Stein variational gradient descent (SVGD) is a prominent particle-based variational inference method used for sampling a target distribution. SVGD has attracted interest for application in machine-learning techniques such as Bayesian inference. In this paper, we propose novel trainable algorithms that incorporate a deep-learning technique called deep unfolding,into SVGD. This approach facilitates the learning of the internal parameters of SVGD, thereby accelerating its convergence speed. To evaluate the proposed trainable SVGD algorithms, we conducted numerical simulations of three tasks: sampling a one-dimensional Gaussian mixture, performing Bayesian logistic regression, and learning Bayesian neural networks. The results show that our proposed algorithms exhibit faster convergence than the conventional variants of SVGD.

This paper presents a neural vocoder based on a denoising diffusion probabilistic model (DDPM) incorporating explicit periodic signals as auxiliary conditioning signals. Recently, DDPM-based neural vocoders have gained prominence as non-autoregressive models that can generate high-quality waveforms. The neural vocoders based on DDPM have the advantage of training with a simple time-domain loss. In practical applications, such as singing voice synthesis, there is a demand for neural vocoders to generate high-fidelity speech waveforms with flexible pitch control. However, conventional DDPM-based neural vocoders struggle to generate speech waveforms under such conditions. Our proposed model aims to accurately capture the periodic structure of speech waveforms by incorporating explicit periodic signals. Experimental results show that our model improves sound quality and provides better pitch control than conventional DDPM-based neural vocoders.

A universal feature of human societies is the adoption of systems of rules and norms in the service of cooperative ends. How can we build learning agents that do the same, so that they may flexibly cooperate with the human institutions they are embedded in? We hypothesize that agents can achieve this by assuming there exists a shared set of norms that most others comply with while pursuing their individual desires, even if they do not know the exact content of those norms. By assuming shared norms, a newly introduced agent can infer the norms of an existing population from observations of compliance and violation. Furthermore, groups of agents can converge to a shared set of norms, even if they initially diverge in their beliefs about what the norms are. This in turn enables the stability of the normative system: since agents can bootstrap common knowledge of the norms, this leads the norms to be widely adhered to, enabling new entrants to rapidly learn those norms. We formalize this framework in the context of Markov games and demonstrate its operation in a multi-agent environment via approximately Bayesian rule induction of obligative and prohibitive norms. Using our approach, agents are able to rapidly learn and sustain a variety of cooperative institutions, including resource management norms and compensation for pro-social labor, promoting collective welfare while still allowing agents to act in their own interests.

Causal Discovery is a field of machine learning and statistics aiming to induce causal knowledge from data [29, 47]. There is a large corpus of algorithms and methodologies in the field, spanning tasks like learning causal models, estimating causal effects, and determining optimal interventions. While there are several public libraries of algorithms for these tasks, combining the algorithms and applying them to any given problem is a challenging endeavor that requires extensive knowledge of the methods and a deep understanding of the theory to interpret results. In this paper, we introduce the concept of Automated Causal Discovery (AutoCD) (not to be confused with Automated Causal Inference [14, 26]; see Section 3), defined as the effort to fully automate the application of causal discovery and causal reasoning. AutoCD's goals should be to deliver not just the optimal causal model that fits the data, but all information, answers to queries, visualizations, interpretations, and explanations that a human expert analyst would.

Hybrid Bayesian networks (HBN) contain complex conditional probabilistic distributions (CPD) specified as partitioned expressions over discrete and continuous variables. The size of these CPDs grows exponentially with the number of parent nodes when using discrete inference, resulting in significant inefficiency. Normally, an effective way to reduce the CPD size is to use a binary factorization (BF) algorithm to decompose the statistical or arithmetic functions in the CPD by factorizing the number of connected parent nodes to sets of size two. However, the BF algorithm was not designed to handle partitioned expressions. Hence, we propose a new algorithm called stacking factorization (SF) to decompose the partitioned expressions. The SF algorithm creates intermediate nodes to incrementally reconstruct the densities in the original partitioned expression, allowing no more than two continuous parent nodes to be connected to each child node in the resulting HBN. SF can be either used independently or combined with the BF algorithm. We show that the SF+BF algorithm significantly reduces the CPD size and contributes to lowering the tree-width of a model, thus improving efficiency.

Bayesian causal inference, i.e., inferring a posterior over causal models for the use in downstream causal reasoning tasks, poses a hard computational inference problem that is little explored in literature. In this work, we combine techniques from order-based MCMC structure learning with recent advances in gradient-based graph learning into an effective Bayesian causal inference framework. Specifically, we decompose the problem of inferring the causal structure into (i) inferring a topological order over variables and (ii) inferring the parent sets for each variable. When limiting the number of parents per variable, we can exactly marginalise over the parent sets in polynomial time. We further use Gaussian processes to model the unknown causal mechanisms, which also allows their exact marginalisation. This introduces a Rao-Blackwellization scheme, where all components are eliminated from the model, except for the causal order, for which we learn a distribution via gradient-based optimisation. The combination of Rao-Blackwellization with our sequential inference procedure for causal orders yields state-of-the-art on linear and non-linear additive noise benchmarks with scale-free and Erdos-Renyi graph structures.

Most leading implementations of black-box variational inference (BBVI) are based on optimizing a stochastic evidence lower bound (ELBO). But such approaches to BBVI often converge slowly due to the high variance of their gradient estimates. In this work, we propose batch and match (BaM), an alternative approach to BBVI based on a score-based divergence. Notably, this score-based divergence can be optimized by a closed-form proximal update for Gaussian variational families with full covariance matrices. We analyze the convergence of BaM when the target distribution is Gaussian, and we prove that in the limit of infinite batch size the variational parameter updates converge exponentially quickly to the target mean and covariance. We also evaluate the performance of BaM on Gaussian and non-Gaussian target distributions that arise from posterior inference in hierarchical and deep generative models. In these experiments, we find that BaM typically converges in fewer (and sometimes significantly fewer) gradient evaluations than leading implementations of BBVI based on ELBO maximization.

In interactive systems, actions are often correlated, presenting an opportunity for more sample-efficient off-policy evaluation (OPE) and learning (OPL) in large action spaces. We introduce a unified Bayesian framework to capture these correlations through structured and informative priors. In this framework, we propose sDM, a generic Bayesian approach designed for OPE and OPL, grounded in both algorithmic and theoretical foundations. Notably, sDM leverages action correlations without compromising computational efficiency. Moreover, inspired by online Bayesian bandits, we introduce Bayesian metrics that assess the average performance of algorithms across multiple problem instances, deviating from the conventional worst-case assessments. We analyze sDM in OPE and OPL, highlighting the benefits of leveraging action correlations. Empirical evidence showcases the strong performance of sDM.

We introduce a novel Information Criterion (IC), termed Learning under Singularity (LS), designed to enhance the functionality of the Widely Applicable Bayes Information Criterion (WBIC) and the Singular Bayesian Information Criterion (sBIC). LS is effective without regularity constraints and demonstrates stability. Watanabe defined a statistical model or a learning machine as regular if the mapping from a parameter to a probability distribution is one-to-one and its Fisher information matrix is positive definite. In contrast, models not meeting these conditions are termed singular. Over the past decade, several information criteria for singular cases have been proposed, including WBIC and sBIC. WBIC is applicable in non-regular scenarios but faces challenges with large sample sizes and redundant estimation of known learning coefficients. Conversely, sBIC is limited in its broader application due to its dependence on maximum likelihood estimates. LS addresses these limitations by enhancing the utility of both WBIC and sBIC. It incorporates the empirical loss from the Widely Applicable Information Criterion (WAIC) to represent the goodness of fit to the statistical model, along with a penalty term similar to that of sBIC. This approach offers a flexible and robust method for model selection, free from regularity constraints.

BlackJAX is a library implementing sampling and variational inference algorithms commonly used in Bayesian computation. It is designed for ease of use, speed, and modularity by taking a functional approach to the algorithms' implementation. BlackJAX is written in Python, using JAX to compile and run NumpPy-like samplers and variational methods on CPUs, GPUs, and TPUs. The library integrates well with probabilistic programming languages by working directly with the (un-normalized) target log density function. BlackJAX is intended as a collection of low-level, composable implementations of basic statistical 'atoms' that can be combined to perform well-defined Bayesian inference, but also provides high-level routines for ease of use. It is designed for users who need cutting-edge methods, researchers who want to create complex sampling methods, and people who want to learn how these work.