Training a classifier exploiting a huge amount of supervised data is expensive or even prohibited in a situation, where the labeling cost is high. The remarkable progress in working with weaker forms of supervision is binary classification from multiple unlabeled datasets which requires the knowledge of exact class priors for all unlabeled datasets. However, the availability of class priors is restrictive in many real-world scenarios. To address this issue, we propose to solve a new problem setting, i.e., binary classification from multiple unlabeled datasets with only one pairwise numerical relationship of class priors (MU-OPPO), which knows the relative order (which unlabeled dataset has a higher proportion of positive examples) of two class-prior probabilities for two datasets among multiple unlabeled datasets. In MU-OPPO, we do not need the class priors for all unlabeled datasets, but we only require that there exists a pair of unlabeled datasets for which we know which unlabeled dataset has a larger class prior. Clearly, this form of supervision is easier to be obtained, which can make labeling costs almost free. We propose a novel framework to handle the MU-OPPO problem, which consists of four sequential modules: (i) pseudo label assignment; (ii) confident example collection; (iii) class prior estimation; (iv) classifier training with estimated class priors. Theoretically, we analyze the gap between estimated class priors and true class priors under the proposed framework. Empirically, we confirm the superiority of our framework with comprehensive experiments. Experimental results demonstrate that our framework brings smaller estimation errors of class priors and better performance of binary classification.

Probabilistic circuits (PCs) are models that allow exact and tractable probabilistic inference. In contrast to neural networks, they are often assumed to be well-calibrated and robust to out-of-distribution (OOD) data. In this paper, we show that PCs are in fact not robust to OOD data, i.e., they don't know what they don't know. We then show how this challenge can be overcome by model uncertainty quantification. To this end, we propose tractable dropout inference (TDI), an inference procedure to estimate uncertainty by deriving an analytical solution to Monte Carlo dropout (MCD) through variance propagation. Unlike MCD in neural networks, which comes at the cost of multiple network evaluations, TDI provides tractable sampling-free uncertainty estimates in a single forward pass. TDI improves the robustness of PCs to distribution shift and OOD data, demonstrated through a series of experiments evaluating the classification confidence and uncertainty estimates on real-world data.

Autonomous robots need to learn the categories of various places by exploring their environments and interacting with users. However, preparing training datasets with linguistic instructions from users is time-consuming and labor-intensive. Moreover, effective exploration is essential for appropriate concept formation and rapid environmental coverage. To address this issue, we propose an active inference method, referred to as spatial concept formation with information gain-based active exploration (SpCoAE) that combines sequential Bayesian inference using particle filters and information gain-based destination determination in a probabilistic generative model. This study interprets the robot's action as a selection of destinations to ask the user, `What kind of place is this?' in the context of active inference. This study provides insights into the technical aspects of the proposed method, including active perception and exploration by the robot, and how the method can enable mobile robots to learn spatial concepts through active exploration. Our experiment demonstrated the effectiveness of the SpCoAE in efficiently determining a destination for learning appropriate spatial concepts in home environments.

Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in their structure. However, compute required to infer these structures is typically super-exponential in the number of variables, as inference requires a sweep of a combinatorially large space of potential structures. That is, until recent advances made it possible to search this space using a differentiable metric, drastically reducing search time. While this technique -- named NOTEARS -- is widely considered a seminal work in DAG-discovery, it concedes an important property in favour of differentiability: transportability. To be transportable, the structures discovered on one dataset must apply to another dataset from the same domain. We introduce D-Struct which recovers transportability in the discovered structures through a novel architecture and loss function while remaining fully differentiable. Because D-Struct remains differentiable, our method can be easily adopted in existing differentiable architectures, as was previously done with NOTEARS. In our experiments, we empirically validate D-Struct with respect to edge accuracy and structural Hamming distance in a variety of settings.

We develop a principled approach to end-to-end learning in stochastic optimization. First, we show that the standard end-to-end learning algorithm admits a Bayesian interpretation and trains a posterior Bayes action map. Building on the insights of this analysis, we then propose new end-to-end learning algorithms for training decision maps that output solutions of empirical risk minimization and distributionally robust optimization problems, two dominant modeling paradigms in optimization under uncertainty. Numerical results for a synthetic newsvendor problem illustrate the key differences between alternative training schemes. We also investigate an economic dispatch problem based on real data to showcase the impact of the neural network architecture of the decision maps on their test performance.

This paper introduces a statistical model and corresponding sequential Bayesian estimation method for terrain-based navigation using side-scan sonar (SSS) data. The presented approach relies on slant range measurements extracted from the received ping of a SSS. In particular, incorporating slant range measurements to landmarks for navigation constrains the location and altitude error of an autonomous platform in GPS-denied environments. The proposed navigation filter consists of a prediction step based on the unscented transform and an update step that relies on particle filtering. The SSS measurement model aims to capture the highly nonlinear nature of SSS data while maintaining reasonable computational requirements in the particle-based update step. For our numerical results, we assume a scenario with a surface vehicle that performs SSS and compass measurements. The simulated scenario is consistent with our current hardware platform. We also discuss how the proposed method can be extended to autonomous underwater vehicles (AUVs) in a straightforward way and why the combination of SSS sensor and compass is particularly suitable for small autonomous platforms.

Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial heterogeneity and dependence. However, implementations of doubly-stochastic spatial models are computationally demanding, often have limited theoretical guarantee, and/or rely on restrictive assumptions. We propose a penalized regression method for estimating covariate effects in doubly-stochastic point processes that is computationally efficient and does not require a parametric form or stationarity of the underlying intensity. We establish the consistency and asymptotic normality of the proposed estimator, and develop a covariance estimator that leads to a conservative statistical inference procedure. A simulation study shows the validity of our approach under less restrictive assumptions on the data generating mechanism, and an application to Seattle crime data demonstrates better prediction accuracy compared with existing alternatives.

We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent flexible preference structure, is that the posterior distribution is a computationally intractable skew GP. The most widely used approach for preferential BO is Gaussian approximation, which ignores the skewness of the true posterior. Alternatively, Markov chain Monte Carlo (MCMC) based preferential BO is also proposed. In this work, we first verify the accuracy of Gaussian approximation, from which we reveal the critical problem that the predictive probability of duels can be inaccurate. This observation motivates us to improve the MCMC-based estimation for skew GP, for which we show the practical efficiency of Gibbs sampling and derive the low variance MC estimator. However, the computational time of MCMC can still be a bottleneck in practice. Towards building a more practical preferential BO, we develop a new method that achieves both high computational efficiency and low sample complexity, and then demonstrate its effectiveness through extensive numerical experiments.

This work deals with the heterogeneous semantic-native communication (SNC) problem. When agents do not share the same communication context, the effectiveness of contextual reasoning (CR) is compromised calling for agents to infer other agents' context. This article proposes a novel framework for solving the inverse problem of CR in SNC using two Bayesian inference methods, namely: Bayesian inverse CR (iCR) and Bayesian inverse linearized CR (iLCR). The first proposed Bayesian iCR method utilizes Markov Chain Monte Carlo (MCMC) sampling to infer the agent's context while being computationally expensive. To address this issue, a Bayesian iLCR method is leveraged which obtains a linearized CR (LCR) model by training a linear neural network. Experimental results show that the Bayesian iLCR method requires less computation and achieves higher inference accuracy compared to Bayesian iCR. Additionally, heterogeneous SNC based on the context obtained through the Bayesian iLCR method shows better communication effectiveness than that of Bayesian iCR. Overall, this work provides valuable insights and methods to improve the effectiveness of SNC in situations where agents have different contexts.

Meta-learning aims to extract useful inductive biases from a set of related datasets. In Bayesian meta-learning, this is typically achieved by constructing a prior distribution over neural network parameters. However, specifying families of computationally viable prior distributions over the high-dimensional neural network parameters is difficult. As a result, existing approaches resort to meta-learning restrictive diagonal Gaussian priors, severely limiting their expressiveness and performance. To circumvent these issues, we approach meta-learning through the lens of functional Bayesian neural network inference, which views the prior as a stochastic process and performs inference in the function space. Specifically, we view the meta-training tasks as samples from the data-generating process and formalize meta-learning as empirically estimating the law of this stochastic process. Our approach can seamlessly acquire and represent complex prior knowledge by meta-learning the score function of the data-generating process marginals instead of parameter space priors. In a comprehensive benchmark, we demonstrate that our method achieves state-of-the-art performance in terms of predictive accuracy and substantial improvements in the quality of uncertainty estimates.