Deep Generative Models: Complexity, Dimensionality, and Approximation

Generative networks have shown remarkable success in learning complex data distributions, particularly in generating high-dimensional data from lower-dimensional inputs. While this capability is well-documented empirically, its theoretical underpinning remains unclear. One common theoretical explanation appeals to the widely accepted manifold hypothesis, which suggests that many real-world datasets, such as images and signals, often possess intrinsic low-dimensional geometric structures. Under this manifold hypothesis, it is widely believed that to approximate a distribution on a $d$-dimensional Riemannian manifold, the latent dimension needs to be at least $d$ or $d+1$. In this work, we show that this requirement on the latent dimension is not necessary by demonstrating that generative networks can approximate distributions on $d$-dimensional Riemannian manifolds from inputs of any arbitrary dimension, even lower than $d$, taking inspiration from the concept of space-filling curves. This approach, in turn, leads to a super-exponential complexity bound of the deep neural networks through expanded neurons. Our findings thus challenge the conventional belief on the relationship between input dimensionality and the ability of generative networks to model data distributions. This novel insight not only corroborates the practical effectiveness of generative networks in handling complex data structures, but also underscores a critical trade-off between approximation error, dimensionality, and model complexity.

Doubly robust identification of treatment effects from multiple environments

Practical and ethical constraints often require the use of observational data for causal inference, particularly in medicine and social sciences. Yet, observational datasets are prone to confounding, potentially compromising the validity of causal conclusions. While it is possible to correct for biases if the underlying causal graph is known, this is rarely a feasible ask in practical scenarios. A common strategy is to adjust for all available covariates, yet this approach can yield biased treatment effect estimates, especially when post-treatment or unobserved variables are present. We propose RAMEN, an algorithm that produces unbiased treatment effect estimates by leveraging the heterogeneity of multiple data sources without the need to know or learn the underlying causal graph. Notably, RAMEN achieves doubly robust identification: it can identify the treatment effect whenever the causal parents of the treatment or those of the outcome are observed, and the node whose parents are observed satisfies an invariance assumption. Empirical evaluations on synthetic and real-world datasets show that our approach outperforms existing methods.

Policy Learning with a Natural Language Action Space: A Causal Approach

This paper introduces a novel causal framework for multi-stage decision-making in natural language action spaces where outcomes are only observed after a sequence of actions. While recent approaches like Proximal Policy Optimization (PPO) can handle such delayed-reward settings in high-dimensional action spaces, they typically require multiple models (policy, value, and reward) and substantial training data. Our approach employs Q-learning to estimate Dynamic Treatment Regimes (DTR) through a single model, enabling data-efficient policy learning via gradient ascent on language embeddings. A key technical contribution of our approach is a decoding strategy that translates optimized embeddings back into coherent natural language. We evaluate our approach on mental health intervention, hate speech countering, and sentiment transfer tasks, demonstrating significant improvements over competitive baselines across multiple metrics. Notably, our method achieves superior transfer strength while maintaining content preservation and fluency, as validated through human evaluation. Our work provides a practical foundation for learning optimal policies in complex language tasks where training data is limited.

Strategic Learning with Local Explanations as Feedback

We investigate algorithmic decision problems where agents can respond strategically to the decision maker's (DM) models. The demand for clear and actionable explanations from DMs to (potentially strategic) agents continues to rise. While prior work often treats explanations as full model disclosures, explanations in practice might convey only partial information, which can lead to misinterpretations and harmful responses. When full disclosure of the predictive model is neither feasible nor desirable, a key open question is how DMs can use explanations to maximise their utility without compromising agent welfare. In this work, we explore well-known local and global explanation methods, and establish a necessary condition to prevent explanations from misleading agents into self-harming actions. Moreover, with conditional homogeneity, we establish that action recommendation (AR)-based explanations are sufficient for non-harmful responses, akin to the revelation principle in information design. To operationalise AR-based explanations, we propose a simple algorithm to jointly optimise the predictive model and AR policy to balance DM outcomes with agent welfare. Our empirical results demonstrate the benefits of this approach as a more refined strategy for safe and effective partial model disclosure in algorithmic decision-making.

Deep Ensembles Secretly Perform Empirical Bayes

Quantifying uncertainty in neural networks is a highly relevant problem which is essential to many applications. The two predominant paradigms to tackle this task are Bayesian neural networks (BNNs) and deep ensembles. Despite some similarities between these two approaches, they are typically surmised to lack a formal connection and are thus understood as fundamentally different. BNNs are often touted as more principled due to their reliance on the Bayesian paradigm, whereas ensembles are perceived as more ad-hoc; yet, deep ensembles tend to empirically outperform BNNs, with no satisfying explanation as to why this is the case. In this work we bridge this gap by showing that deep ensembles perform exact Bayesian averaging with a posterior obtained with an implicitly learned data-dependent prior. In other words deep ensembles are Bayesian, or more specifically, they implement an empirical Bayes procedure wherein the prior is learned from the data. This perspective offers two main benefits: (i) it theoretically justifies deep ensembles and thus provides an explanation for their strong empirical performance; and (ii) inspection of the learned prior reveals it is given by a mixture of point masses -- the use of such a strong prior helps elucidate observed phenomena about ensembles. Overall, our work delivers a newfound understanding of deep ensembles which is not only of interest in it of itself, but which is also likely to generate future insights that drive empirical improvements for these models.

Exponential Family Attention

The self-attention mechanism is the backbone of the transformer neural network underlying most large language models. It can capture complex word patterns and long-range dependencies in natural language. This paper introduces exponential family attention (EFA), a probabilistic generative model that extends self-attention to handle high-dimensional sequence, spatial, or spatial-temporal data of mixed data types, including both discrete and continuous observations. The key idea of EFA is to model each observation conditional on all other existing observations, called the context, whose relevance is learned in a data-driven way via an attention-based latent factor model. In particular, unlike static latent embeddings, EFA uses the self-attention mechanism to capture dynamic interactions in the context, where the relevance of each context observations depends on other observations. We establish an identifiability result and provide a generalization guarantee on excess loss for EFA. Across real-world and synthetic data sets -- including U.S. city temperatures, Instacart shopping baskets, and MovieLens ratings -- we find that EFA consistently outperforms existing models in capturing complex latent structures and reconstructing held-out data.

Posterior Mean Matching: Generative Modeling through Online Bayesian Inference

This paper introduces posterior mean matching (PMM), a new method for generative modeling that is grounded in Bayesian inference. PMM uses conjugate pairs of distributions to model complex data of various modalities like images and text, offering a flexible alternative to existing methods like diffusion models. PMM models iteratively refine noisy approximations of the target distribution using updates from online Bayesian inference. PMM is flexible because its mechanics are based on general Bayesian models. We demonstrate this flexibility by developing specialized examples: a generative PMM model of real-valued data using the Normal-Normal model, a generative PMM model of count data using a Gamma-Poisson model, and a generative PMM model of discrete data using a Dirichlet-Categorical model. For the Normal-Normal PMM model, we establish a direct connection to diffusion models by showing that its continuous-time formulation converges to a stochastic differential equation (SDE). Additionally, for the Gamma-Poisson PMM, we derive a novel SDE driven by a Cox process, which is a significant departure from traditional Brownian motion-based generative models. PMMs achieve performance that is competitive with generative models for language modeling and image generation.

Adaptive Nonparametric Perturbations of Parametric Bayesian Models

Parametric Bayesian modeling offers a powerful and flexible toolbox for scientific data analysis. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we study nonparametrically perturbed parametric (NPP) Bayesian models, in which a parametric Bayesian model is relaxed via a distortion of its likelihood. We analyze the properties of NPP models when the target of inference is the true data distribution or some functional of it, such as in causal inference. We show that NPP models can offer the robustness of nonparametric models while retaining the data efficiency of parametric models, achieving fast convergence when the parametric model is close to true. To efficiently analyze data with an NPP model, we develop a generalized Bayes procedure to approximate its posterior. We demonstrate our method by estimating causal effects of gene expression from single cell RNA sequencing data. NPP modeling offers an efficient approach to robust Bayesian inference and can be used to robustify any parametric Bayesian model.

Ordinal Preference Optimization: Aligning Human Preferences via NDCG

Aligning Large Language Models (LLMs) with diverse human preferences is a pivotal technique for controlling model behaviors and enhancing generation quality. Reinforcement Learning from Human Feedback (RLHF), Direct Preference Optimization (DPO), and their variants optimize language models by pairwise comparisons. However, when multiple responses are available, these approaches fall short of leveraging the extensive information in the ranking given by the reward models or human feedback. In this work, we propose a novel listwise approach named Ordinal Preference Optimization (OPO), which employs the Normalized Discounted Cumulative Gain (NDCG), a widely-used ranking metric, to better utilize relative proximity within ordinal multiple responses. We develop an end-to-end preference optimization algorithm by approximating NDCG with a differentiable surrogate loss. This approach builds a connection between ranking models in information retrieval and the alignment problem. In aligning multi-response datasets assigned with ordinal rewards, OPO outperforms existing pairwise and listwise approaches on evaluation sets and general benchmarks like AlpacaEval. Moreover, we demonstrate that increasing the pool of negative samples can enhance model performance by reducing the adverse effects of trivial negatives.

Brain-Cognition Fingerprinting via Graph-GCCA with Contrastive Learning

Many longitudinal neuroimaging studies aim to improve the understanding of brain aging and diseases by studying the dynamic interactions between brain function and cognition. Doing so requires accurate encoding of their multidimensional relationship while accounting for individual variability over time. For this purpose, we propose an unsupervised learning model (called \underline{\textbf{Co}}ntrastive Learning-based \underline{\textbf{Gra}}ph Generalized \underline{\textbf{Ca}}nonical Correlation Analysis (CoGraCa)) that encodes their relationship via Graph Attention Networks and generalized Canonical Correlational Analysis. To create brain-cognition fingerprints reflecting unique neural and cognitive phenotype of each person, the model also relies on individualized and multimodal contrastive learning. We apply CoGraCa to longitudinal dataset of healthy individuals consisting of resting-state functional MRI and cognitive measures acquired at multiple visits for each participant. The generated fingerprints effectively capture significant individual differences and outperform current single-modal and CCA-based multimodal models in identifying sex and age. More importantly, our encoding provides interpretable interactions between those two modalities.