However, before ice core data can have scientific value, the chronology must be inferred by estimating the age as a function of depth. Under certain conditions, chemicals locked in the ice display quasi-periodic cycles that delineate annual layers. Manually counting these noisy seasonal patterns to infer the chronology can be an imperfect and time-consuming process, and does not capture uncertainty in a principled fashion. In addition, several ice cores may be collected from a region, introducing an aspect of spatial correlation between them. We present an exploration of the use of probabilistic models for automatic dating of ice cores, using probabilistic programming to showcase its use for prototyping, automatic inference and maintainability, and demonstrate common failure modes of these tools.

While discrete latent variable models have had great success in self-supervised learning, most models assume that frames are independent. Due to the segmental nature of phonemes in speech perception, modeling dependencies among latent variables at the frame level can potentially improve the learned representations on phonetic-related tasks. In this work, we assume Markovian dependencies among latent variables, and propose to learn speech representations with neural hidden Markov models. Our general framework allows us to compare to self-supervised models that assume independence, while keeping the number of parameters fixed. The added dependencies improve the accessibility of phonetic information, phonetic segmentation, and the cluster purity of phones, showcasing the benefit of the assumed dependencies.

We study the problem of inferring user intent from noninvasive electroencephalography (EEG) to restore communication for people with severe speech and physical impairments (SSPI). The focus of this work is improving the estimation of posterior symbol probabilities in a typing task. At each iteration of the typing procedure, a subset of symbols is chosen for the next query based on the current probability estimate. Evidence about the user's response is collected from event-related potentials (ERP) in order to update symbol probabilities, until one symbol exceeds a predefined confidence threshold. We provide a graphical model describing this task, and derive a recursive Bayesian update rule based on a discriminative probability over label vectors for each query, which we approximate using a neural network classifier. We evaluate the proposed method in a simulated typing task and show that it outperforms previous approaches based on generative modeling.

Uncertainty on human behaviors poses a significant challenge to autonomous driving in crowded urban environments. The partially observable Markov decision processes (POMDPs) offer a principled framework for planning under uncertainty, often leveraging Monte Carlo sampling to achieve online performance for complex tasks. However, sampling also raises safety concerns by potentially missing critical events. To address this, we propose a new algorithm, LEarning Attention over Driving bEhavioRs (LEADER), that learns to attend to critical human behaviors during planning. LEADER learns a neural network generator to provide attention over human behaviors in real-time situations. It integrates the attention into a belief-space planner, using importance sampling to bias reasoning towards critical events. To train the algorithm, we let the attention generator and the planner form a min-max game. By solving the min-max game, LEADER learns to perform risk-aware planning without human labeling.

Language model (LM) pre-training is useful in many language processing tasks. But can pre-trained LMs be further leveraged for more general machine learning problems? We propose an approach for using LMs to scaffold learning and generalization in general sequential decision-making problems. In this approach, goals and observations are represented as a sequence of embeddings, and a policy network initialized with a pre-trained LM predicts the next action. We demonstrate that this framework enables effective combinatorial generalization across different environments and supervisory modalities. We begin by assuming access to a set of expert demonstrations, and show that initializing policies with LMs and fine-tuning them via behavior cloning improves task completion rates by 43.6% in the VirtualHome environment. Next, we integrate an active data gathering procedure in which agents iteratively interact with the environment, relabel past "failed" experiences with new goals, and update their policies in a self-supervised loop. Active data gathering further improves combinatorial generalization, outperforming the best baseline by 25.1%. Finally, we explain these results by investigating three possible factors underlying the effectiveness of the LM-based policy. We find that sequential input representations (vs. fixed-dimensional feature vectors) and LM-based weight initialization are both important for generalization. Surprisingly, however, the format of the policy inputs encoding (e.g. as a natural language string vs. an arbitrary sequential encoding) has little influence. Together, these results suggest that language modeling induces representations that are useful for modeling not just language, but also goals and plans; these representations can aid learning and generalization even outside of language processing.

A fundamental problem in statistics is to estimate a probability distribution from independent samples. In order to make the question precise, we choose a notion of distance \(\rho\) between distributions, pick two small numbers \(\delta, \varepsilon 0\) and can for instance say that an estimator is good, when with high probability \(1 - \delta\) over the random choice of the sample, the estimator is \(\varepsilon\) close to the true distribution. The problem of determining \(n_0\) is then typically addressed by providing two distinct answers. On one hand, we construct an estimator that would be good for any distribution given that \(n n_0 {UB}\). Conversely, we set up a hard problem such that no estimator can be good when \(n n_0 {LB}\).

Bayesian inference applied to microseismic activity monitoring allows the accurate location of microseismic events from recorded seismograms and the estimation of the associated uncertainties. However, the forward modelling of these microseismic events, which is necessary to perform Bayesian source inversion, can be prohibitively expensive in terms of computational resources. A viable solution is to train a surrogate model based on machine learning techniques, to emulate the forward model and thus accelerate Bayesian inference. In this paper, we substantially enhance previous work, which considered only sources with isotropic moment tensors. We train a machine learning algorithm on the power spectrum of the recorded pressure wave and show that the trained emulator allows complete and fast event locations for $\textit{any}$ source mechanism. Moreover, we show that our approach is computationally inexpensive, as it can be run in less than 1 hour on a commercial laptop, while yielding accurate results using less than $10^4$ training seismograms. We additionally demonstrate how the trained emulators can be used to identify the source mechanism through the estimation of the Bayesian evidence. Finally, we demonstrate that our approach is robust to real noise as measured in field data. This work lays the foundations for efficient, accurate future joint determinations of event location and moment tensor, and associated uncertainties, which are ultimately key for accurately characterising human-induced and natural earthquakes, and for enhanced quantitative seismic hazard assessments.

Reinforcement learning (RL) is a promising method to solve control problems. However, model-free RL algorithms are sample inefficient and require thousands if not millions of samples to learn optimal control policies. A major source of computational cost in RL corresponds to the transition function, which is dictated by the model dynamics. This is especially problematic when model dynamics is represented with coupled PDEs. In such cases, the transition function often involves solving a large-scale discretization of the said PDEs. We propose a multilevel RL framework in order to ease this cost by exploiting sublevel models that correspond to coarser scale discretization (i.e. multilevel models). This is done by formulating an approximate multilevel Monte Carlo estimate of the objective function of the policy and / or value network instead of Monte Carlo estimates, as done in the classical framework. As a demonstration of this framework, we present a multilevel version of the proximal policy optimization (PPO) algorithm. Here, the level refers to the grid fidelity of the chosen simulation-based environment. We provide two examples of simulation-based environments that employ stochastic PDEs that are solved using finite-volume discretization. For the case studies presented, we observed substantial computational savings using multilevel PPO compared to its classical counterpart.

Bayesian additive regression tree (BART) models have seen increased attention in recent years as a general-purpose nonparametric modeling technique. BART combines the flexibility of modern machine learning techniques with the principled uncertainty quantification of Bayesian inference, and it has been shown to be uniquely appropriate for addressing the high-noise problems that occur commonly in many areas of science, including medicine and the social sciences. This paper introduces the SoftBart package for fitting the Soft BART algorithm of Linero and Yang (2018). In addition to improving upon the predictive performance of other BART packages, a major goal of this package has been to facilitate the inclusion of BART in larger models, making it ideal for researchers in Bayesian statistics. I show both how to use this package for standard prediction tasks and how to embed BART models in larger models; I illustrate by using SoftBart to implement a nonparametric probit regression model, a semiparametric varying coefficient model, and a partial linear model.

This paper addresses the problem of fault diagnosis in multistation assembly systems. Fault diagnosis is to identify process faults that cause the excessive dimensional variation of the product using dimensional measurements. For such problems, the challenge is solving an underdetermined system caused by a common phenomenon in practice; namely, the number of measurements is less than that of the process errors. To address this challenge, this paper attempts to solve the following two problems: (1) how to utilize the temporal correlation in the time series data of each process error and (2) how to apply prior knowledge regarding which process errors are more likely to be process faults. A novel sparse Bayesian learning method is proposed to achieve the above objectives. The method consists of three hierarchical layers. The first layer has parameterized prior distribution that exploits the temporal correlation of each process error. Furthermore, the second and third layers achieve the prior distribution representing the prior knowledge of process faults. Then, these prior distributions are updated with the likelihood function of the measurement samples from the process, resulting in the accurate posterior distribution of process faults from an underdetermined system. Since posterior distributions of process faults are intractable, this paper derives approximate posterior distributions via Variational Bayes inference. Numerical and simulation case studies using an actual autobody assembly process are performed to demonstrate the effectiveness of the proposed method.