Our work bridges ABC with deep neural implicit samplers based on generative adversarial networks (GANs) and adversarial variational Bayes. Both ABC and GANs compare aspects of observed and fake data to simulate from posteriors and likelihoods, respectively. We develop a Bayesian GAN (B-GAN) sampler that directly targets the posterior by solving an adversarial optimization problem. B-GAN is driven by a deterministic mapping learned on the ABC reference by conditional GANs. Once the mapping has been trained, iid posterior samples are obtained by filtering noise at a negligible additional cost. We propose two post-processing local refinements using (1) data-driven proposals with importance reweighting, and (2) variational Bayes. We support our findings with frequentist-Bayesian results, showing that the typical total variation distance between the true and approximate posteriors converges to zero for certain neural network generators and discriminators. Our findings on simulated data show highly competitive performance relative to some of the most recent likelihood-free posterior simulators.

This paper presents a substantial extension of our work published at ICLR. Our ICLR work advocated for enhancing transferability in adversarial examples by incorporating a Bayesian formulation into model parameters, which effectively emulates the ensemble of infinitely many deep neural networks, while, in this paper, we introduce a novel extension by incorporating the Bayesian formulation into the model input as well, enabling the joint diversification of both the model input and model parameters. Our empirical findings demonstrate that: 1) the combination of Bayesian formulations for both the model input and model parameters yields significant improvements in transferability; 2) by introducing advanced approximations of the posterior distribution over the model input, adversarial transferability achieves further enhancement, surpassing all state-of-the-arts when attacking without model fine-tuning. Moreover, we propose a principled approach to fine-tune model parameters in such an extended Bayesian formulation. The derived optimization objective inherently encourages flat minima in the parameter space and input space. Extensive experiments demonstrate that our method achieves a new state-of-the-art on transfer-based attacks, improving the average success rate on ImageNet and CIFAR-10 by 19.14% and 2.08%, respectively, when comparing with our ICLR basic Bayesian method. We will make our code publicly available.

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent progress in designing fast samplers for DPMs achieves a trade-off between sampling speed and sample quality by knowledge distillation or adjusting the variance schedule or the denoising equation. However, it can't be optimal in both aspects and often suffer from mode mixture in short steps. To tackle this problem, we innovatively regard inverse diffusion as an optimal transport (OT) problem between latents at different stages and propose the DPM-OT, a unified learning framework for fast DPMs with a direct expressway represented by OT map, which can generate high-quality samples within around 10 function evaluations. By calculating the semi-discrete optimal transport map between the data latents and the white noise, we obtain an expressway from the prior distribution to the data distribution, while significantly alleviating the problem of mode mixture. In addition, we give the error bound of the proposed method, which theoretically guarantees the stability of the algorithm. Extensive experiments validate the effectiveness and advantages of DPM-OT in terms of speed and quality (FID and mode mixture), thus representing an efficient solution for generative modeling. Source codes are available at https://github.com/cognaclee/DPM-OT

How should my own decisions affect my beliefs about the outcomes I expect to achieve? If taking a certain action makes me view myself as a certain type of person, it might affect how I think others view me, and how I view others who are similar to me. This can influence my expected utility calculations and change which action I perceive to be best. Whether and how it should is subject to debate, with contenders for how to think about it including evidential decision theory, causal decision theory, and functional decision theory. In this paper, we show that mechanised causal models can be used to characterise and differentiate the most important decision theories, and generate a taxonomy of different decision theories.

The aggregation of multiple opinions plays a crucial role in decision-making, such as in hiring and loan review, and in labeling data for supervised learning. Although majority voting and existing opinion aggregation models are effective for simple tasks, they are inappropriate for tasks without objectively true labels in which disagreements may occur. In particular, when voter attributes such as gender or race introduce bias into opinions, the aggregation results may vary depending on the composition of voter attributes. A balanced group of voters is desirable for fair aggregation results but may be difficult to prepare. In this study, we consider methods to achieve fair opinion aggregation based on voter attributes and evaluate the fairness of the aggregated results. To this end, we consider an approach that combines opinion aggregation models such as majority voting and the Dawid and Skene model (D&S model) with fairness options such as sample weighting. To evaluate the fairness of opinion aggregation, probabilistic soft labels are preferred over discrete class labels. First, we address the problem of soft label estimation without considering voter attributes and identify some issues with the D&S model. To address these limitations, we propose a new Soft D&S model with improved accuracy in estimating soft labels. Moreover, we evaluated the fairness of an opinion aggregation model, including Soft D&S, in combination with different fairness options using synthetic and semi-synthetic data. The experimental results suggest that the combination of Soft D&S and data splitting as a fairness option is effective for dense data, whereas weighted majority voting is effective for sparse data. These findings should prove particularly valuable in supporting decision-making by human and machine-learning models with balanced opinion aggregation.

We present a new framework called KorraAI for conceiving and building embodied conversational agents (ECAs). Our framework models ECAs' behavior considering contextual information, for example, about environment and interaction time, and uncertain information provided by the human interaction partner. Moreover, agents built with KorraAI can show proactive behavior, as they can initiate interactions with human partners. For these purposes, KorraAI exploits probabilistic programming. Probabilistic models in KorraAI are used to model its behavior and interactions with the user. They enable adaptation to the user's preferences and a certain degree of indeterminism in the ECAs to achieve more natural behavior. Human-like internal states, such as moods, preferences, and emotions (e.g., surprise), can be modeled in KorraAI with distributions and Bayesian networks. These models can evolve over time, even without interaction with the user. ECA models are implemented as plugins and share a common interface. This enables ECA designers to focus more on the character they are modeling and less on the technical details, as well as to store and exchange ECA models. Several applications of KorraAI ECAs are possible, such as virtual sales agents, customer service agents, virtual companions, entertainers, or tutors.

Abstract--With the emergence of new application areas, such as cyber-physical systems and human-in-the-loop applications, there is a need to guarantee a certain level of end-to-end network latency with extremely high reliability, e.g., 99.999%. While mechanisms specified under IEEE 802.1as time-sensitive networking (TSN) can be used to achieve these requirements for switched Ethernet networks, implementing TSN mechanisms in wireless networks is challenging due to their stochastic nature. To conform the wireless link to a reliability level of 99.999%, the behavior of extremely rare outliers in the latency probability distribution, or the tail of the distribution, must be analyzed and controlled. This work proposes predicting the tail of the latency distribution using state-of-the-art data-driven approaches, such as mixture density networks (MDN) and extreme value mixture models, to estimate the likelihood of rare latencies conditioned on the network parameters, which can be used to make more informed decisions in wireless transmission. Actual latency measurements of IEEE 802.11g (WiFi), commercial private and a software-defined 5G network are used to benchmark the proposed approaches and evaluate their sensitivities concerning the tail probabilities.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be computed piecewise in terms of the component processes. We study the structure of this compositional rule, noting that it relates to the lens pattern in functional programming. Working in a suitably general axiomatic presentation of a category of Markov kernels, we see how we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a fibred category. We discuss the compositional nature of this, formulated as a functor on the underlying category and explore how this can used for a more type-driven approach to statistical inference.

The motion objectives of a planning as inference problem are formulated as a joint distribution over coupled random variables on a factor graph. Leveraging optimization-inference duality, a fast solution to the maximum a posteriori estimation of the factor graph can be obtained via least-squares optimization. The computational efficiency of this approach can be used in competitive autonomous racing for finding the minimum curvature raceline. Finding the raceline is classified as a global planning problem that entails the computation of a minimum curvature path for a racecar which offers highest cornering speed for a given racetrack resulting in reduced lap time. This work introduces a novel methodology for formulating the minimum curvature raceline planning problem as probabilistic inference on a factor graph. By exploiting the tangential geometry and structural properties inherent in the minimum curvature planning problem, we represent it on a factor graph, which is subsequently solved via sparse least-squares optimization. The results obtained by performing comparative analysis with the quadratic programming-based methodology, the proposed approach demonstrated the superior computing performance, as it provides comparable lap time reduction while achieving fourfold improvement in computational efficiency.

We propose a novel Bayesian-Optimistic Frequentist Upper Confidence Bound (BOF-UCB) algorithm for stochastic contextual linear bandits in non-stationary environments. This unique combination of Bayesian and frequentist principles enhances adaptability and performance in dynamic settings. The BOF-UCB algorithm utilizes sequential Bayesian updates to infer the posterior distribution of the unknown regression parameter, and subsequently employs a frequentist approach to compute the Upper Confidence Bound (UCB) by maximizing the expected reward over the posterior distribution. We provide theoretical guarantees of BOF-UCB's performance and demonstrate its effectiveness in balancing exploration and exploitation on synthetic datasets and classical control tasks in a reinforcement learning setting. Our results show that BOF-UCB outperforms existing methods, making it a promising solution for sequential decision-making in non-stationary environments.