Balancing computational efficiency with robust predictive performance is crucial in supervised learning, especially for critical applications. Standard deep learning models, while accurate and scalable, often lack probabilistic features like calibrated predictions and uncertainty quantification. Bayesian methods address these issues but can be computationally expensive as model and data complexity increase. Previous work shows that fast variational methods can reduce the compute requirements of Bayesian methods by eliminating the need for gradient computation or sampling, but are often limited to simple models. We demonstrate that conditional mixture networks (CMNs), a probabilistic variant of the mixture-of-experts (MoE) model, are suitable for fast, gradient-free inference and can solve complex classification tasks. CMNs employ linear experts and a softmax gating network. By exploiting conditional conjugacy and P\'olya-Gamma augmentation, we furnish Gaussian likelihoods for the weights of both the linear experts and the gating network. This enables efficient variational updates using coordinate ascent variational inference (CAVI), avoiding traditional gradient-based optimization. We validate this approach by training two-layer CMNs on standard benchmarks from the UCI repository. Our method, CAVI-CMN, achieves competitive and often superior predictive accuracy compared to maximum likelihood estimation (MLE) with backpropagation, while maintaining competitive runtime and full posterior distributions over all model parameters. Moreover, as input size or the number of experts increases, computation time scales competitively with MLE and other gradient-based solutions like black-box variational inference (BBVI), making CAVI-CMN a promising tool for deep, fast, and gradient-free Bayesian networks.

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve according to simple locally linear dynamics. However, existing methods for latent variable estimation are not robust to dynamical noise and system nonlinearity due to noise-sensitive inference procedures and limited model formulations. This can lead to inconsistent results on signals with similar dynamics, limiting the model's ability to provide scientific insight. In this work, we address these limitations and propose a probabilistic approach to latent variable estimation in decomposed models that improves robustness against dynamical noise. Additionally, we introduce an extended latent dynamics model to improve robustness against system nonlinearities. We evaluate our approach on several synthetic dynamical systems, including an empirically-derived brain-computer interface experiment, and demonstrate more accurate latent variable inference in nonlinear systems with diverse noise conditions. Furthermore, we apply our method to a real-world clinical neurophysiology dataset, illustrating the ability to identify interpretable and coherent structure where previous models cannot.

Variational continual learning (VCL) is a turn-key learning algorithm that has state-of-the-art performance among the best continual learning models. In our work, we explore an extension of the generalized variational continual learning (GVCL) model, named AutoVCL, which combines task heuristics for informed learning and model optimization. We demonstrate that our model outperforms the standard GVCL with fixed hyperparameters, benefiting from the automatic adjustment of the hyperparameter based on the difficulty and similarity of the incoming task compared to the previous tasks.

Learning a transition model via Maximum Likelihood Estimation (MLE) followed by planning inside the learned model is perhaps the most standard and simplest Model-based Reinforcement Learning (RL) framework. In this work, we show that such a simple Model-based RL scheme, when equipped with optimistic and pessimistic planning procedures, achieves strong regret and sample complexity bounds in online and offline RL settings. Particularly, we demonstrate that under the conditions where the trajectory-wise reward is normalized between zero and one and the transition is time-homogenous, it achieves horizon-free and second-order bounds. Horizon-free means that our bounds have no polynomial dependence on the horizon of the Markov Decision Process. A second-order bound is a type of instance-dependent bound that scales with respect to the variances of the returns of the policies which can be small when the system is nearly deterministic and (or) the optimal policy has small values. We highlight that our algorithms are simple, fairly standard, and indeed have been extensively studied in the RL literature: they learn a model via MLE, build a version space around the MLE solution, and perform optimistic or pessimistic planning depending on whether operating in the online or offline mode. These algorithms do not rely on additional specialized algorithmic designs such as learning variances and performing variance-weighted learning and thus can leverage rich function approximations that are significantly beyond linear or tabular structures. The simplicity of the algorithms also implies that our horizon-free and second-order regret analysis is actually standard and mainly follows the general framework of optimism/pessimism in the face of uncertainty.

Neural Networks (NNs) are promising models for refining the accuracy of molecular dynamics, potentially opening up new fields of application. Typically trained bottom-up, atomistic NN potential models can reach first-principle accuracy, while coarse-grained implicit solvent NN potentials surpass classical continuum solvent models. However, overcoming the limitations of costly generation of accurate reference data and data inefficiency of common bottom-up training demands efficient incorporation of data from many sources. This paper introduces the framework chemtrain to learn sophisticated NN potential models through customizable training routines and advanced training algorithms. These routines can combine multiple top-down and bottom-up algorithms, e.g., to incorporate both experimental and simulation data or pre-train potentials with less costly algorithms. chemtrain provides an object-oriented high-level interface to simplify the creation of custom routines. On the lower level, chemtrain relies on JAX to compute gradients and scale the computations to use available resources. We demonstrate the simplicity and importance of combining multiple algorithms in the examples of parametrizing an all-atomistic model of titanium and a coarse-grained implicit solvent model of alanine dipeptide.

Generative Flow Networks (GFlowNets) are a class of generative models that sample objects in proportion to a specified reward function through a learned policy. They can be trained either on-policy or off-policy, needing a balance between exploration and exploitation for fast convergence to a target distribution. While exploration strategies for discrete GFlowNets have been studied, exploration in the continuous case remains to be investigated, despite the potential for novel exploration algorithms due to the local connectedness of continuous domains. Here, we introduce Adapted Metadynamics, a variant of metadynamics that can be applied to arbitrary black-box reward functions on continuous domains. We use Adapted Metadynamics as an exploration strategy for continuous GFlowNets. We show three continuous domains where the resulting algorithm, MetaGFN, accelerates convergence to the target distribution and discovers more distant reward modes than previous off-policy exploration strategies used for GFlowNets.

The optimization of atomic structures plays a pivotal role in understanding and designing materials with desired properties. However, conventional methods often struggle with the formidable task of navigating the vast potential energy surface, especially in high-dimensional spaces with numerous local minima. Recent advancements in machine learning-driven surrogate models offer a promising avenue for alleviating this computational burden. In this study, we propose a novel approach that combines the strengths of universal machine learning potentials with a Bayesian approach of the GOFEE/BEACON framework. By leveraging the comprehensive chemical knowledge encoded in pretrained universal machine learning potentials as a prior estimate of energy and forces, we enable the Gaussian process to focus solely on capturing the intricate nuances of the potential energy surface. We demonstrate the efficacy of our approach through comparative analyses across diverse systems, including periodic bulk materials, surface structures, and a cluster.

In this paper, we investigate the use of probabilistic graphical models, specifically stochastic blockmodels, for the purpose of hierarchical entity clustering on knowledge graphs. These models, seldom used in the Semantic Web community, decompose a graph into a set of probability distributions. The parameters of these distributions are then inferred allowing for their subsequent sampling to generate a random graph. In a non-parametric setting, this allows for the induction of hierarchical clusterings without prior constraints on the hierarchy's structure. Specifically, this is achieved by the integration of the Nested Chinese Restaurant Process and the Stick Breaking Process into the generative model. In this regard, we propose a model leveraging such integration and derive a collapsed Gibbs sampling scheme for its inference. To aid in understanding, we describe the steps in this derivation and provide an implementation for the sampler. We evaluate our model on synthetic and real-world datasets and quantitatively compare against benchmark models. We further evaluate our results qualitatively and find that our model is capable of inducing coherent cluster hierarchies in small scale settings. The work presented in this paper provides the first step for the further application of stochastic blockmodels for knowledge graphs on a larger scale. We conclude the paper with potential avenues for future work on more scalable inference schemes.

Generative Bayesian Computation (GBC) methods are developed to provide an efficient computational solution for maximum expected utility (MEU). We propose a density-free generative method based on quantiles that naturally calculates expected utility as a marginal of quantiles. Our approach uses a deep quantile neural estimator to directly estimate distributional utilities. Generative methods assume only the ability to simulate from the model and parameters and as such are likelihood-free. A large training dataset is generated from parameters and output together with a base distribution. Our method a number of computational advantages primarily being density-free with an efficient estimator of expected utility. A link with the dual theory of expected utility and risk taking is also discussed. To illustrate our methodology, we solve an optimal portfolio allocation problem with Bayesian learning and a power utility (a.k.a. fractional Kelly criterion). Finally, we conclude with directions for future research.

Chain-of-Thought (CoT) prompting and its variants have gained popularity as effective methods for solving multi-step reasoning problems using pretrained large language models (LLMs). In this work, we analyze CoT prompting from a statistical estimation perspective, providing a comprehensive characterization of its sample complexity. To this end, we introduce a multi-step latent variable model that encapsulates the reasoning process, where the latent variable encodes the task information. Under this framework, we demonstrate that when the pretraining dataset is sufficiently large, the estimator formed by CoT prompting is equivalent to a Bayesian estimator. This estimator effectively solves the multi-step reasoning problem by aggregating a posterior distribution inferred from the demonstration examples in the prompt. Moreover, we prove that the statistical error of the CoT estimator can be decomposed into two main components: (i) a prompting error, which arises from inferring the true task using CoT prompts, and (ii) the statistical error of the pretrained LLM. We establish that, under appropriate assumptions, the prompting error decays exponentially to zero as the number of demonstrations increases. Additionally, we explicitly characterize the approximation and generalization errors of the pretrained LLM. Notably, we construct a transformer model that approximates the target distribution of the multi-step reasoning problem with an error that decreases exponentially in the number of transformer blocks. Our analysis extends to other variants of CoT, including Self-Consistent CoT, Tree-of-Thought, and Selection-Inference, offering a broad perspective on the efficacy of these methods. We also provide numerical experiments to validate the theoretical findings.