NeurIPS 2024 Papers

Binary statistical decision making involves choosing between two states based on statistical evidence. The optimal decision strategy is typically formulated through a constrained optimization problem, where both the objective and constraints are expressed as integrals involving two Lebesgue measurable functions, one of which represents the strategy being optimized. In this work, we present a comprehensive formulation of the binary decision making problem and provide a detailed characterization of the optimal solution. Our framework encompasses a wide range of well-known and recently proposed decision making problems as specific cases. We demonstrate how our generic approach can be used to derive the optimal decision strategies for these diverse instances. Our results offer a robust mathematical tool that simplifies the process of solving both existing and novel formulations of binary decision making problems which are in the core of many Machine Learning algorithms.

Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference queries become tractable, such as model counting and most probable configuration. Recent works have explored analyzing probabilistic and causal inference queries as compositions of basic operators to derive tractability conditions. In this paper, we take an algebraic perspective for compositional inference, and show that a large class of queries—including marginal MAP, probabilistic answer set programming inference, and causal backdoor adjustment—correspond to a combination of basic operators over semirings: aggregation, product, and elementwise mapping. Using this framework, we uncover simple and general sufficient conditions for tractable composition of these operators, in terms of circuit properties (e.g., marginal determinism, compatibility) and conditions on the elementwise mappings. Applying our analysis, we derive novel tractability conditions for many such compositional queries. Our results unify tractability conditions for existing problems on circuits, while providing a blueprint for analysing novel compositional inference queries.

We consider Bayesian algorithm execution (BAX), a framework for efficiently selecting evaluation points of an expensive function to infer a property of interest encoded as the output of a base algorithm. Since the base algorithm typically requires more evaluations than are feasible, it cannot be directly applied. Instead, BAX methods sequentially select evaluation points using a probabilistic numerical approach. Current BAX methods use expected information gain to guide this selection. However, this approach is computationally intensive. Observing that, in many tasks, the property of interest corresponds to a target set of points defined by the function, we introduce PS-BAX, a simple, effective, and scalable BAX method based on posterior sampling. PS-BAX is applicable to a wide range of problems, including many optimization variants and level set estimation. Experiments across diverse tasks demonstrate that PS-BAX performs competitively with existing baselines while being significantly faster, simpler to implement, and easily parallelizable, setting a strong baseline for future research. Additionally, we establish conditions under which PS-BAX is asymptotically convergent, offering new insights into posterior sampling as an algorithm design paradigm.

We present a general method for lossless compression of unordered data structures, including multisets and graphs. It is a variant of shuffle coding that is many orders of magnitude faster than the original and enables 'one-shot' compression of single unordered objects. Our method achieves state-of-the-art compression rates on various large-scale network graphs at speeds of megabytes per second, efficiently handling even a multi-gigabyte plain graph with one billion edges. We release an implementation that can be easily adapted to different data types and statistical models.

We present variational inference with sequential sample-average approximations (VISA), a method for approximate inference in computationally intensive models, such as those based on numerical simulations. VISA extends importance-weighted forward-KL variational inference by employing a sequence of sample-average approximations, which are considered valid inside a trust region. This makes it possible to reuse model evaluations across multiple gradient steps, thereby reducing computational cost. We perform experiments on high-dimensional Gaussians, Lotka-Volterra dynamics, and a Pickover attractor, which demonstrate that VISA can achieve comparable approximation accuracy to standard importance-weighted forward-KL variational inference with computational savings of a factor two or more for conservatively chosen learning rates.

Modern neural networks are often massively overparameterized leading to high compute costs during training and at inference. One effective method to improve both the compute and energy efficiency of neural networks while maintaining good performance is structured pruning, where full network structures (e.g. neurons or convolutional filters) that have limited impact on the model output are removed. In this work, we propose Bayesian Model Reduction for Structured pruning (BMRS), a fully end-to-end Bayesian method of structured pruning. BMRS is based on two recent methods: Bayesian structured pruning with multiplicative noise, and Bayesian model reduction (BMR), a method which allows efficient comparison of Bayesian models under a change in prior. We present two realizations of BMRS derived from different priors which yield different structured pruning characteristics: 1) BMRS_N with the truncated log-normal prior, which offers reliable compression rates and accuracy without the need for tuning any thresholds and 2) BMRS_U with the truncated log-uniform prior that can achieve more aggressive compression based on the boundaries of truncation. Overall, we find that BMRS offers a theoretically grounded approach to structured pruning of neural networks yielding both high compression rates and accuracy. Experiments on multiple datasets and neural networks of varying complexity showed that the two BMRS methods offer a competitive performance-efficiency trade-off compared to other pruning methods.

Recently, through a unified gradient flow perspective of Markov chain Monte Carlo (MCMC) and variational inference (VI), particle-based variational inference methods (ParVIs) have been proposed that tend to combine the best of both worlds. While typical ParVIs such as Stein Variational Gradient Descent (SVGD) approximate the gradient flow within a reproducing kernel Hilbert space (RKHS), many attempts have been made recently to replace RKHS with more expressive function spaces, such as neural networks. While successful, these methods are mainly designed for sampling from unconstrained domains. In this paper, we offer a general solution to constrained sampling by introducing a boundary condition for the gradient flow which would confine the particles within the specific domain. This allows us to propose a new functional gradient ParVI method for constrained sampling, called *constrained functional gradient flow* (CFG), with provable continuous-time convergence in total variation (TV). We also present novel numerical strategies to handle the boundary integral term arising from the domain constraints. Our theory and experiments demonstrate the effectiveness of the proposed framework.

Bayesian Optimization (BO) has proven to be very successful at optimizing a static, noisy, costly-to-evaluate black-box function $f : \mathcal{S} \to \mathbb{R}$. However, optimizing a black-box which is also a function of time (*i.e.*, a *dynamic* function) $f : \mathcal{S} \times \mathcal{T} \to \mathbb{R}$ remains a challenge, since a dynamic Bayesian Optimization (DBO) algorithm has to keep track of the optimum over time. This changes the nature of the optimization problem in at least three aspects: (i) querying an arbitrary point in $\mathcal{S} \times \mathcal{T}$ is impossible, (ii) past observations become less and less relevant for keeping track of the optimum as time goes by and (iii) the DBO algorithm must have a high sampling frequency so it can collect enough relevant observations to keep track of the optimum through time. In this paper, we design a Wasserstein distance-based criterion able to quantify the relevancy of an observation with respect to future predictions. Then, we leverage this criterion to build W-DBO, a DBO algorithm able to remove irrelevant observations from its dataset on the fly, thus maintaining simultaneously a good predictive performance and a high sampling frequency, even in continuous-time optimization tasks with unknown horizon. Numerical experiments establish the superiority of W-DBO, which outperforms state-of-the-art methods by a comfortable margin.

We present a theoretical analysis of the Elo rating system, a popular method for ranking skills of players in an online setting. In particular, we study Elo under the Bradley-Terry-Luce model and, using techniques from Markov chain theory, show that Elo learns the model parameters at a rate competitive with the state-of-the-art. We apply our results to the problem of efficient tournament design and discuss a connection with the fastest-mixing Markov chain problem.

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.

Determinantal point processes (DPPs) are random configurations of points with tunable negative dependence. Because sampling is tractable, DPPs are natural candidates for subsampling tasks, such as minibatch selection or coreset construction. A \emph{coreset} is a subset of a (large) training set, such that minimizing an empirical loss averaged over the coreset is a controlled replacement for the intractable minimization of the original empirical loss. Typically, the control takes the form of a guarantee that the average loss over the coreset approximates the total loss uniformly across the parameter space. Recent work has provided significant empirical support in favor of using DPPs to build randomized coresets, coupled with interesting theoretical results that are suggestive but leave some key questions unanswered. In particular, the central question of whether the cardinality of a DPP-based coreset is fundamentally smaller than one based on independent sampling remained open. In this paper, we answer this question in the affirmative, demonstrating that \emph{DPPs can provably outperform independently drawn coresets}. In this vein, we contribute a conceptual understanding of coreset loss as a \emph{linear statistic} of the (random) coreset. We leverage this structural observation to connect the coresets problem to a more general problem of concentration phenomena for linear statistics of DPPs, wherein we obtain \emph{effective concentration inequalities that extend well-beyond the state-of-the-art}, encompassing general non-projection, even non-symmetric kernels. The latter have been recently shown to be of interest in machine learning beyond coresets, but come with a limited theoretical toolbox, to the extension of which our result contributes. Finally, we are also able to address the coresets problem for vector-valued objective functions, a novelty in the coresets literature.

Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of nonstationary kernels. This technique relaxes the constraints on kernel types and stationarity, allowing for more flexible modeling while reducing computational complexity to the linear level. Additionally, we introduce a deep kernel variant by hierarchically stacking multiple spectral feature mappings, further enhancing the model's expressiveness to capture complex patterns in data. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of our approach, particularly in scenarios with pronounced data nonstationarity. Additionally, ablation studies are conducted to provide insights into the impact of various hyperparameters on model performance.

Reliable prediction of protein variant effects is crucial for both protein optimization and for advancing biological understanding. For practical use in protein engineering, it is important that we can also provide reliable uncertainty estimates for our predictions, and while prediction accuracy has seen much progress in recent years, uncertainty metrics are rarely reported. We here provide a Gaussian process regression model, Kermut, with a novel composite kernel for modeling mutation similarity, which obtains state-of-the-art performance for supervised protein variant effect prediction while also offering estimates of uncertainty through its posterior. An analysis of the quality of the uncertainty estimates demonstrates that our model provides meaningful levels of overall calibration, but that instance-specific uncertainty calibration remains more challenging.

Despite the success of contrastive learning (CL) in vision and language, its theoretical foundations and mechanisms for building representations remain poorly understood. In this work, we build connections between noise contrastive estimation losses widely used in CL and distribution alignment with entropic optimal transport (OT). This connection allows us to develop a family of different losses and multistep iterative variants for existing CL methods. Intuitively, by using more information from the distribution of latents, our approach allows a more distribution-aware manipulation of the relationships within augmented sample sets. We provide theoretical insights and experimental evidence demonstrating the benefits of our approach for generalized contrastive alignment. Through this framework, it is possible to leverage tools in OT to build unbalanced losses to handle noisy views and customize the representation space by changing the constraints on alignment. By reframing contrastive learning as an alignment problem and leveraging existing optimization tools for OT, our work provides new insights and connections between different self-supervised learning models in addition to new tools that can be more easily adapted to incorporate domain knowledge into learning.

Recently developed quasi-Bayesian (QB) methods \cite{fong2023martingale} proposed a stimulating change of paradigm in Bayesian computation by directly constructing the Bayesian predictive distribution through recursion, removing the need for expensive computations involved in sampling the Bayesian posterior distribution. This has proved to be data-efficient for univariate predictions, however, existing constructions for higher dimensional densities are only possible by relying on restrictive assumptions on the model's multivariate structure. Here, we propose a wholly different approach to extend Quasi-Bayesian prediction to high dimensions through the use of Sklar's theorem, by decomposing the predictive distribution into one-dimensional predictive marginals and a high-dimensional copula. We use the efficient recursive QB construction for the one-dimensional marginals and model the dependence using highly expressive vine copulas. Further, we tune hyperparameters using robust divergences (eg. energy score) and show that our proposed Quasi-Bayesian Vine (QB-Vine) is a fully non-parametric density estimator with \emph{an analytical form} and convergence rate independent of the dimension of the data in some situations. Our experiments illustrate that the QB-Vine is appropriate for high dimensional distributions ($\sim$64), needs very few samples to train ($\sim$200) and outperforms state-of-the-art methods with analytical forms for density estimation and supervised tasks by a considerable margin.

Diffusion models have emerged as effective distribution estimators in vision, language, and reinforcement learning, but their use as priors in downstream tasks poses an intractable posterior inference problem. This paper studies *amortized* sampling of the posterior over data, $\mathbf{x}\sim p^{\rm post}(\mathbf{x})\propto p(\mathbf{x})r(\mathbf{x})$, in a model that consists of a diffusion generative model prior $p(\mathbf{x})$ and a black-box constraint or likelihood function $r(\mathbf{x})$. We state and prove the asymptotic correctness of a data-free learning objective, *relative trajectory balance*, for training a diffusion model that samples from this posterior, a problem that existing methods solve only approximately or in restricted cases. Relative trajectory balance arises from the generative flow network perspective on diffusion models, which allows the use of deep reinforcement learning techniques to improve mode coverage. Experiments illustrate the broad potential of unbiased inference of arbitrary posteriors under diffusion priors: in vision (classifier guidance), language (infilling under a discrete diffusion LLM), and multimodal data (text-to-image generation). Beyond generative modeling, we apply relative trajectory balance to the problem of continuous control with a score-based behavior prior, achieving state-of-the-art results on benchmarks in offline reinforcement learning. Code is available at [this link](https://github.com/GFNOrg/diffusion-finetuning).

Conformal Prediction (CP) is a distribution-free uncertainty estimation framework that constructs prediction sets guaranteed to contain the true answer with a user-specified probability. Intuitively, the size of the prediction set encodes a general notion of uncertainty, with larger sets associated with higher degrees of uncertainty. In this work, we leverage information theory to connect conformal prediction to other notions of uncertainty. More precisely, we prove three different ways to upper bound the intrinsic uncertainty, as described by the conditional entropy of the target variable given the inputs, by combining CP with information theoretical inequalities. Moreover, we demonstrate two direct and useful applications of such connection between conformal prediction and information theory: (i) more principled and effective conformal training objectives that generalize previous approaches and enable end-to-end training of machine learning models from scratch, and (ii) a natural mechanism to incorporate side information into conformal prediction. We empirically validate both applications in centralized and federated learning settings, showing our theoretical results translate to lower inefficiency (average prediction set size) for popular CP methods.

Convergence rate analysis for general state-space Markov chains is fundamentally important in operations research (stochastic systems) and machine learning (stochastic optimization). This problem, however, is notoriously difficult because traditional analytical methods often do not generate practically useful convergence bounds for realistic Markov chains. We propose the Deep Contractive Drift Calculator (DCDC), the first general-purpose sample-based algorithm for bounding the convergence of Markov chains to stationarity in Wasserstein distance. The DCDC has two components. First, inspired by the new convergence analysis framework in (Qu et.al, 2023), we introduce the Contractive Drift Equation (CDE), the solution of which leads to an explicit convergence bound. Second, we develop an efficient neural-network-based CDE solver. Equipped with these two components, DCDC solves the CDE and converts the solution into a convergence bound. We analyze the sample complexity of the algorithm and further demonstrate the effectiveness of the DCDC by generating convergence bounds for realistic Markov chains arising from stochastic processing networks as well as constant step-size stochastic optimization.

Computer simulations have long presented the exciting possibility of scientific insight into complex real-world processes. Despite the power of modern computing, however, it remains challenging to systematically perform inference under simulation models. This has led to the rise of simulation-based inference (SBI), a class of machine learning-enabled techniques for approaching inverse problems with stochastic simulators. Many such methods, however, require large numbers of simulation samples and face difficulty scaling to high-dimensional settings, often making inference prohibitive under resource-intensive simulators. To mitigate these drawbacks, we introduce active sequential neural posterior estimation (ASNPE). ASNPE brings an active learning scheme into the inference loop to estimate the utility of simulation parameter candidates to the underlying probabilistic model. The proposed acquisition scheme is easily integrated into existing posterior estimation pipelines, allowing for improved sample efficiency with low computational overhead. We further demonstrate the effectiveness of the proposed method in the travel demand calibration setting, a high-dimensional inverse problem commonly requiring computationally expensive traffic simulators. Our method outperforms well-tuned benchmarks and state-of-the-art posterior estimation methods on a large-scale real-world traffic network, as well as demonstrates a performance advantage over non-active counterparts on a suite of SBI benchmark environments.