We introduce Neural Conditional Probability (NCP), an operator-theoretic approach to learning conditional distributions with a focus on statistical inference tasks. NCP can be used to build conditional confidence regions and extract key statistics such as conditional quantiles, mean, and covariance. It offers streamlined learning via a single unconditional training phase, allowing efficient inference without the need for retraining even when conditioning changes. By leveraging the approximation capabilities of neural networks, NCP efficiently handles a wide variety of complex probability distributions. We provide theoretical guarantees that ensure both optimization consistency and statistical accuracy. In experiments, we show that NCP with a 2-hidden-layer network matches or outperforms leading methods. This demonstrates that a a minimalistic architecture with a theoretically grounded loss can achieve competitive results, even in the face of more complex architectures.

Weighted model integration (WMI) is a framework to perform advanced probabilistic inference in hybrid domains, i.e., on distributions over mixed continuous-discrete random variables and in the presence of complex logical and arithmetic constraints. In this work, we advance the WMI framework on both the theoretical and algorithmic side. First, we trace the boundaries of tractability for WMI inference in terms of two key properties of a WMI problem's dependency structure: sparsity and diameter. We prove that exact inference is only efficient if that structure is tree-shaped with logarithmic diameter. While this result deepens our theoretical understanding of WMI it hinders the practical applicability of exact WMI solvers to large problems. To overcome this, we propose the first approximate WMI solver that does not resort to sampling, but performs exact inference on an approximate model. Our solution iteratively performs message passing in a relaxed problem structure to recover lost dependencies. As our experiments show, it scales to problems that are out of the reach of exact WMI solvers while delivering accurate approximations.

Inferring causal structure poses a combinatorial search problem that typically involves evaluating structures with a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior knowledge is difficult. In this work, we propose to amortize causal structure learning. Rather than searching over structures, we train a variational inference model to directly predict the causal structure from observational or interventional data. This allows our inference model to acquire domain-specific inductive biases for causal discovery solely from data generated by a simulator, bypassing both the hand-engineering of suitable score functions and the search over graphs. The architecture of our inference model emulates permutation invariances that are crucial for statistical efficiency in structure learning, which facilitates generalization to significantly larger problem instances than seen during training. On synthetic data and semisynthetic gene expression data, our models exhibit robust generalization capabilities when subject to substantial distribution shifts and significantly outperform existing algorithms, especially in the challenging genomics domain. Our code and models are publicly available at: https://github.com/larslorch/avici.

Procedural activities are sequences of key-steps aimed at achieving specific goals. They are crucial to build intelligent agents able to assist users effectively. In this context, task graphs have emerged as a human-understandable representation of procedural activities, encoding a partial ordering over the key-steps. While previous works generally relied on hand-crafted procedures to extract task graphs from videos, in this paper, we propose an approach based on direct maximum likelihood optimization of edges' weights, which allows gradient-based learning of task graphs and can be naturally plugged into neural network architectures. Experiments on the CaptainCook4D dataset demonstrate the ability of our approach to predict accurate task graphs from the observation of action sequences, with an improvement of +16.7% over previous approaches. Owing to the differentiability of the proposed framework, we also introduce a feature-based approach, aiming to predict task graphs from key-step textual or video embeddings, for which we observe emerging video understanding abilities. Task graphs learned with our approach are also shown to significantly enhance online mistake detection in procedural egocentric videos, achieving notable gains of +19.8% and +7.5% on the Assembly101-O and EPIC-Tent-O datasets.

Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?"

A natural strategy for continual learning is to weigh a Bayesian ensemble of fixed functions. This suggests that if a (single) neural network could be interpreted as an ensemble, one could design effective algorithms that learn without forgetting. To realize this possibility, we observe that a neural network classifier with N parameters can be interpreted as a weighted ensemble of N classifiers, and that in the lazy regime limit these classifiers are fixed throughout learning. We call these classifiers the neural tangent experts and show they output valid probability distributions over the labels. We then derive the likelihood and posterior probability of each expert given past data. Surprisingly, the posterior updates for these experts are equivalent to a scaled and projected form of stochastic gradient descent (SGD) over the network weights. Away from the lazy regime, networks can be seen as ensembles of adaptive experts which improve over time. These results offer a new interpretation of neural networks as Bayesian ensembles of experts, providing a principled framework for understanding and mitigating catastrophic forgetting in continual learning settings.

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single-and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.

Contrastive Learning (CL) plays a crucial role in molecular representation learning, enabling unsupervised learning from large scale unlabeled molecule datasets. It has inspired various applications in molecular property prediction and drug design. However, existing molecular representation learning methods often introduce potential false positive and false negative pairs through conventional graph augmentations like node masking and subgraph removal. The issue can lead to suboptimal performance when applying standard contrastive learning techniques to molecular datasets. To address the issue of false positive and negative pairs in molecular representation learning, we propose a novel probability-based contrastive learning (CL) framework. Unlike conventional methods, our approach introduces a learnable weight distribution via Bayesian modeling to automatically identify and mitigate false positive and negative pairs. This method is particularly effective because it dynamically adjusts to the data, improving the accuracy of the learned representations. Our model is learned by a stochastic expectation-maximization process, which optimizes the model by iteratively refining the probability estimates of sample weights and updating the model parameters. Experimental results indicate that our method outperforms existing approaches in 13 out of 15 molecular property prediction benchmarks in MoleculeNet dataset and 8 out of 12 benchmarks in the QM9 benchmark, achieving new state-of-the-art results on average.

Differentially private mechanisms protect privacy by introducing additional randomness into the data. Restricting access to only the privatized data makes it challenging to perform valid statistical inference on parameters underlying the confidential data. Specifically, the likelihood function of the privatized data requires integrating over the large space of confidential databases and is typically intractable. For Bayesian analysis, this results in a posterior distribution that is doubly intractable, rendering traditional MCMC techniques inapplicable. We propose an MCMC framework to perform Bayesian inference from the privatized data, which is applicable to a wide range of statistical models and privacy mechanisms.

We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior distribution, (2) the choice of divergence, and (3) the optimization of the variational objective. We show that even in the best-case scenario when the exact posterior belongs to the assumed variational family, common stochastic optimization methods lead to poor variational approximations if the problem dimension is moderately large. We also demonstrate that these methods are not robust across diverse model types. Motivated by these findings, we develop a more robust and accurate stochastic optimization framework by viewing the underlying optimization algorithm as producing a Markov chain. Our approach is theoretically motivated and includes a diagnostic for convergence and a novel stopping rule, both of which are robust to noisy evaluations of the objective function. We show empirically that the proposed framework works well on a diverse set of models: it can automatically detect stochastic optimization failure or inaccurate variational approximation.