Much of Bayesian inference centers around the design of estimators for inverse problems which are optimal assuming the data comes from a known prior. But what do these optimality guarantees mean if the prior is unknown? In recent years, algorithm unrolling has emerged as deep learning's answer to this age-old question: design a neural network whose layers can in principle simulate iterations of inference algorithms and train on data generated by the unknown prior. Despite its empirical success, however, it has remained unclear whether this method can provably recover the performance of its optimal, prior-aware counterparts.In this work, we prove the first rigorous learning guarantees for neural networks based on unrolling approximate message passing (AMP). For compressed sensing, we prove that when trained on data drawn from a product prior, the layers of the network approximately converge to the same denoisers used in Bayes AMP. We also provide extensive numerical experiments for compressed sensing and rank-one matrix estimation demonstrating the advantages of our unrolled architecture --- in addition to being able to obliviously adapt to general priors, it exhibits improvements over Bayes AMP in more general settings of low dimensions, non-Gaussian designs, and non-product priors.

This paper studies the problem of \emph{entropy identity testing}: given sample access to a distribution p and a fully described distribution q (both are discrete distributions over the support of size k), and the promise that either p q or H(p) - H(q) \geqslant \varepsilon, where H(\cdot) denotes the Shannon entropy, a tester needs to distinguish between the two cases with high probability. This improves on the sample complexity bound of \tilde{O}(2 {d/2}n 2/\varepsilon 4) from Canonne, Diakonikolas, Kane, and Stewart (2020), which required an additional assumption on the structure of the (unknown) Bayesian network.

This paper introduces a novel prior called Diversified Block Sparse Prior to characterize the widespread block sparsity phenomenon in real-world data. By allowing diversification on intra-block variance and inter-block correlation matrices, we effectively address the sensitivity issue of existing block sparse learning methods to pre-defined block information, which enables adaptive block estimation while mitigating the risk of overfitting. Based on this, a diversified block sparse Bayesian learning method (DivSBL) is proposed, utilizing EM algorithm and dual ascent method for hyperparameter estimation. Moreover, we establish the global and local optimality theory of our model.

In tasks aiming for long-term returns, planning becomes essential. We study generative modeling for planning with datasets repurposed from offline reinforcement learning. Specifically, we identify temporal consistency in the absence of step-wise rewards as one key technical challenge. We introduce the Latent Plan Transformer (LPT), a novel model that leverages a latent variable to connect a Transformer- based trajectory generator and the final return. LPT can be learned with maximum likelihood estimation on trajectory-return pairs.

One of the grand challenges of cell biology is inferring the gene regulatory network (GRN) which describes interactions between genes and their products that control gene expression and cellular function. We can treat this as a causal discovery problem but with two non-standard challenges: (1) regulatory networks are inherently cyclic so we should not model a GRN as a directed acyclic graph (DAG), and (2) observations have significant measurement noise so for typical sample sizes, there will always be a large equivalence class of graphs that are likely given the data, and we want methods that capture this uncertainty. Existing methods either focus on challenge (1), identifying cyclic structure from dynamics, or on challenge (2) learning complex Bayesian posteriors over directed acyclic graphs, but not both. In this paper we leverage the fact that it is possible to estimate the velocity'' of the expression of a gene with RNA velocity techniques to develop an approach that addresses both challenges. Because we have access to velocity information, we can treat the Bayesian structure learning problem as a problem of sparse identification of a dynamical system, capturing cyclic feedback loops through time.

Federated learning (FL), through its privacy-preserving collaborative learning approach, has significantly empowered decentralized devices. However, constraints in either data and/or computational resources among participating clients introduce several challenges in learning, including the inability to train large model architectures, heightened risks of overfitting, and more. In this work, we present a novel FL framework grounded in Bayesian learning to address these challenges. Our approach involves training personalized Bayesian models at each client tailored to the unique complexities of the clients' datasets and efficiently collaborating across these clients. By leveraging Bayesian neural networks and their uncertainty quantification capabilities, our local training procedure robustly learns from small datasets.

Neural radiance fields (NeRFs) have gained popularity with multiple works showing promising results across various applications. However, to the best of our knowledge, existing works do not explicitly model the distribution of training camera poses, or consequently the triangulation quality, a key factor affecting reconstruction quality dating back to classical vision literature. We close this gap with ProvNeRF, an approach that models the provenance for each point -- i.e., the locations where it is likely visible -- of NeRFs as a stochastic field. We achieve this by extending implicit maximum likelihood estimation (IMLE) to functional space with an optimizable objective. We show that modeling per-point provenance during the NeRF optimization enriches the model with information on triangulation leading to improvements in novel view synthesis and uncertainty estimation under the challenging sparse, unconstrained view setting against competitive baselines.

When a model's predicted number of events within any time interval is similar to the observed number, it is called well-calibrated. A survival model's calibration can be measured using, for instance, distributional calibration (D-CALIBRATION) [Haider et al., 2020] which computes the squared difference between the observed and predicted number of events within different time intervals. Classically, calibration is addressed in post-training analysis. We develop explicit calibration (X-CAL), which turns D-CALIBRATION into a differentiable objective that can be used in survival modeling alongside maximum likelihood estimation and other objectives. X-CAL allows us to directly optimize calibration and strike a desired trade-off between predictive power and calibration.

Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the computation of which typically involves an intractable high-dimensional integral. Among available approximation methods, sampling-based approaches come with strong theoretical guarantees but scale poorly to large problems, while variational approaches scale well but offer few theoretical guarantees. In particular, variational methods are known to produce overconfident estimates of posterior uncertainty and are typically non-identifiable, with many latent variable configurations generating equivalent predictions. Here, we address these challenges by showing how diffusion-based models (DBMs), which have recently produced state-of-the-art performance in generative modeling tasks, can be repurposed for performing calibrated, identifiable Bayesian inference.

The majority of language model training builds on imitation learning. It covers pretraining, supervised fine-tuning, and affects the starting conditions for reinforcement learning from human feedback (RLHF). The simplicity and scalability of maximum likelihood estimation (MLE) for next token prediction led to its role as predominant paradigm. However, the broader field of imitation learning can more effectively utilize the sequential structure underlying autoregressive generation. We focus on investigating the inverse reinforcement learning (IRL) perspective to imitation, extracting rewards and directly optimizing sequences instead of individual token likelihoods and evaluate its benefits for fine-tuning large language models.