Emulators, or reduced complexity climate models, are surrogate Earth system models that produce projections of key climate quantities with minimal computational resources. Using time-series modeling or more advanced machine learning techniques, data-driven emulators have emerged as a promising avenue of research, producing spatially resolved climate responses that are visually indistinguishable from state-of-the-art Earth system models. Yet, their lack of physical interpretability limits their wider adoption. In this work, we introduce FaIRGP, a data-driven emulator that satisfies the physical temperature response equations of an energy balance model. The result is an emulator that (i) enjoys the flexibility of statistical machine learning models and can learn from observations, and (ii) has a robust physical grounding with interpretable parameters that can be used to make inference about the climate system. Further, our Bayesian approach allows a principled and mathematically tractable uncertainty quantification. Our model demonstrates skillful emulation of global mean surface temperature and spatial surface temperatures across realistic future scenarios. Its ability to learn from data allows it to outperform energy balance models, while its robust physical foundation safeguards against the pitfalls of purely data-driven models. We also illustrate how FaIRGP can be used to obtain estimates of top-of-atmosphere radiative forcing and discuss the benefits of its mathematical tractability for applications such as detection and attribution or precipitation emulation. We hope that this work will contribute to widening the adoption of data-driven methods in climate emulation.

Obesity is a critical healthcare issue affecting the United States. The least risky treatments available for obesity are behavioral interventions meant to promote diet and exercise. Often these interventions contain a mobile component that allows interventionists to collect participants level data and provide participants with incentives and goals to promote long term behavioral change. Recently, there has been interest in using direct financial incentives to promote behavior change. However, adherence is challenging in these interventions, as each participant will react differently to different incentive structure and amounts, leading researchers to consider personalized interventions. The key challenge for personalization, is that the clinicians do not know a priori how best to administer incentives to participants, and given finite intervention budgets how to disburse costly resources efficiently. In this paper, we consider this challenge of designing personalized weight loss interventions that use direct financial incentives to motivate weight loss while remaining within a budget. We create a machine learning approach that is able to predict how individuals may react to different incentive schedules within the context of a behavioral intervention. We use this predictive model in an adaptive framework that over the course of the intervention computes what incentives to disburse to participants and remain within the study budget. We provide both theoretical guarantees for our modeling and optimization approaches as well as demonstrate their performance in a simulated weight loss study. Our results highlight the cost efficiency and effectiveness of our personalized intervention design for weight loss.

The age of social media has opened new opportunities for businesses. This flourishing wealth of information is outside traditional channels and frameworks of classical marketing research, including that of Marketing Mix Modeling (MMM). Textual data, in particular, poses many challenges that data analysis practitioners must tackle. Social media constitute massive, heterogeneous, and noisy document sources. Industrial data acquisition processes include some amount of ETL. However, the variability of noise in the data and the heterogeneity induced by different sources create the need for ad-hoc tools. Put otherwise, customer insight extraction in fully unsupervised, noisy contexts is an arduous task. This research addresses the challenge of fully unsupervised topic extraction in noisy, Big Data contexts. We present three approaches we built on the Variational Autoencoder framework: the Embedded Dirichlet Process, the Embedded Hierarchical Dirichlet Process, and the time-aware Dynamic Embedded Dirichlet Process. These nonparametric approaches concerning topics present the particularity of determining word embeddings and topic embeddings. These embeddings do not require transfer learning, but knowledge transfer remains possible. We test these approaches on benchmark and automotive industry-related datasets from a real-world use case. We show that our models achieve equal to better performance than state-of-the-art methods and that the field of topic modeling would benefit from improved evaluation metrics.

Even though the brain operates in pure darkness, within the skull, it can infer the most likely causes of its sensory input. An approach to modelling this inference is to assume that the brain has a generative model of the world, which it can invert to infer the hidden causes behind its sensory stimuli, that is, perception. This assumption raises key questions: how to formulate the problem of designing brain-inspired generative models, how to invert them for the tasks of inference and learning, what is the appropriate loss function to be optimised, and, most importantly, what are the different choices of mean field approximation (MFA) and their implications for variational inference (VI).

Training energy-based models (EBMs) on discrete spaces is challenging because sampling over such spaces can be difficult. We propose to train discrete EBMs with energy discrepancy (ED), a novel type of contrastive loss functional which only requires the evaluation of the energy function at data points and their perturbed counter parts, thus not relying on sampling strategies like Markov chain Monte Carlo (MCMC). Energy discrepancy offers theoretical guarantees for a broad class of perturbation processes of which we investigate three types: perturbations based on Bernoulli noise, based on deterministic transforms, and based on neighbourhood structures. We demonstrate their relative performance on lattice Ising models, binary synthetic data, and discrete image data sets.

Bayesian inference offers benefits over maximum likelihood, but it also comes with computational costs. Computing the posterior is typically intractable, as is marginalizing that posterior to form the posterior predictive distribution. In this paper, we present variational prediction, a technique for directly learning a variational approximation to the posterior predictive distribution using a variational bound. This approach can provide good predictive distributions without test time marginalization costs. We demonstrate Variational Prediction on an illustrative toy example.

Federated Learning (FL) emerges as a distributed machine learning paradigm without end-user data transmission, effectively avoiding privacy leakage. Participating devices in FL are usually bandwidth-constrained, and the uplink is much slower than the downlink in wireless networks, which causes a severe uplink communication bottleneck. A prominent direction to alleviate this problem is federated dropout, which drops fractional weights of local models. However, existing federated dropout studies focus on random or ordered dropout and lack theoretical support, resulting in unguaranteed performance. In this paper, we propose Federated learning with Bayesian Inference-based Adaptive Dropout (FedBIAD), which regards weight rows of local models as probability distributions and adaptively drops partial weight rows based on importance indicators correlated with the trend of local training loss. By applying FedBIAD, each client adaptively selects a high-quality dropping pattern with accurate approximations and only transmits parameters of non-dropped weight rows to mitigate uplink costs while improving accuracy. Theoretical analysis demonstrates that the convergence rate of the average generalization error of FedBIAD is minimax optimal up to a squared logarithmic factor. Extensive experiments on image classification and next-word prediction show that compared with status quo approaches, FedBIAD provides 2x uplink reduction with an accuracy increase of up to 2.41% even on non-Independent and Identically Distributed (non-IID) data, which brings up to 72% decrease in training time.

Incorporating unstructured data into physical models is a challenging problem that is emerging in data assimilation. Traditional approaches focus on well-defined observation operators whose functional forms are typically assumed to be known. This prevents these methods from achieving a consistent model-data synthesis in configurations where the mapping from data-space to model-space is unknown. To address these shortcomings, in this paper we develop a physics-informed dynamical variational autoencoder ($\Phi$-DVAE) to embed diverse data streams into time-evolving physical systems described by differential equations. Our approach combines a standard, possibly nonlinear, filter for the latent state-space model and a VAE, to assimilate the unstructured data into the latent dynamical system. Unstructured data, in our example systems, comes in the form of video data and velocity field measurements, however the methodology is suitably generic to allow for arbitrary unknown observation operators. A variational Bayesian framework is used for the joint estimation of the encoding, latent states, and unknown system parameters. To demonstrate the method, we provide case studies with the Lorenz-63 ordinary differential equation, and the advection and Korteweg-de Vries partial differential equations. Our results, with synthetic data, show that $\Phi$-DVAE provides a data efficient dynamics encoding methodology which is competitive with standard approaches. Unknown parameters are recovered with uncertainty quantification, and unseen data are accurately predicted.

Despite the existence of numerous designs, significant research efforts, and successful applications in the field of control systems, the development of a reliable and secure controller that combines robust theoretical foundations with exceptional performance continues to present a formidable challenge. This challenge has captured the attention of researchers from diverse fields, including robotics [1] and healthcare [2], among others. In the context of control systems, safety is evaluated based on the system state. In this study, we focus on probabilistic safe control, wherein a safe controller is expected to prevent the system from entering hazardous states with an acceptable probability [3-5]. Due to the intricate nature of calculating the safe state space for a general dynamics-driven system, ensuring safety by designing or learning a safe controller is rather complex. Existing safe control strategies include model predictive control [6], reachability analysis [7], and control barrier function (CBF) method [8]. In our research, we build upon the CBF method, which ensures that the system state remains within safe regions by defining a forward invariant set. This set is a subset of the safe region and restricts the system state within its boundaries. Furthermore, we take into account the presence of uncertainty, which not only have a more significant impact on the system state than small disturbances [9], and does not have an analytical format as well [10].

In their seminal 1990 paper, Wasserman and Kadane establish an upper bound for the Bayes' posterior probability of a measurable set $A$, when the prior lies in a class of probability measures $\mathcal{P}$ and the likelihood is precise. They also give a sufficient condition for such upper bound to hold with equality. In this paper, we introduce a generalization of their result by additionally addressing uncertainty related to the likelihood. We give an upper bound for the posterior probability when both the prior and the likelihood belong to a set of probabilities. Furthermore, we give a sufficient condition for this upper bound to become an equality. This result is interesting on its own, and has the potential of being applied to various fields of engineering (e.g. model predictive control), machine learning, and artificial intelligence.