We introduce a principled study on establishing Gaussian processes (GPs) with inputs on the product of directional manifolds. A circular kernel is first presented according to the von Mises distribution. Based thereon, the so-called hypertoroidal von Mises (HvM) kernel is proposed to establish GPs on hypertori with consideration of correlational circular components. The proposed HvM kernel is demonstrated with multi-output GP regression for learning vector-valued functions defined on hypertori using the intrinsic coregionalization model. Analytical derivatives in hyperparameter optimization are provided for runtime-critical applications. For evaluation, we synthesize a ranging-based sensor network and employ the HvM-based GPs for data-driven recursive localization. The numerical results show that the HvM-based GP achieves superior tracking accuracy compared to parametric model and GPs based on conventional kernel designs.

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.

To cope with real-world dynamics, an intelligent agent needs to incrementally acquire, update, accumulate, and exploit knowledge throughout its lifetime. This ability, known as continual learning, provides a foundation for AI systems to develop themselves adaptively. In a general sense, continual learning is explicitly limited by catastrophic forgetting, where learning a new task usually results in a dramatic performance degradation of the old tasks. Beyond this, increasingly numerous advances have emerged in recent years that largely extend the understanding and application of continual learning. The growing and widespread interest in this direction demonstrates its realistic significance as well as complexity. In this work, we present a comprehensive survey of continual learning, seeking to bridge the basic settings, theoretical foundations, representative methods, and practical applications. Based on existing theoretical and empirical results, we summarize the general objectives of continual learning as ensuring a proper stability-plasticity trade-off and an adequate intra/inter-task generalizability in the context of resource efficiency. Then we provide a state-of-the-art and elaborated taxonomy, extensively analyzing how representative strategies address continual learning, and how they are adapted to particular challenges in various applications. Through an in-depth discussion of promising directions, we believe that such a holistic perspective can greatly facilitate subsequent exploration in this field and beyond.

Conducting valid statistical analyses is challenging in the presence of missing-not-at-random (MNAR) data, where the missingness mechanism is dependent on the missing values themselves even conditioned on the observed data. Here, we consider a MNAR model that generalizes several prior popular MNAR models in two ways: first, it is less restrictive in terms of statistical independence assumptions imposed on the underlying joint data distribution, and second, it allows for all variables in the observed sample to have missing values. This MNAR model corresponds to a so-called criss-cross structure considered in the literature on graphical models of missing data that prevents nonparametric identification of the entire missing data model. Nonetheless, part of the complete-data distribution remains nonparametrically identifiable. By exploiting this fact and considering a rich class of exponential family distributions, we establish sufficient conditions for identification of the complete-data distribution as well as the entire missingness mechanism. We then propose methods for testing the independence restrictions encoded in such models using odds ratio as our parameter of interest. We adopt two semiparametric approaches for estimating the odds ratio parameter and establish the corresponding asymptotic theories: one involves maximizing a conditional likelihood with order statistics and the other uses estimating equations. The utility of our methods is illustrated via simulation studies.

Imitation learning (IL) has proven to be an effective method for learning good policies from expert demonstrations. Adversarial imitation learning (AIL), a subset of IL methods, is particularly promising, but its theoretical foundation in the presence of unknown transitions has yet to be fully developed. This paper explores the theoretical underpinnings of AIL in this context, where the stochastic and uncertain nature of environment transitions presents a challenge. We examine the expert sample complexity and interaction complexity required to recover good policies. To this end, we establish a framework connecting reward-free exploration and AIL, and propose an algorithm, MB-TAIL, that achieves the minimax optimal expert sample complexity of $\widetilde{O} (H^{3/2} |S|/\varepsilon)$ and interaction complexity of $\widetilde{O} (H^{3} |S|^2 |A|/\varepsilon^2)$. Here, $H$ represents the planning horizon, $|S|$ is the state space size, $|A|$ is the action space size, and $\varepsilon$ is the desired imitation gap. MB-TAIL is the first algorithm to achieve this level of expert sample complexity in the unknown transition setting and improves upon the interaction complexity of the best-known algorithm, OAL, by $O(H)$. Additionally, we demonstrate the generalization ability of MB-TAIL by extending it to the function approximation setting and proving that it can achieve expert sample and interaction complexity independent of $|S|$

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.

Models for human choice prediction in preference learning and psychophysics often consider only binary response data, requiring many samples to accurately learn preferences or perceptual detection thresholds. The response time (RT) to make each choice captures additional information about the decision process, however existing models incorporating RTs for choice prediction do so in fully parametric settings or over discrete stimulus sets. This is in part because the de-facto standard model for choice RTs, the diffusion decision model (DDM), does not admit tractable, differentiable inference. The DDM thus cannot be easily integrated with flexible models for continuous, multivariate function approximation, particularly Gaussian process (GP) models. We propose a novel differentiable approximation to the DDM likelihood using a family of known, skewed three-parameter distributions. We then use this new likelihood to incorporate RTs into GP models for binary choices. Our RT-choice GPs enable both better latent value estimation and held-out choice prediction relative to baselines, which we demonstrate on three real-world multivariate datasets covering both human psychophysics and preference learning applications.

This study aims to investigate the utilization of Bayesian techniques for the calibration of micro-electro-mechanical systems (MEMS) accelerometers. These devices have garnered substantial interest in various practical applications and typically require calibration through error-correcting functions. The parameters of these error-correcting functions are determined during a calibration process. However, due to various sources of noise, these parameters cannot be determined with precision, making it desirable to incorporate uncertainty in the calibration models. Bayesian modeling offers a natural and complete way of reflecting uncertainty by treating the model parameters as variables rather than fixed values. Additionally, Bayesian modeling enables the incorporation of prior knowledge, making it an ideal choice for calibration. Nevertheless, it is infrequently used in sensor calibration. This study introduces Bayesian methods for the calibration of MEMS accelerometer data in a straightforward manner using recent advances in probabilistic programming.

In the field of behavior-related brain computation, it is necessary to meaningfully align raw neural population activities against the drastic shift between them. However, the alignment is non-trivial since most neural population activities are in a multivariate time-series manner. An instrumental framework within neuroscience research posits that trial-based neural population activities rely on low-dimensional latent dynamics. Focusing on such latent dynamics greatly facilitates the alignment procedure. Despite the considerable progress we have reached, existing methods usually ignore the intrinsic spatio-temporal structures within latent dynamics. Thus, those solutions lead to poor quality in dynamics structures and overall performance after alignment. To tackle this problem, we propose a method leveraging the expressiveness of diffusion model to relieve such issues. Specifically, the latent dynamics structures of the source domain are first extracted by the diffusion model. Then, such structures are well-recovered through a maximum likelihood alignment procedure on the target domain. We first demonstrate the effectiveness of our proposed method on a synthetic dataset. Then, when applied to neural recordings from primate motor cortex, under both cross-day and inter-subject settings, our method consistently manifests its capability of preserving the spatio-temporal structure of latent dynamics and outperforms existing approaches in alignment quality.