Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e. objective function queries) with maximal expected utility with respect to the posterior distribution of a Bayesian model, which quantifies reducible, epistemic uncertainty about query outcomes. In practice, subjectively implausible outcomes can occur regularly for two reasons: 1) model misspecification and 2) covariate shift. Conformal prediction is an uncertainty quantification method with coverage guarantees even for misspecified models and a simple mechanism to correct for covariate shift. We propose conformal Bayesian optimization, which directs queries towards regions of search space where the model predictions have guaranteed validity, and investigate its behavior on a suite of black-box optimization tasks and tabular ranking tasks. In many cases we find that query coverage can be significantly improved without harming sample-efficiency.

We address the consistency of a kernel ridge regression estimate of the conditional mean embedding (CME), which is an embedding of the conditional distribution of $Y$ given $X$ into a target reproducing kernel Hilbert space $\mathcal{H}_Y$. The CME allows us to take conditional expectations of target RKHS functions, and has been employed in nonparametric causal and Bayesian inference. We address the misspecified setting, where the target CME is in the space of Hilbert-Schmidt operators acting from an input interpolation space between $\mathcal{H}_X$ and $L_2$, to $\mathcal{H}_Y$. This space of operators is shown to be isomorphic to a newly defined vector-valued interpolation space. Using this isomorphism, we derive a novel and adaptive statistical learning rate for the empirical CME estimator under the misspecified setting. Our analysis reveals that our rates match the optimal $O(\log n / n)$ rates without assuming $\mathcal{H}_Y$ to be finite dimensional. We further establish a lower bound on the learning rate, which shows that the obtained upper bound is optimal.

The randomly pivoted partial Cholesky algorithm (RPCholesky) computes a factorized rank-k approximation of an N x N positive-semidefinite (psd) matrix. RPCholesky requires only (k + 1) N entry evaluations and O(k^2 N) additional arithmetic operations, and it can be implemented with just a few lines of code. The method is particularly useful for approximating a kernel matrix. This paper offers a thorough new investigation of the empirical and theoretical behavior of this fundamental algorithm. For matrix approximation problems that arise in scientific machine learning, experiments show that RPCholesky matches or beats the performance of alternative algorithms. Moreover, RPCholesky provably returns low-rank approximations that are nearly optimal. The simplicity, effectiveness, and robustness of RPCholesky strongly support its use in scientific computing and machine learning applications.

Simple stochastic momentum methods are widely used in machine learning optimization, but their good practical performance is at odds with an absence of theoretical guarantees of acceleration in the literature. In this work, we aim to close the gap between theory and practice by showing that stochastic heavy ball momentum retains the fast linear rate of (deterministic) heavy ball momentum on quadratic optimization problems, at least when minibatching with a sufficiently large batch size. The algorithm we study can be interpreted as an accelerated randomized Kaczmarz algorithm with minibatching and heavy ball momentum. The analysis relies on carefully decomposing the momentum transition matrix, and using new spectral norm concentration bounds for products of independent random matrices. We provide numerical illustrations demonstrating that our bounds are reasonably sharp.

We propose score dynamics, a general framework for learning accelerated evolution operators with large timesteps from molecular-dynamics simulations. SD is centered around scores, or derivatives of the transition log-probability with respect to the dynamical degrees of freedom. The latter play the same role as force fields in MD but are used in denoising diffusion probability models to generate discrete transitions of the dynamical variables in an SD timestep, which can be orders of magnitude larger than a typical MD timestep. In this work, we construct graph neural network based score dynamics models of realistic molecular systems that are evolved with 10 ps timesteps. We demonstrate the efficacy of score dynamics with case studies of alanine dipeptide and short alkanes in aqueous solution. Both equilibrium predictions derived from the stationary distributions of the conditional probability and kinetic predictions for the transition rates and transition paths are in good agreement with MD. Our current SD implementation is about two orders of magnitude faster than the MD counterpart for the systems studied in this work. Open challenges and possible future remedies to improve score dynamics are also discussed.

High-Performance Computing (HPC) systems need to be constantly monitored to ensure their stability. The monitoring systems collect a tremendous amount of data about different parameters or Key Performance Indicators (KPIs), such as resource usage, IO waiting time, etc. A proper analysis of this data, usually stored as time series, can provide insight in choosing the right management strategies as well as the early detection of issues. In this paper, we introduce a methodology to cluster HPC jobs according to their KPI indicators. Our approach reduces the inherent high dimensionality of the collected data by applying two techniques to the time series: literature-based and variance-based feature extraction. We also define a procedure to visualize the obtained clusters by combining the two previous approaches and the Principal Component Analysis (PCA). Finally, we have validated our contributions on a real data set to conclude that those KPIs related to CPU usage provide the best cohesion and separation for clustering analysis and the good results of our visualization methodology.

Human annotations are vital to supervised learning, yet annotators often disagree on the correct label, especially as annotation tasks increase in complexity. A common strategy to improve label quality is to ask multiple annotators to label the same item and then aggregate their labels. To date, many aggregation models have been proposed for simple categorical or numerical annotation tasks, but far less work has considered more complex annotation tasks, such as those involving open-ended, multivariate, or structured responses. Similarly, while a variety of bespoke models have been proposed for specific tasks, our work is the first we are aware of to introduce aggregation methods that generalize across many, diverse complex tasks, including sequence labeling, translation, syntactic parsing, ranking, bounding boxes, and keypoints. This generality is achieved by applying readily available task-specific distance functions, then devising a task-agnostic method to model these distances between labels, rather than the labels themselves. This article presents a unified treatment of our prior work on complex annotation modeling and extends that work with investigation of three new research questions. First, how do complex annotation task and dataset properties impact aggregation accuracy? Second, how should a task owner navigate the many modeling choices in order to maximize aggregation accuracy? Finally, what tests and diagnoses can verify that aggregation models are specified correctly for the given data? To understand how various factors impact accuracy and to inform model selection, we conduct large-scale simulation studies and broad experiments on real, complex datasets. Regarding testing, we introduce the concept of unit tests for aggregation models and present a suite of such tests to ensure that a given model is not mis-specified and exhibits expected behavior. Beyond investigating these research questions above, we discuss the foundational concept and nature of annotation complexity, present a new aggregation model as a conceptual bridge between traditional models and our own, and contribute a new general semisupervised learning method for complex label aggregation that outperforms prior work.

This work presents an algorithm for scene change detection from point clouds to enable autonomous robotic caretaking in future space habitats. Autonomous robotic systems will help maintain future deep-space habitats, such as the Gateway space station, which will be uncrewed for extended periods. Existing scene analysis software used on the International Space Station (ISS) relies on manually-labeled images for detecting changes. In contrast, the algorithm presented in this work uses raw, unlabeled point clouds as inputs. The algorithm first applies modified Expectation-Maximization Gaussian Mixture Model (GMM) clustering to two input point clouds. It then performs change detection by comparing the GMMs using the Earth Mover's Distance. The algorithm is validated quantitatively and qualitatively using a test dataset collected by an Astrobee robot in the NASA Ames Granite Lab comprising single frame depth images taken directly by Astrobee and full-scene reconstructed maps built with RGB-D and pose data from Astrobee. The runtimes of the approach are also analyzed in depth. The source code is publicly released to promote further development.

Ovarian cancer (OC) is one of the most prevalent types of cancer in women. Early and accurate diagnosis is crucial for the survival of the patients. However, the majority of women are diagnosed in advanced stages due to the lack of effective biomarkers and accurate screening tools. While previous studies sought a common biomarker, our study suggests different biomarkers for the premenopausal and postmenopausal populations. This can provide a new perspective in the search for novel predictors for the effective diagnosis of OC. Lack of explainability is one major limitation of current AI systems. The stochastic nature of the ML algorithms raises concerns about the reliability of the system as it is difficult to interpret the reasons behind the decisions. To increase the trustworthiness and accountability of the diagnostic system as well as to provide transparency and explanations behind the predictions, explainable AI has been incorporated into the ML framework. SHAP is employed to quantify the contributions of the selected biomarkers and determine the most discriminative features. A hybrid decision support system has been established that can eliminate the bottlenecks caused by the black-box nature of the ML algorithms providing a safe and trustworthy AI tool. The diagnostic accuracy obtained from the proposed system outperforms the existing methods as well as the state-of-the-art ROMA algorithm by a substantial margin which signifies its potential to be an effective tool in the differential diagnosis of OC.

Likelihood-free inference is quickly emerging as a powerful tool to perform fast/effective parameter estimation. We demonstrate a technique of optimizing likelihood-free inference to make it even faster by marginalizing symmetries in a physical problem. In this approach, physical symmetries, for example, time-translation are learned using joint-embedding via self-supervised learning with symmetry data augmentations. Subsequently, parameter inference is performed using a normalizing flow where the embedding network is used to summarize the data before conditioning the parameters. We present this approach on two simple physical problems and we show faster convergence in a smaller number of parameters compared to a normalizing flow that does not use a pre-trained symmetry-informed representation.