In this work, minibatch MCMC sampling for feedforward neural networks is made more feasible. To this end, it is proposed to sample subgroups of parameters via a blocked Gibbs sampling scheme. By partitioning the parameter space, sampling is possible irrespective of layer width. It is also possible to alleviate vanishing acceptance rates for increasing depth by reducing the proposal variance in deeper layers. Increasing the length of a non-convergent chain increases the predictive accuracy in classification tasks, so avoiding vanishing acceptance rates and consequently enabling longer chain runs have practical benefits. Moreover, non-convergent chain realizations aid in the quantification of predictive uncertainty. An open problem is how to perform minibatch MCMC sampling for feedforward neural networks in the presence of augmented data.

Machine Learning (ML) models are ubiquitous in real-world applications and are a constant focus of research. Modern ML models have become more complex, deeper, and harder to reason about. At the same time, the community has started to realize the importance of protecting the privacy of the training data that goes into these models. Differential Privacy (DP) has become a gold standard for making formal statements about data anonymization. However, while some adoption of DP has happened in industry, attempts to apply DP to real world complex ML models are still few and far between. The adoption of DP is hindered by limited practical guidance of what DP protection entails, what privacy guarantees to aim for, and the difficulty of achieving good privacy-utility-computation trade-offs for ML models. Tricks for tuning and maximizing performance are scattered among papers or stored in the heads of practitioners, particularly with respect to the challenging task of hyperparameter tuning. Furthermore, the literature seems to present conflicting evidence on how and whether to apply architectural adjustments and which components are “safe” to use with DP. In this survey paper, we attempt to create a self-contained guide that gives an in-depth overview of the field of DP ML. We aim to assemble information about achieving the best possible DP ML model with rigorous privacy guarantees. Our target audience is both researchers and practitioners. Researchers interested in DP for ML will benefit from a clear overview of current advances and areas for improvement. We also include theory-focused sections that highlight important topics such as privacy accounting and convergence. For a practitioner, this survey provides a background in DP theory and a clear step-by-step guide for choosing an appropriate privacy definition and approach, implementing DP training, potentially updating the model architecture, and tuning hyperparameters. For both researchers and practitioners, consistently and fully reporting privacy guarantees is critical, so we propose a set of specific best practices for stating guarantees. With sufficient computation and a sufficiently large training set or supplemental nonprivate data, both good accuracy (that is, almost as good as a non-private model) and good privacy can often be achievable. And even when computation and dataset size are limited, there are advantages to training with even a weak (but still finite) formal DP guarantee. Hence, we hope this work will facilitate more widespread deployments of DP ML models.

Motivated by the need for the development of safe and reliable methods for uncertainty quantification in machine learning, I propose and develop ideas for a model-free statistical framework for imprecise probabilistic prediction inference. This framework facilitates uncertainty quantification in the form of prediction sets that offer finite sample control of type 1 errors, a property shared with conformal prediction sets, but this new approach also offers more versatile tools for imprecise probabilistic reasoning. Furthermore, I propose and consider the theoretical and empirical properties of a precise probabilistic approximation to the model-free imprecise framework. Approximating a belief/plausibility measure pair by an [optimal in some sense] probability measure in the credal set is a critical resolution needed for the broader adoption of imprecise probabilistic approaches to inference in statistical and machine learning communities. It is largely undetermined in the statistical and machine learning literatures, more generally, how to properly quantify uncertainty in that there is no generally accepted standard of accountability of stated uncertainties. The research I present in this manuscript is aimed at motivating a framework for statistical inference with reliability and accountability as the guiding principles.

Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and epistemic uncertainties, which represent the inherent randomness in the data-generating process and the variability due to insufficient data, respectively. They analyzed those uncertainties in an information-theoretic way, assuming that the model is well-specified and treating the model's parameters as latent variables. However, the existing information-theoretic analysis of uncertainty cannot explain the widely believed property of uncertainty, known as the sensitivity between the test and training data. It implies that when test data are similar to training data in some sense, the epistemic uncertainty should become small. In this work, we study such uncertainty sensitivity using our novel decomposition method for the predictive uncertainty. Our analysis successfully defines such sensitivity using information-theoretic quantities. Furthermore, we extend the existing analysis of Bayesian meta-learning and show the novel sensitivities among tasks for the first time.

Forgetting refers to the loss or deterioration of previously acquired information or knowledge. While the existing surveys on forgetting have primarily focused on continual learning, forgetting is a prevalent phenomenon observed in various other research domains within deep learning. Forgetting manifests in research fields such as generative models due to generator shifts, and federated learning due to heterogeneous data distributions across clients. Addressing forgetting encompasses several challenges, including balancing the retention of old task knowledge with fast learning of new tasks, managing task interference with conflicting goals, and preventing privacy leakage, etc. Moreover, most existing surveys on continual learning implicitly assume that forgetting is always harmful. In contrast, our survey argues that forgetting is a double-edged sword and can be beneficial and desirable in certain cases, such as privacy-preserving scenarios. By exploring forgetting in a broader context, we aim to present a more nuanced understanding of this phenomenon and highlight its potential advantages. Through this comprehensive survey, we aspire to uncover potential solutions by drawing upon ideas and approaches from various fields that have dealt with forgetting. By examining forgetting beyond its conventional boundaries, in future work, we hope to encourage the development of novel strategies for mitigating, harnessing, or even embracing forgetting in real applications. A comprehensive list of papers about forgetting in various research fields is available at \url{https://github.com/EnnengYang/Awesome-Forgetting-in-Deep-Learning}.

In electromagnetic inverse scattering, the goal is to reconstruct object permittivity using scattered waves. While deep learning has shown promise as an alternative to iterative solvers, it is primarily used in supervised frameworks which are sensitive to distribution drift of the scattered fields, common in practice. Moreover, these methods typically provide a single estimate of the permittivity pattern, which may be inadequate or misleading due to noise and the ill-posedness of the problem. In this paper, we propose a data-driven framework for inverse scattering based on deep generative models. Our approach learns a low-dimensional manifold as a regularizer for recovering target permittivities. Unlike supervised methods that necessitate both scattered fields and target permittivities, our method only requires the target permittivities for training; it can then be used with any experimental setup. We also introduce a Bayesian framework for approximating the posterior distribution of the target permittivity, enabling multiple estimates and uncertainty quantification. Extensive experiments with synthetic and experimental data demonstrate that our framework outperforms traditional iterative solvers, particularly for strong scatterers, while achieving comparable reconstruction quality to state-of-the-art supervised learning methods like the U-Net.

This problem is of scientific and practical relevance since event data is common in many real-world scenarios and sparks interest in many fields including medicine, epidemiology, engineering, earth science, economics, finance, and social science. In medicine, events can represent various situations, such as incidents, test results, diagnoses and symptoms, and medications. The advent of wearable devices and apps also allows tracking human activities, such as eating, working, sleeping, traveling, etc. Events also characterize movement patterns such as trajectories or taxi/car/public transportation adoptions. In engineering, events can represent phenomena occurring in complex environments, such as failures occurring in industrial processes. In earth science, monitoring and modeling phenomena such as volcano eruptions, seismic events, or floods are of crucial importance.

Robot learning is often difficult due to the expense of gathering data. The need for large amounts of data can, and should, be tackled with effective algorithms and leveraging expert information on robot dynamics. Bayesian reinforcement learning (BRL), thanks to its sample efficiency and ability to exploit prior knowledge, is uniquely positioned as such a solution method. Unfortunately, the application of BRL has been limited due to the difficulties of representing expert knowledge as well as solving the subsequent inference problem. This paper advances BRL for robotics by proposing a specialized framework for physical systems. In particular, we capture this knowledge in a factored representation, then demonstrate the posterior factorizes in a similar shape, and ultimately formalize the model in a Bayesian framework. We then introduce a sample-based online solution method, based on Monte-Carlo tree search and particle filtering, specialized to solve the resulting model. This approach can, for example, utilize typical low-level robot simulators and handle uncertainty over unknown dynamics of the environment. We empirically demonstrate its efficiency by performing on-robot learning in two human-robot interaction tasks with uncertainty about human behavior, achieving near-optimal performance after only a handful of real-world episodes. A video of learned policies is at https://youtu.be/H9xp60ngOes.

Large-dimensional empirical data in science and engineering frequently has low-rank structure and can be represented as a combination of just a few eigenmodes. Because of this structure, we can use just a few spatially localized sensor measurements to reconstruct the full state of a complex system. The quality of this reconstruction, especially in the presence of sensor noise, depends significantly on the spatial configuration of the sensors. Multiple algorithms based on gappy interpolation and QR factorization have been proposed to optimize sensor placement. Here, instead of an algorithm that outputs a singular "optimal" sensor configuration, we take a thermodynamic view to compute the full landscape of sensor interactions induced by the training data. The landscape takes the form of the Ising model in statistical physics, and accounts for both the data variance captured at each sensor location and the crosstalk between sensors. Mapping out these data-induced sensor interactions allows combining them with external selection criteria and anticipating sensor replacement impacts.

The El Niño-Southern Oscillation (ENSO), characterized by anomalous sea surface temperature (SST) in the tropical Pacific, exhibits notable diversity in its temporal evolution and spatial distribution of anomalies. The El Niño events of 1982-83 and 1997-98, for instance, recorded exceptionally high sea surface temperature anomaly (SSTA) values in the eastern equatorial Pacific, whereas the El Niño of 2002-03 were notably less extreme and primarily restricted to the central equatorial Pacific (McPhaden, 2004). Despite each being categorized as an El Niño, the 2002-03 event exhibited global climate conditions distinct from those of the earlier two events. In order to describe these event-to-event differences, El Niño events have been categorized as Eastern Pacific (EP), and Central Pacific (CP) types (Capotondi et al., 2020). EP El Niño events typically have their peak SSTA in the Eastern Pacific, exhibit stronger intensities, and a largely reduced zonal thermocline slope, resulting in the discharge of warm water from the equatorial thermocline. In contrast, CP events show peak SSTA in the Central Pacific and are comparatively weaker with more limited changes in zonal thermocline slope and reduced warm water discharge (Kug, Jin, and An, 2009; Capotondi, 2013). Despite considerable research, the underlying causes of ENSO diversity remain elusive (Lee and McPhaden, 2010; Capotondi et al., 2015; Capotondi et al., 2020). And while some general circulation models (GCMs) do exhibit ENSO event-to-event differences, their representation of ENSO diversity appears to be model dependent and is often different in intensity, pattern and duration than observed (Cai et al., 2018). The different types of ENSO events have substantially different downstream impacts on the global climate and dynamics (Strnad et al., 2022).