Figure 1: We consider sampling from the positive class of a 2D mixture of uniforms (a) using the probability flow ODE with the conditional score (b) and the guided score (c).

Neural Information Processing Systems http://nips.cc/

Conditional inference on arbitrary subsets of variables is a core problem in probabilistic inference with important applications such as masked language modeling and image inpainting. In recent years, the family of Any-Order Autoregressive Models (AO-ARMs) - closely related to popular models such as BERT and XL-Net - has shown breakthrough performance in arbitrary conditional tasks across a sweeping range of domains. But, in spite of their success, in this paper we identify significant improvements to be made to previous formulations of AO-ARMs. First, we show that AO-ARMs suffer from redundancy in their probabilistic model, i.e., they define the same distribution in multiple different ways. We alleviate this redundancy by training on a smaller set of univariate conditionals that still maintains support for efficient arbitrary conditional inference. Second, we upweight the training loss for univariate conditionals that are evaluated more frequently during inference. Our method leads to improved performance with no compromises on tractability, giving state-of-the-art likelihoods in arbitrary conditional modeling on text (Text8), image (CIFAR10, ImageNet32), and continuous tabular data domains.

Neural Information Processing Systems http://nips.cc/

Dynamic Bayesian networks (DBNs) are increasingly used in healthcare due to their ability to model complex temporal relationships in patient data while maintaining interpretability, an essential feature for clinical decision-making. However, existing approaches to handling missing data in longitudinal clinical datasets are largely derived from static Bayesian networks literature, failing to properly account for the temporal nature of the data. This gap limits the ability to quantify uncertainty over time, which is particularly critical in settings such as intensive care, where understanding the temporal dynamics is fundamental for model trustworthiness and applicability across diverse patient groups. Despite the potential of DBNs, a full Bayesian framework that integrates missing data handling remains underdeveloped. In this work, we propose a novel Gibbs sampling-based method for learning DBNs from incomplete data. Our method treats each missing value as an unknown parameter following a Gaussian distribution. At each iteration, the unobserved values are sampled from their full conditional distributions, allowing for principled imputation and uncertainty estimation. We evaluate our method on both simulated datasets and real-world intensive care data from critically ill patients. Compared to standard model-agnostic techniques such as MICE, our Bayesian approach demonstrates superior reconstruction accuracy and convergence properties. These results highlight the clinical relevance of incorporating full Bayesian inference in temporal models, providing more reliable imputations and offering deeper insight into model behavior. Our approach supports safer and more informed clinical decision-making, particularly in settings where missing data are frequent and potentially impactful.

We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed form parametric expression for the conditional likelihood, in which hyper-parameters are recursively updated as a function of the streaming data assuming conjugate priors. Motivated by large-sample asymptotics, we propose a novel adaptive low-complexity design for the Dirichlet process concentration parameter and show that the number of classes grow at most at a logarithmic rate. We further prove that in the large-sample limit, the conditional likelihood and data predictive distribution become asymptotically Gaussian. We demonstrate through experiments on synthetic and real data sets that our approach is superior to other online state-of-the-art methods.

Acoustic spatial capture-recapture (ASCR) surveys with an array of synchronized acoustic detectors can be an effective way of estimating animal density or call density. However, constructing the capture histories required for ASCR analysis is challenging, as recognizing which detections at different detectors are of which calls is not a trivial task. Because calls from different distances take different times to arrive at detectors, the order in which calls are detected is not necessarily the same as the order in which they are made, and without knowing which detections are of the same call, we do not know how many different calls are detected. We propose a Monte Carlo expectation-maximization (MCEM) estimation method to resolve this unknown call identity problem. To implement the MCEM method in this context, we sample the latent variables from a complete-data likelihood model in the expectation step and use a semi-complete-data likelihood or conditional likelihood in the maximization step. We use a parametric bootstrap to obtain confidence intervals. When we apply our method to a survey of moss frogs, it gives an estimate within 15% of the estimate obtained using data with call capture histories constructed by experts, and unlike this latter estimate, our confidence interval incorporates the uncertainty about call identities. Simulations show it to have a low bias (6%) and coverage probabilities close to the nominal 95% value.

The use of guidance in diffusion models was originally motivated by the premise that the guidance-modified score is that of the data distribution tilted by a conditional likelihood raised to some power. In this work we clarify this misconception by rigorously proving that guidance fails to sample from the intended tilted distribution. Our main result is to give a fine-grained characterization of the dynamics of guidance in two cases, (1) mixtures of compactly supported distributions and (2) mixtures of Gaussians, which reflect salient properties of guidance that manifest on real-world data. In both cases, we prove that as the guidance parameter increases, the guided model samples more heavily from the boundary of the support of the conditional distribution. We also prove that for any nonzero level of score estimation error, sufficiently large guidance will result in sampling away from the support, theoretically justifying the empirical finding that large guidance results in distorted generations. In addition to verifying these results empirically in synthetic settings, we also show how our theoretical insights can offer useful prescriptions for practical deployment.

In this paper, we address the problem of learning the structure of a pairwise graphical model from samples in a high-dimensional setting. Our first main result studies the sparsistency, or consistency in sparsity pattern recovery, properties of a forward-backward greedy algorithm as applied to general statistical models. As a special case, we then apply this algorithm to learn the structure of a discrete graphical model via neighborhood estimation. As a corollary of our general result, we derive sufficient conditions on the number of samples n, the maximum nodedegreed and the problem size p, as well as other conditions on the model parameters, so that the algorithm recovers all the edges with high probability.