arXiv subjects
Publications and source records attributed to Katherine Heller.
We investigate the isometric composition operators on the analytic Besov spaces. For $1 2$, we extend previous work on the subject. Finally, we analyze this same problem for the Besov spaces with an equivalent norm.
In this paper, we study the multiplication operators on $S^2$, the space of analytic functions on the open unit disk $\mathbb D$ whose first derivative is in $H^2$. Specifically, we characterize the bounded and the compact multiplication operators, establish estimates on the operator norm, and determine the spectrum. Finally, we prove that the isometric multiplication operators are precisely those induced by a constant function of modulus one.
Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces $\mathcal{D}_α$. Specifically we study differences of composition operators on the Dirichlet space $\mathcal{D}$ and $S^2$, the space of analytic functions whose first derivative is in $H^2$, and then use Calderón's complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.
We investigate composition-differentiation operators acting on the Dirichlet space of the unit disk. Specifically, we determine characterizations for bounded, compact, and Hilbert-Schmidt composition-differentiation operators. In addition, for particular classes of inducing maps, we derive an adjoint formula, compute the norm, and identify the spectrum.
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological differences. We compute the basic reproduction number for each model, as well as analyze the sensitivity of $R_0$ to changes in sociological parameter values.
Survival analysis is a challenging variation of regression modeling because of the presence of censoring, where the outcome measurement is only partially known, due to, for example, loss to follow up. Such problems come up frequently in medical applications, making survival analysis a key endeavor in biostatistics and machine learning for healthcare, with Cox regression models being amongst the most commonly employed models. We describe a new approach for survival analysis regression models, based on learning mixtures of Cox regressions to model individual survival distributions. We propose an approximation to the Expectation Maximization algorithm for this model that does hard assignments to mixture groups to make optimization efficient. In each group assignment, we fit the hazard ratios within each group using deep neural networks, and the baseline hazard for each mixture component non-parametrically. We perform experiments on multiple real world datasets, and look at the mortality rates of patients across ethnicity and gender. We emphasize the importance of calibration in healthcare settings and demonstrate that our approach outperforms classical and modern survival analysis baselines, both in terms of discriminative performance and calibration, with large gains in performance on the minority demographics.
Forming a reliable judgement of a machine learning (ML) model's appropriateness for an application ecosystem is critical for its responsible use, and requires considering a broad range of factors including harms, benefits, and responsibilities. In practice, however, evaluations of ML models frequently focus on only a narrow range of decontextualized predictive behaviours. We examine the evaluation gaps between the idealized breadth of evaluation concerns and the observed narrow focus of actual evaluations. Through an empirical study of papers from recent high-profile conferences in the Computer Vision and Natural Language Processing communities, we demonstrate a general focus on a handful of evaluation methods. By considering the metrics and test data distributions used in these methods, we draw attention to which properties of models are centered in the field, revealing the properties that are frequently neglected or sidelined during evaluation. By studying these properties, we demonstrate the machine learning discipline's implicit assumption of a range of commitments which have normative impacts; these include commitments to consequentialism, abstractability from context, the quantifiability of impacts, the limited role of model inputs in evaluation, and the equivalence of different failure modes. Shedding light on these assumptions enables us to question their appropriateness for ML system contexts, pointing the way towards more contextualized evaluation methodologies for robustly examining the trustworthiness of ML models
Literature on machine learning for multiple sclerosis has primarily focused on the use of neuroimaging data such as magnetic resonance imaging and clinical laboratory tests for disease identification. However, studies have shown that these modalities are not consistent with disease activity such as symptoms or disease progression. Furthermore, the cost of collecting data from these modalities is high, leading to scarce evaluations. In this work, we used multi-dimensional, affordable, physical and smartphone-based performance outcome measures (POM) in conjunction with demographic data to predict multiple sclerosis disease progression. We performed a rigorous benchmarking exercise on two datasets and present results across 13 clinically actionable prediction endpoints and 6 machine learning models. To the best of our knowledge, our results are the first to show that it is possible to predict disease progression using POMs and demographic data in the context of both clinical trials and smartphone-base studies by using two datasets. Moreover, we investigate our models to understand the impact of different POMs and demographics on model performance through feature ablation studies. We also show that model performance is similar across different demographic subgroups (based on age and sex). To enable this work, we developed an end-to-end reusable pre-processing and machine learning framework which allows quicker experimentation over disparate MS datasets.
Machine learning (ML) approaches have demonstrated promising results in a wide range of healthcare applications. Data plays a crucial role in developing ML-based healthcare systems that directly affect people's lives. Many of the ethical issues surrounding the use of ML in healthcare stem from structural inequalities underlying the way we collect, use, and handle data. Developing guidelines to improve documentation practices regarding the creation, use, and maintenance of ML healthcare datasets is therefore of critical importance. In this work, we introduce Healthsheet, a contextualized adaptation of the original datasheet questionnaire ~\cite{gebru2018datasheets} for health-specific applications. Through a series of semi-structured interviews, we adapt the datasheets for healthcare data documentation. As part of the Healthsheet development process and to understand the obstacles researchers face in creating datasheets, we worked with three publicly-available healthcare datasets as our case studies, each with different types of structured data: Electronic health Records (EHR), clinical trial study data, and smartphone-based performance outcome measures. Our findings from the interviewee study and case studies show 1) that datasheets should be contextualized for healthcare, 2) that despite incentives to adopt accountability practices such as datasheets, there is a lack of consistency in the broader use of these practices 3) how the ML for health community views datasheets and particularly \textit{Healthsheets} as diagnostic tool to surface the limitations and strength of datasets and 4) the relative importance of different fields in the datasheet to healthcare concerns.
ML models often exhibit unexpectedly poor behavior when they are deployed in real-world domains. We identify underspecification as a key reason for these failures. An ML pipeline is underspecified when it can return many predictors with equivalently strong held-out performance in the training domain. Underspecification is common in modern ML pipelines, such as those based on deep learning. Predictors returned by underspecified pipelines are often treated as equivalent based on their training domain performance, but we show here that such predictors can behave very differently in deployment domains. This ambiguity can lead to instability and poor model behavior in practice, and is a distinct failure mode from previously identified issues arising from structural mismatch between training and deployment domains. We show that this problem appears in a wide variety of practical ML pipelines, using examples from computer vision, medical imaging, natural language processing, clinical risk prediction based on electronic health records, and medical genomics. Our results show the need to explicitly account for underspecification in modeling pipelines that are intended for real-world deployment in any domain.
Bayesian neural networks (BNNs) demonstrate promising success in improving the robustness and uncertainty quantification of modern deep learning. However, they generally struggle with underfitting at scale and parameter efficiency. On the other hand, deep ensembles have emerged as alternatives for uncertainty quantification that, while outperforming BNNs on certain problems, also suffer from efficiency issues. It remains unclear how to combine the strengths of these two approaches and remediate their common issues. To tackle this challenge, we propose a rank-1 parameterization of BNNs, where each weight matrix involves only a distribution on a rank-1 subspace. We also revisit the use of mixture approximate posteriors to capture multiple modes, where unlike typical mixtures, this approach admits a significantly smaller memory increase (e.g., only a 0.4% increase for a ResNet-50 mixture of size 10). We perform a systematic empirical study on the choices of prior, variational posterior, and methods to improve training. For ResNet-50 on ImageNet, Wide ResNet 28-10 on CIFAR-10/100, and an RNN on MIMIC-III, rank-1 BNNs achieve state-of-the-art performance across log-likelihood, accuracy, and calibration on the test sets and out-of-distribution variants.
In medicine, both ethical and monetary costs of incorrect predictions can be significant, and the complexity of the problems often necessitates increasingly complex models. Recent work has shown that changing just the random seed is enough for otherwise well-tuned deep neural networks to vary in their individual predicted probabilities. In light of this, we investigate the role of model uncertainty methods in the medical domain. Using RNN ensembles and various Bayesian RNNs, we show that population-level metrics, such as AUC-PR, AUC-ROC, log-likelihood, and calibration error, do not capture model uncertainty. Meanwhile, the presence of significant variability in patient-specific predictions and optimal decisions motivates the need for capturing model uncertainty. Understanding the uncertainty for individual patients is an area with clear clinical impact, such as determining when a model decision is likely to be brittle. We further show that RNNs with only Bayesian embeddings can be a more efficient way to capture model uncertainty compared to ensembles, and we analyze how model uncertainty is impacted across individual input features and patient subgroups.
The use of collaborative and decentralized machine learning techniques such as federated learning have the potential to enable the development and deployment of clinical risk predictions models in low-resource settings without requiring sensitive data be shared or stored in a central repository. This process necessitates communication of model weights or updates between collaborating entities, but it is unclear to what extent patient privacy is compromised as a result. To gain insight into this question, we study the efficacy of centralized versus federated learning in both private and non-private settings. The clinical prediction tasks we consider are the prediction of prolonged length of stay and in-hospital mortality across thirty one hospitals in the eICU Collaborative Research Database. We find that while it is straightforward to apply differentially private stochastic gradient descent to achieve strong privacy bounds when training in a centralized setting, it is considerably more difficult to do so in the federated setting.
In textual conversation threads, as found on many popular social media platforms, each particular user text comment either originates a new thread of discussion, or replies to a previous comment. An individual who makes an original comment ---termed as the "root source''---is a topic initiator or even an information source, and identifying such individuals is of particular interest. The reply structure of comments is not always available (e.g. in the proliferation of a news event), and thus identifying root sources is a nontrivial task. In this paper, we develop a generative model based on marked multivariate Hawkes processes, and introduce a novel concept, "root source probability", to quantify the uncertainty in attributing possible root sources to each comment. A dynamic-programming-based algorithm is then derived to efficiently compute root source probabilities. Experiments on synthetic and real-world data show that our method identifies root sources that match ground truth and human intuition.
Learning-to-learn or meta-learning leverages data-driven inductive bias to increase the efficiency of learning on a novel task. This approach encounters difficulty when transfer is not advantageous, for instance, when tasks are considerably dissimilar or change over time. We use the connection between gradient-based meta-learning and hierarchical Bayes to propose a Dirichlet process mixture of hierarchical Bayesian models over the parameters of an arbitrary parametric model such as a neural network. In contrast to consolidating inductive biases into a single set of hyperparameters, our approach of task-dependent hyperparameter selection better handles latent distribution shift, as demonstrated on a set of evolving, image-based, few-shot learning benchmarks.
We develop a hierarchical infinite latent factor model (HIFM) to appropriately account for the covariance structure across subpopulations in data. We propose a novel Hierarchical Dirichlet Process shrinkage prior on the loadings matrix that flexibly captures the underlying structure of our data across subpopulations while sharing information to improve inference and prediction. The stick-breaking construction of the prior assumes infinite number of factors and allows for each subpopulation to utilize different subsets of the factor space and select the number of factors needed to best explain the variation. Theoretical results are provided to show support of the prior. We develop the model into a latent factor regression method that excels at prediction and inference of regression coefficients. Simulations are used to validate this strong performance compared to baseline methods. We apply this work to the problem of predicting surgical complications using electronic health record data for geriatric patients at Duke University Health System (DUHS). We utilize additional surgical encounters at DUHS to enhance learning for the targeted patients. Using HIFM to identify high risk patients improves the sensitivity of predicting death to 91% from 35% based on the currently used heuristic.
This paper develops metrics from a social network perspective that are directly translatable to the outcome of a basketball game. We extend a state-of-the-art multi-resolution stochastic process approach to modeling basketball by modeling passes between teammates as directed dynamic relational links on a network and introduce multiplicative latent factors to study higher-order patterns in players' interactions that distinguish a successful game from a loss. Parameters are estimated using a Markov chain Monte Carlo sampler. Results in simulation experiments suggest that the sampling scheme is effective in recovering the parameters. We then apply the model to the first high-resolution optical tracking dataset collected in college basketball games. The learned latent factors demonstrate significant differences between players' passing and receiving tendencies in a loss than those in a win. The model is applicable to team sports other than basketball, as well as other time-varying network observations.
We propose a new method that uses deep learning techniques to solve the inverse problems. The inverse problem is cast in the form of learning an end-to-end mapping from observed data to the ground-truth. Inspired by the splitting strategy widely used in regularized iterative algorithm to tackle inverse problems, the mapping is decomposed into two networks, with one handling the inversion of the physical forward model associated with the data term and one handling the denoising of the output from the former network, i.e., the inverted version, associated with the prior/regularization term. The two networks are trained jointly to learn the end-to-end mapping, getting rid of a two-step training. The training is annealing as the intermediate variable between these two networks bridges the gap between the input (the degraded version of output) and output and progressively approaches to the ground-truth. The proposed network, referred to as InverseNet, is flexible in the sense that most of the existing end-to-end network structure can be leveraged in the first network and most of the existing denoising network structure can be used in the second one. Extensive experiments on both synthetic data and real datasets on the tasks, motion deblurring, super-resolution, and colorization, demonstrate the efficiency and accuracy of the proposed method compared with other image processing algorithms.