focus on the multi-modal registration problem for functional MRI (fMRI) brain images which improves the performance of brain activation detection.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120701/1/yuhuic_1.pd

Modeling Errors in Biometric Surveillance and De-duplication Systems

In biometrics-based surveillance and de-duplication applications, the system commonly determines if a given individual has been encountered before. In this dissertation, these applications are viewed as specific instances of a broader class of problems known as Anonymous Identification. Here, the system does not necessarily determine the identity of a person; rather, it merely establishes if the given input biometric data was encountered previously. This dissertation demonstrates that traditional biometric evaluation measures cannot adequately estimate the error rate of an anonymous identification system in general and a de-duplication system in particular. In this regard, the first contribution is the design of an error prediction model for an anonymous identification system. The model shows that the order in which individuals are encountered impacts the error rate of the system. The second contribution - in the context of an identification system in general - is an explanatory model that explains the relationship between the Receiver Operating Characteristic (ROC) curve and the Cumulative Match Characteristic (CMC) curve of a closed-set biometric system. The phenomenon of biometrics menagerie is used to explain the possibility of deducing multiple CMC curves from the same ROC curve. Consequently, it is shown that a good\u27\u27 verification system can be a poor\u27\u27 identification system and vice-versa.;Besides the aforementioned contributions, the dissertation also explores the use of gait as a biometric modality in surveillance systems operating in the thermal or shortwave infrared (SWIR) spectrum. In this regard, a new gait representation scheme known as Gait Curves is developed and evaluated on thermal and SWIR data. Finally, a clustering scheme is used to demonstrate that gait patterns can be clustered into multiple categories; further, specific physical traits related to gender and body area are observed to impact cluster generation.;In sum, the dissertation provides some new insights into modeling anonymous identification systems and gait patterns for biometrics-based surveillance systems

Inference on Counterfactual Distributions

Counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics. In this article we develop modeling and inference tools for counterfactual distributions based on regression methods. The counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates. For either of these scenarios we derive joint functional central limit theorems and bootstrap validity results for regression-based estimators of the status quo and counterfactual outcome distributions. These results allow us to construct simultaneous confidence sets for function-valued effects of the counterfactual changes, including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals. These confidence sets can be used to test functional hypotheses such as no-effect, positive effect, or stochastic dominance. Our theory applies to general counterfactual changes and covers the main regression methods including classical, quantile, duration, and distribution regressions. We illustrate the results with an empirical application to wage decompositions using data for the United States. As a part of developing the main results, we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the \textit{entire} conditional distribution. We show that distribution regression encompasses the Cox duration regression and represents a useful alternative to quantile regression. We establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals.Comment: 55 pages, 1 table, 3 figures, supplementary appendix with additional results available from the authors' web site