Natural data observed in $\mathbb{R}^n$ is often constrained to an $m$-dimensional manifold $\mathcal{M}$, where $m < n$. This work focuses on the task of building theoretically principled generative models for such data. Current generative models learn $\mathcal{M}$ by mapping an $m$-dimensional latent variable through a neural network $f_\theta: \mathbb{R}^m \to \mathbb{R}^n$. These procedures, which we call pushforward models, incur a straightforward limitation: manifolds cannot in general be represented with a single parameterization, meaning that attempts to do so will incur either computational instability or the inability to learn probability densities within the manifold. To remedy this problem, we propose to model $\mathcal{M}$ as a neural implicit manifold: the set of zeros of a neural network. We then learn the probability density within $\mathcal{M}$ with a constrained energy-based model, which employs a constrained variant of Langevin dynamics to train and sample from the learned manifold. In experiments on synthetic and natural data, we show that our model can learn manifold-supported distributions with complex topologies more accurately than pushforward models.

Alerting the public when heat may harm their health is a crucial service, especially considering that extreme heat events will be more frequent under climate change. Current practice for issuing heat alerts in the US does not take advantage of modern data science methods for optimizing local alert criteria. Specifically, application of reinforcement learning (RL) has the potential to inform more health-protective policies, accounting for regional and sociodemographic heterogeneity as well as sequential dependence of alerts. In this work, we formulate the issuance of heat alerts as a sequential decision making problem and develop modifications to the RL workflow to address challenges commonly encountered in environmental health settings. Key modifications include creating a simulator that pairs hierarchical Bayesian modeling of low-signal health effects with sampling of real weather trajectories (exogenous features), constraining the total number of alerts issued as well as preventing alerts on less-hot days, and optimizing location-specific policies. Post-hoc contrastive analysis offers insights into scenarios when using RL for heat alert issuance may protect public health better than the current or alternative policies. This work contributes to a broader movement of advancing data-driven policy optimization for public health and climate change adaptation.

Human annotations are vital to supervised learning, yet annotators often disagree on the correct label, especially as annotation tasks increase in complexity. A strategy to improve label quality is to ask multiple annotators to label the same item and aggregate their labels. Many aggregation models have been proposed for categorical or numerical annotation tasks, but far less work has considered more complex annotation tasks involving open-ended, multivariate, or structured responses. While a variety of bespoke models have been proposed for specific tasks, our work is the first 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 devising a task-agnostic method to model distances between labels rather than the labels themselves. This article extends our prior work with investigation of three new research questions. First, how do complex annotation properties impact aggregation accuracy? Second, how should a task owner navigate the many modeling choices to maximize aggregation accuracy? Finally, what 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 simulation studies and experiments on real, complex datasets. Regarding testing, we introduce 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 of annotation complexity, present a new aggregation model as a bridge between traditional models and our own, and contribute a new semi-supervised learning method for complex label aggregation that outperforms prior work.

Diffusion models have gained traction as powerful algorithms for synthesizing high-quality images. Central to these algorithms is the diffusion process, which maps data to noise according to equations inspired by thermodynamics and can significantly impact performance. A widely held assumption is that the ELBO objective of a diffusion model is invariant to the noise process (Kingma et al.,2021). In this work, we dispel this assumption -- we propose multivariate learned adaptive noise (MuLAN), a learned diffusion process that applies Gaussian noise at different rates across an image. Our method consists of three components -- a multivariate noise schedule, instance-conditional diffusion, and auxiliary variables -- which ensure that the learning objective is no longer invariant to the choice of the noise schedule as in previous works. Our work is grounded in Bayesian inference and casts the learned diffusion process as an approximate variational posterior that yields a tighter lower bound on marginal likelihood. Empirically, MuLAN sets a new state-of-the-art in density estimation on CIFAR-10 and ImageNet compared to classical diffusion. Code is available at https://github.com/s-sahoo/MuLAN

This study investigates the misclassification excess risk bound in the context of 1-bit matrix completion, a significant problem in machine learning involving the recovery of an unknown matrix from a limited subset of its entries. Matrix completion has garnered considerable attention in the last two decades due to its diverse applications across various fields. Unlike conventional approaches that deal with real-valued samples, 1-bit matrix completion is concerned with binary observations. While prior research has predominantly focused on the estimation error of proposed estimators, our study shifts attention to the prediction error. This paper offers theoretical analysis regarding the prediction errors of two previous works utilizing the logistic regression model: one employing a max-norm constrained minimization and the other employing nuclear-norm penalization. Significantly, our findings demonstrate that the latter achieves the minimax-optimal rate without the need for an additional logarithmic term. These novel results contribute to a deeper understanding of 1-bit matrix completion by shedding light on the predictive performance of specific methodologies.

Bayesian optimization (BO) is a sample-efficient method and has been widely used for optimizing expensive black-box functions. Recently, there has been a considerable interest in BO literature in optimizing functions that are affected by context variable in the environment, which is uncontrollable by decision makers. In this paper, we focus on the optimization of functions' expectations over continuous context variable, subject to an unknown distribution. To address this problem, we propose two algorithms that employ kernel density estimation to learn the probability density function (PDF) of continuous context variable online. The first algorithm is simpler, which directly optimizes the expectation under the estimated PDF. Considering that the estimated PDF may have high estimation error when the true distribution is complicated, we further propose the second algorithm that optimizes the distributionally robust objective. Theoretical results demonstrate that both algorithms have sub-linear Bayesian cumulative regret on the expectation objective. Furthermore, we conduct numerical experiments to empirically demonstrate the effectiveness of our algorithms.

Declarative process specifications define the behavior of processes by means of rules based on Linear Temporal Logic on Finite Traces (LTLf). In a mining context, these specifications are inferred from, and checked on, multi-sets of runs recorded by information systems (namely, event logs). To this end, being able to gauge the degree to which process data comply with a specification is key. However, existing mining and verification techniques analyze the rules in isolation, thereby disregarding their interplay. In this paper, we introduce a framework to devise probabilistic measures for declarative process specifications. Thereupon, we propose a technique that measures the degree of satisfaction of specifications over event logs. To assess our approach, we conduct an evaluation with real-world data, evidencing its applicability in discovery, checking, and drift detection contexts.

Online deep clustering refers to the joint use of a feature extraction network and a clustering model to assign cluster labels to each new data point or batch as it is processed. While faster and more versatile than offline methods, online clustering can easily reach the collapsed solution where the encoder maps all inputs to the same point and all are put into a single cluster. Successful existing models have employed various techniques to avoid this problem, most of which require data augmentation or which aim to make the average soft assignment across the dataset the same for each cluster. We propose a method that does not require data augmentation, and that, differently from existing methods, regularizes the hard assignments. Using a Bayesian framework, we derive an intuitive optimization objective that can be straightforwardly included in the training of the encoder network. Tested on four image datasets and one human-activity recognition dataset, it consistently avoids collapse more robustly than other methods and leads to more accurate clustering. We also conduct further experiments and analyses justifying our choice to regularize the hard cluster assignments. Code is available at https://github.com/Lou1sM/online_hard_clustering.

Models of eye-movement control during reading, developed largely within psychology, usually focus on visual, attentional, lexical, and motor processes but neglect post-lexical language processing; by contrast, models of sentence comprehension processes, developed largely within psycholinguistics, generally focus only on post-lexical language processes. We present a model that combines these two research threads, by integrating eye-movement control and sentence processing. Developing such an integrated model is extremely challenging and computationally demanding, but such an integration is an important step toward complete mathematical models of natural language comprehension in reading. We combine the SWIFT model of eye-movement control (Seelig et al., 2020, doi:10.1016/j.jmp.2019.102313) with key components of the Lewis and Vasishth sentence processing model (Lewis & Vasishth, 2005, doi:10.1207/s15516709cog0000_25). This integration becomes possible, for the first time, due in part to recent advances in successful parameter identification in dynamical models, which allows us to investigate profile log-likelihoods for individual model parameters. We present a fully implemented proof-of-concept model demonstrating how such an integrated model can be achieved; our approach includes Bayesian model inference with Markov Chain Monte Carlo (MCMC) sampling as a key computational tool. The integrated Sentence-Processing and Eye-Movement Activation-Coupled Model (SEAM) can successfully reproduce eye movement patterns that arise due to similarity-based interference in reading. To our knowledge, this is the first-ever integration of a complete process model of eye-movement control with linguistic dependency completion processes in sentence comprehension. In future work, this proof of concept model will need to be evaluated using a comprehensive set of benchmark data.

Transfer learning is a burgeoning concept in statistical machine learning that seeks to improve inference and/or predictive accuracy on a domain of interest by leveraging data from related domains. While the term "transfer learning" has garnered much recent interest, its foundational principles have existed for years under various guises. Prior literature reviews in computer science and electrical engineering have sought to bring these ideas into focus, primarily surveying general methodologies and works from these disciplines. This article highlights Bayesian approaches to transfer learning, which have received relatively limited attention despite their innate compatibility with the notion of drawing upon prior knowledge to guide new learning tasks. Our survey encompasses a wide range of Bayesian transfer learning frameworks applicable to a variety of practical settings. We discuss how these methods address the problem of finding the optimal information to transfer between domains, which is a central question in transfer learning. We illustrate the utility of Bayesian transfer learning methods via a simulation study where we compare performance against frequentist competitors.