Kernelized Stein discrepancy (KSD) is a score-based discrepancy widely used in goodness-of-fit tests. It can be applied even when the target distribution has an unknown normalising factor, such as in Bayesian analysis. We show theoretically and empirically that the KSD test can suffer from low power when the target and the alternative distributions have the same well-separated modes but differ in mixing proportions. We propose to perturb the observed sample via Markov transition kernels, with respect to which the target distribution is invariant. This allows us to then employ the KSD test on the perturbed sample. We provide numerical evidence that with suitably chosen transition kernels the proposed approach can lead to substantially higher power than the KSD test.

Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty in the parameter values, functional forms with diverse parameterizations, level of complexity needed, and thus in the state fields. We develop a Bayesian model learning methodology that allows interpolation in the space of candidate models and discovery of new models from noisy, sparse, and indirect observations, all while estimating state fields and parameter values, as well as the joint PDFs of all learned quantities. We address the challenges of high-dimensional and multidisciplinary dynamics governed by PDEs by using state augmentation and the computationally efficient GMM-DO filter. Our innovations include stochastic formulation and complexity parameters to unify candidate models into a single general model as well as stochastic expansion parameters within piecewise function approximations to generate dense candidate model spaces. These innovations allow handling many compatible and embedded candidate models, possibly none of which are accurate, and learning elusive unknown functional forms. Our new methodology is generalizable, interpretable, and extrapolates out of the space of models to discover new ones. We perform a series of twin experiments based on flows past a ridge coupled with three-to-five component ecosystem models, including flows with chaotic advection. The probabilities of known, uncertain, and unknown model formulations, and of state fields and parameters, are updated jointly using Bayes' law. Non-Gaussian statistics, ambiguity, and biases are captured. The parameter values and model formulations that best explain the data are identified. When observations are sufficiently informative, model complexity and functions are discovered.

Understanding the gradient variance of blackbox Despite the advances of BBVI, little is known about its theoretical variational inference (BBVI) is a crucial step properties. Even when restricted to the locationscale for establishing its convergence and developing family (Definition 2), it is unknown whether BBVI algorithmic improvements. However, existing is guaranteed to converge without having to modify the studies have yet to show that the gradient variance algorithms used in practice, for example, by enforcing of BBVI satisfies the conditions used to bounded domains, bounded support, bounded gradients, study the convergence of stochastic gradient descent and such. This theoretical insight is necessary since BBVI (SGD), the workhorse of BBVI. In this methods are known to be less robust (Yao et al., 2018; work, we show that BBVI satisfies a matching Dhaka et al., 2020; Welandawe et al., 2022; Dhaka et al., bound corresponding to the condition used 2021; Domke, 2020) compared to other inference methods in the SGD literature when applied to smooth and such as Markov chain Monte Carlo. Although progress has quadratically-growing log-likelihoods. Our results been made to formalize the theory of BBVI with some generality, generalize to nonlinear covariance parameterizations the gap between our understanding of BBVI and the widely used in the practice of BBVI.

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable the seamless fusion of different experimental modalities. When the dynamics are discrete and stochastic, one may employ powerful techniques such as Kalman, particle, or variational filters. Practitioners commonly apply these methods to continuous-time, deterministic dynamical systems after discretizing the dynamics and introducing fictitious transition probabilities. However, approaches based on time-discretization suffer from the curse of dimensionality since the number of random variables grows linearly with the number of time-steps. Furthermore, the introduction of fictitious transition probabilities is an unsatisfactory solution because it increases the number of model parameters and may lead to inference bias. To address these drawbacks, the objective of this paper is to develop a scalable Bayesian approach to state and parameter estimation suitable for continuous-time, deterministic dynamical systems. Our methodology builds upon information field theory. Specifically, we construct a physics-informed prior probability measure on the function space of system responses so that functions that satisfy the physics are more likely. This prior allows us to quantify model form errors. We connect the system's response to observations through a probabilistic model of the measurement process. The joint posterior over the system responses and all parameters is given by Bayes' rule. To approximate the intractable posterior, we develop a stochastic variational inference algorithm. In summary, the developed methodology offers a powerful framework for Bayesian estimation in dynamical systems.

Message passing on factor graphs is a powerful framework for probabilistic inference, which finds important applications in various scientific domains. The most wide-spread message passing scheme is the sum-product algorithm (SPA) which gives exact results on trees but often fails on graphs with many small cycles. We search for an alternative message passing algorithm that works particularly well on such cyclic graphs. Therefore, we challenge the extrinsic principle of the SPA, which loses its objective on graphs with cycles. We further replace the local SPA message update rule at the factor nodes of the underlying graph with a generic mapping, which is optimized in a data-driven fashion. These modifications lead to a considerable improvement in performance while preserving the simplicity of the SPA. We evaluate our method for two classes of cyclic graphs: the 2x2 fully connected Ising grid and factor graphs for symbol detection on linear communication channels with inter-symbol interference. To enable the method for large graphs as they occur in practical applications, we develop a novel loss function that is inspired by the Bethe approximation from statistical physics and allows for training in an unsupervised fashion.

Measurement error occurs when a set of covariates influencing a response variable are corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and response variables is crucial, such as causal effect estimation. Existing methods for dealing with measurement error often rely on strong assumptions such as knowledge of the error distribution or its variance and availability of replicated measurements of the covariates. We propose a Bayesian Nonparametric Learning framework which is robust to mismeasured covariates, does not require the preceding assumptions, and is able to incorporate prior beliefs about the true error distribution. Our approach gives rise to two methods that are robust to measurement error via different loss functions: one based on the Total Least Squares objective and the other based on Maximum Mean Discrepancy (MMD). The latter allows for generalisation to non-Gaussian distributed errors and non-linear covariate-response relationships. We provide bounds on the generalisation error using the MMD-loss and showcase the effectiveness of the proposed framework versus prior art in real-world mental health and dietary datasets that contain significant measurement errors.

Score matching is an alternative to maximum likelihood (ML) for estimating a probability distribution parametrized up to a constant of proportionality. By fitting the ''score'' of the distribution, it sidesteps the need to compute this constant of proportionality (which is often intractable). While score matching and variants thereof are popular in practice, precise theoretical understanding of the benefits and tradeoffs with maximum likelihood -- both computational and statistical -- are not well understood. In this work, we give the first example of a natural exponential family of distributions such that the score matching loss is computationally efficient to optimize, and has a comparable statistical efficiency to ML, while the ML loss is intractable to optimize using a gradient-based method. The family consists of exponentials of polynomials of fixed degree, and our result can be viewed as a continuous analogue of recent developments in the discrete setting. Precisely, we show: (1) Designing a zeroth-order or first-order oracle for optimizing the maximum likelihood loss is NP-hard. (2) Maximum likelihood has a statistical efficiency polynomial in the ambient dimension and the radius of the parameters of the family. (3) Minimizing the score matching loss is both computationally and statistically efficient, with complexity polynomial in the ambient dimension.

Cooperative multi-agent reinforcement learning (MARL) methods equip a group of autonomous agents with the capability Executing actions in a correlated manner is a common of planning and learning to maximize their joint strategy for human coordination that often utility, or reward signals in the reinforcement learning (RL) leads to better cooperation, which is also potentially literature, which provides a promising paradigm for a range beneficial for cooperative multi-agent reinforcement of real-world applications, such as traffic control (Chu et al., learning (MARL). However, the recent 2019), coordination of multi-robot systems (Corke et al., success of MARL relies heavily on the convenient 2005), and power grid management (Callaway & Hiskens, paradigm of purely decentralized execution, 2010). As a key distinction from the single-agent setting, where there is no action correlation among agents multi-agent joint action spaces grow exponentially with for scalability considerations. In this work, we the number of agents, which imposes significant scalability introduce a Bayesian network to inaugurate correlations issues. As a convenient and commonly adopted solution, between agents' action selections in their most existing cooperative MARL methods only consider joint policy. Theoretically, we establish a theoretical product policies, i.e., each agent selects its local action independently justification for why action dependencies given the state or its observations. Restricting are beneficial by deriving the multi-agent policy to product policies, however, does come at a cost for cooperative gradient formula under such a Bayesian network tasks: consider an example where cars wait at a joint policy and proving its global convergence crossroads, it would be hard for the cars to coordinate their to Nash equilibria under tabular softmax policy movements without knowing others' intentions, potentially parameterization in cooperative Markov games.

As machine learning (ML) classifiers increasingly oversee the automated monitoring of network traffic, studying their resilience against adversarial attacks becomes critical. This paper focuses on poisoning attacks, specifically backdoor attacks, against network traffic flow classifiers. We investigate the challenging scenario of clean-label poisoning where the adversary's capabilities are constrained to tampering only with the training data - without the ability to arbitrarily modify the training labels or any other component of the training process. We describe a trigger crafting strategy that leverages model interpretability techniques to generate trigger patterns that are effective even at very low poisoning rates. Finally, we design novel strategies to generate stealthy triggers, including an approach based on generative Bayesian network models, with the goal of minimizing the conspicuousness of the trigger, and thus making detection of an ongoing poisoning campaign more challenging. Our findings provide significant insights into the feasibility of poisoning attacks on network traffic classifiers used in multiple scenarios, including detecting malicious communication and application classification.

Artificial intelligence (AI) models trained on published scientific findings have been used to invent valuable materials and targeted therapies, but they typically ignore the human scientists who continually alter the landscape of discovery. Here we show that incorporating the distribution of human expertise by training unsupervised models on simulated inferences cognitively accessible to experts dramatically improves (up to 400%) AI prediction of future discoveries beyond those focused on research content alone, especially when relevant literature is sparse. These models succeed by predicting human predictions and the scientists who will make them. By tuning human-aware AI to avoid the crowd, we can generate scientifically promising "alien" hypotheses unlikely to be imagined or pursued without intervention until the distant future, which hold promise to punctuate scientific advance beyond questions currently pursued. Accelerating human discovery or probing its blind spots, human-aware AI enables us to move toward and beyond the contemporary scientific frontier.