If two agents disagree in their decisions, we may suspect they are not both correct. This intuition is formalized for evaluating agents that have carried out a binary classification task. Their agreements and disagreements on a joint test allow us to establish the only group evaluations logically consistent with their responses. This is done by establishing a set of axioms (algebraic relations) that must be universally obeyed by all evaluations of binary responders. A complete set of such axioms are possible for each ensemble of size N. The axioms for $N = 1, 2$ are used to construct a fully logical alarm - one that can prove that at least one ensemble member is malfunctioning using only unlabeled data. The similarities of this approach to formal software verification and its utility for recent agendas of safe guaranteed AI are discussed.

We study supervised classification for datasets with a very large number of input variables. The na\"ive Bayes classifier is attractive for its simplicity, scalability and effectiveness in many real data applications. When the strong na\"ive Bayes assumption of conditional independence of the input variables given the target variable is not valid, variable selection and model averaging are two common ways to improve the performance. In the case of the na\"ive Bayes classifier, the resulting weighting scheme on the models reduces to a weighting scheme on the variables. Here we focus on direct estimation of variable weights in such a weighted na\"ive Bayes classifier. We propose a sparse regularization of the model log-likelihood, which takes into account prior penalization costs related to each input variable. Compared to averaging based classifiers used up until now, our main goal is to obtain parsimonious robust models with less variables and equivalent performance. The direct estimation of the variable weights amounts to a non-convex optimization problem for which we propose and compare several two-stage algorithms. First, the criterion obtained by convex relaxation is minimized using several variants of standard gradient methods. Then, the initial non-convex optimization problem is solved using local optimization methods initialized with the result of the first stage. The various proposed algorithms result in optimization-based weighted na\"ive Bayes classifiers, that are evaluated on benchmark datasets and positioned w.r.t. to a reference averaging-based classifier.

Image-goal navigation enables a robot to reach the location where a target image was captured, using visual cues for guidance. However, current methods either rely heavily on data and computationally expensive learning-based approaches or lack efficiency in complex environments due to insufficient exploration strategies. To address these limitations, we propose Bayesian Embodied Image-goal Navigation Using Gaussian Splatting, a novel method that formulates ImageNav as an optimal control problem within a model predictive control framework. BEINGS leverages 3D Gaussian Splatting as a scene prior to predict future observations, enabling efficient, real-time navigation decisions grounded in the robot's sensory experiences. By integrating Bayesian updates, our method dynamically refines the robot's strategy without requiring extensive prior experience or data. Our algorithm is validated through extensive simulations and physical experiments, showcasing its potential for embodied robot systems in visually complex scenarios.

This paper presents P2U-SLAM, a visual Simultaneous Localization And Mapping (SLAM) system with a wide Field of View (FoV) camera, which utilizes pose uncertainty and point uncertainty. While the wide FoV enables considerable repetitive observations of historical map points for matching cross-view features, the data properties of the historical map points and the poses of historical keyframes have changed during the optimization process. The neglect of data property changes triggers the absence of a partial information matrix in optimization and leads to the risk of long-term positioning performance degradation. The purpose of our research is to reduce the risk of the wide field of view visual input to the SLAM system. Based on the conditional probability model, this work reveals the definite impact of the above data properties changes on the optimization process, concretizes it as point uncertainty and pose uncertainty, and gives a specific mathematical form. P2U-SLAM respectively embeds point uncertainty and pose uncertainty into the tracking module and local mapping, and updates these uncertainties after each optimization operation including local mapping, map merging, and loop closing. We present an exhaustive evaluation in 27 sequences from two popular public datasets with wide-FoV visual input. P2U-SLAM shows excellent performance compared with other state-of-the-art methods. The source code will be made publicly available at https://github.com/BambValley/P2U-SLAM.

AI fairness measurements, including tests for equal treatment, often take the form of disaggregated evaluations of AI systems. Such measurements are an important part of Responsible AI operations. These measurements compare system performance across demographic groups or sub-populations and typically require member-level demographic signals such as gender, race, ethnicity, and location. However, sensitive member-level demographic attributes like race and ethnicity can be challenging to obtain and use due to platform choices, legal constraints, and cultural norms. In this paper, we focus on the task of enabling AI fairness measurements on race/ethnicity for \emph{U.S. LinkedIn members} in a privacy-preserving manner. We present the Privacy-Preserving Probabilistic Race/Ethnicity Estimation (PPRE) method for performing this task. PPRE combines the Bayesian Improved Surname Geocoding (BISG) model, a sparse LinkedIn survey sample of self-reported demographics, and privacy-enhancing technologies like secure two-party computation and differential privacy to enable meaningful fairness measurements while preserving member privacy. We provide details of the PPRE method and its privacy guarantees. We then illustrate sample measurement operations. We conclude with a review of open research and engineering challenges for expanding our privacy-preserving fairness measurement capabilities.

We are motivated primarily by the adaptation of text-to-speech synthesis models; however we argue that more generic parameter-efficient fine-tuning (PEFT) is an appropriate framework to do such adaptation. Nevertheless, catastrophic forgetting remains an issue with PEFT, damaging the pre-trained model's inherent capabilities. We demonstrate that existing Bayesian learning techniques can be applied to PEFT to prevent catastrophic forgetting as long as the parameter shift of the fine-tuned layers can be calculated differentiably. In a principled series of experiments on language modeling and speech synthesis tasks, we utilize established Laplace approximations, including diagonal and Kronecker-factored approaches, to regularize PEFT with the low-rank adaptation (LoRA) and compare their performance in pre-training knowledge preservation. Our results demonstrate that catastrophic forgetting can be overcome by our methods without degrading the fine-tuning performance, and using the Kronecker-factored approximation produces a better preservation of the pre-training knowledge than the diagonal ones.

Recent advancements in unsupervised domain adaptation (UDA) and semi-supervised learning (SSL), particularly incorporating causality, have led to significant methodological improvements in these learning problems. However, a formal theory that explains the role of causality in the generalization performance of UDA/SSL is still lacking. In this paper, we consider the UDA/SSL scenarios where we access $m$ labelled source data and $n$ unlabelled target data as training instances under different causal settings with a parametric probabilistic model. We study the learning performance (e.g., excess risk) of prediction in the target domain from an information-theoretic perspective. Specifically, we distinguish two scenarios: the learning problem is called causal learning if the feature is the cause and the label is the effect, and is called anti-causal learning otherwise. We show that in causal learning, the excess risk depends on the size of the source sample at a rate of $O(\frac{1}{m})$ only if the labelling distribution between the source and target domains remains unchanged. In anti-causal learning, we show that the unlabelled data dominate the performance at a rate of typically $O(\frac{1}{n})$. These results bring out the relationship between the data sample size and the hardness of the learning problem with different causal mechanisms.

The interplay between stochastic processes and optimal control has been extensively explored in the literature. With the recent surge in the use of diffusion models, stochastic processes have increasingly been applied to sample generation. This paper builds on the log transform, known as the Cole-Hopf transform in Brownian motion contexts, and extends it within a more abstract framework that includes a linear operator. Within this framework, we found that the well-known relationship between the Cole-Hopf transform and optimal transport is a particular instance where the linear operator acts as the infinitesimal generator of a stochastic process. We also introduce a novel scenario where the linear operator is the adjoint of the generator, linking to Bayesian inference under specific initial and terminal conditions. Leveraging this theoretical foundation, we develop a new algorithm, named the HJ-sampler, for Bayesian inference for the inverse problem of a stochastic differential equation with given terminal observations. The HJ-sampler involves two stages: (1) solving the viscous Hamilton-Jacobi partial differential equations, and (2) sampling from the associated stochastic optimal control problem. Our proposed algorithm naturally allows for flexibility in selecting the numerical solver for viscous HJ PDEs. We introduce two variants of the solver: the Riccati-HJ-sampler, based on the Riccati method, and the SGM-HJ-sampler, which utilizes diffusion models. We demonstrate the effectiveness and flexibility of the proposed methods by applying them to solve Bayesian inverse problems involving various stochastic processes and prior distributions, including applications that address model misspecifications and quantifying model uncertainty.

Nonreciprocal thermal emitters that break Kirchhoff's law of thermal radiation promise exciting applications for thermal and energy applications. The design of the bandwidth and angular range of the nonreciprocal effect, which directly affects the performance of nonreciprocal emitters, typically relies on physical intuition. In this study, we present a general numerical approach to maximize the nonreciprocal effect. We choose doped magneto-optic materials and magnetic Weyl semimetal materials as model materials and focus on pattern-free multilayer structures. The optimization randomly starts from a less effective structure and incrementally improves the broadband nonreciprocity through the combination of Bayesian optimization and reparameterization. Optimization results show that the proposed approach can discover structures that can achieve broadband nonreciprocal emission at wavelengths from 5 to 40 micrometers using only a fewer layers, significantly outperforming current state-of-the-art designs based on intuition in terms of both performance and simplicity.

As humans can explore and understand the world through the sense of touch, tactile sensing is also an important aspect of robotic perception. In unstructured environments, robots can encounter both known and novel objects, this calls for a method to address both known and novel objects. In this study, we combine a particle filter (PF) and Gaussian process implicit surface (GPIS) in a unified Bayesian framework. The framework can differentiate between known and novel objects, perform object recognition, estimate pose for known objects, and reconstruct shapes for unknown objects, in an active learning fashion. By grounding the selection of the GPIS prior with the maximum-likelihood-estimation (MLE) shape from the PF, the knowledge about known objects' shapes can be transferred to learn novel shapes. An exploration procedure with global shape estimation is proposed to guide active data acquisition and conclude the exploration when sufficient information is obtained. The performance of the proposed Bayesian framework is evaluated through simulations on known and novel objects, initialized with random poses. The results show that the proposed exploration procedure, utilizing global shape estimation, achieves faster exploration than a local exploration procedure based on rapidly explore random tree (RRT). Overall, our results indicate that the proposed framework is effective and efficient in object recognition, pose estimation and shape reconstruction. Moreover, we show that a learned shape can be included as a new prior and used effectively for future object recognition and pose estimation.