Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization objectives for algorithms searching through sets of graphs or for selection of tuning parameters of other methods such as the graphical lasso, which is a likelihood penalization technique. In this paper we establish the consistency of an extended Bayesian information criterion for Gaussian graphical models in a scenario where both the number of variables p and the sample size n grow. Compared to earlier work on the regression case, our treatment allows for growth in the number of non-zero parameters in the true model, which is necessary in order to cover connected graphs. We demonstrate the performance of this criterion on simulated data when used in conjunction with the graphical lasso, and verify that the criterion indeed performs better than either cross-validation or the ordinary Bayesian information criterion when p and the number of non-zero parameters q both scale with n.

We develop a novel Bayesian nonparametric model for random bipartite graphs. The model is based on the theory of completely random measures and is able to handle a potentially infinite number of nodes. We show that the model has appealing properties and in particular it may exhibit a power-law behavior. We derive a posterior characterization, a generative process for network growth, and a simple Gibbs sampler for posterior simulation. Our model is shown to be well fitted to several real-world social networks.

Dependent Dirichlet processes (DPs) are dependent sets of random measures, each being marginally DP distributed. They are used in Bayesian nonparametric models when the usual exchangeability assumption does not hold. We propose a simple and general framework to construct dependent DPs by marginalizing and normalizing a single gamma process over an extended space. The result is a set of DPs, each associated with a point in a space such that neighbouring DPs are more dependent. We describe Markov chain Monte Carlo inference involving Gibbs sampling and three different Metropolis-Hastings proposals to speed up convergence. We report an empirical study of convergence on a synthetic dataset and demonstrate an application of the model to topic modeling through time.

Accurate and detailed models of neurodegenerative disease progression are crucially important for reliable early diagnosis and the determination of effective treatments. We introduce the ALPACA (Alzheimer's disease Probabilistic Cascades) model, a generative model linking latent Alzheimer's progression dynamics to observable biomarker data. In contrast with previous works which model disease progression as a fixed event ordering, we explicitly model the variability over such orderings among patients which is more realistic, particularly for highly detailed progression models. We describe efficient learning algorithms for ALPACA and discuss promising experimental results on a real cohort of Alzheimer's patients from the Alzheimer's Disease Neuroimaging Initiative.

In the quest to advance human-centric natural language generation (NLG) systems, ensuring alignment between NLG models and human preferences is crucial. For this alignment, current popular methods leverage a reinforcement learning (RL) approach with a reward model trained on feedback from humans. However, inherent disagreements due to the subjective nature of human preferences pose a significant challenge for training the reward model, resulting in a deterioration of the NLG performance. To tackle this issue, previous approaches typically rely on majority voting or averaging to consolidate multiple inconsistent preferences into a merged one. Although straightforward to understand and execute, such methods suffer from an inability to capture the nuanced degrees of disaggregation among humans and may only represent a specialized subset of individuals, thereby lacking the ability to quantitatively disclose the universality of human preferences.

We present a novel extension of the Weak Neural Variational Inference (WNVI) framework for probabilistic material property estimation that explicitly quantifies model errors in PDE-based inverse problems. Traditional approaches assume the correctness of all governing equations, including potentially unreliable constitutive laws, which can lead to biased estimates and misinterpretations. Our proposed framework addresses this limitation by distinguishing between reliable governing equations, such as conservation laws, and uncertain constitutive relationships. By treating all state variables as latent random variables, we enforce these equations through separate sets of residuals, leveraging a virtual likelihood approach with weighted residuals. This formulation not only identifies regions where constitutive laws break down but also improves robustness against model uncertainties without relying on a fully trustworthy forward model. We demonstrate the effectiveness of our approach in the context of elastography, showing that it provides a structured, interpretable, and computationally efficient alternative to traditional model error correction techniques. Our findings suggest that the proposed framework enhances the accuracy and reliability of material property estimation by offering a principled way to incorporate uncertainty in constitutive modeling.

Behavior cloning (BC) traditionally relies on demonstration data, assuming the demonstrated actions are optimal. This can lead to overfitting under noisy data, particularly when expressive models are used (e.g., the energy-based model in Implicit BC). To address this, we extend behavior cloning into an iterative process of optimal action estimation within the Interactive Imitation Learning framework. Specifically, we introduce Contrastive policy Learning from Interactive Corrections (CLIC). CLIC leverages human corrections to estimate a set of desired actions and optimizes the policy to select actions from this set. We provide theoretical guarantees for the convergence of the desired action set to optimal actions in both single and multiple optimal action cases. Extensive simulation and real-robot experiments validate CLIC's advantages over existing state-of-the-art methods, including stable training of energy-based models, robustness to feedback noise, and adaptability to diverse feedback types beyond demonstrations. Our code will be publicly available soon.

We show that variational learning naturally induces an adaptive label smoothing where label noise is specialized for each example. Such label-smoothing is useful to handle examples with labeling errors and distribution shifts, but designing a good adaptivity strategy is not always easy. We propose to skip this step and simply use the natural adaptivity induced during the optimization of a variational objective. We show empirical results where a variational algorithm called IVON outperforms traditional label smoothing and yields adaptivity strategies similar to those of an existing approach. By connecting Bayesian methods to label smoothing, our work provides a new way to handle overconfident predictions.

Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities. In practice, the time score has to be estimated based on samples from the two densities. However, existing methods for this problem remain computationally expensive and can yield inaccurate estimates. Inspired by recent advances in generative modeling, we introduce a novel framework for time score estimation, based on a conditioning variable. Choosing the conditioning variable judiciously enables a closed-form objective function. We demonstrate that, compared to previous approaches, our approach results in faster learning of the time score and competitive or better estimation accuracies of the density ratio on challenging tasks. Furthermore, we establish theoretical guarantees on the error of the estimated density ratio.

Monte Carlo (MC) methods are powerful tools for numerical inference and optimization widely employed in statistics, signal processing and machine learning Liu (2004); Robert and Casella (2004). They are mainly used for computing approximately the solution of definite integrals, and by extension, of differential equations (for this reason, MC schemes can be considered stochastic quadrature rules). Although exact analytical solutions to integrals are always desirable, such unicorns are rarely available, specially in real-world systems. Many applications inevitably require the approximation of intractable integrals. Specifically, Bayesian methods need the computation of expectations with respect to posterior probability density function (pdf) which, generally, are analytically intractable Gelman et al. (2013). The MC methods can be divided in four main families: direct methods (based on transformations or random variables), accept-reject techniques, Markov chain Monte Carlo (MCMC) algorithms, and importance sampling (IS) schemes Luengo et al. (2020); Martino et al. (2018). The last two families are the most popular for the facility and universality of their possible application Liang et al. (2010); Liu (2004); Robert and Casella (2004). All the MC methods require the choice of a suitable proposal density that is crucial for their performance Luengo et al. (2020); Robert and Casella (2004).