UAI 2023 Papers

We focus on the learning of generalized neural policies for Relational Markov Decision Processes (RMDPs) expressed in RDDL. Recent work first converts the instances of a relational domain into an instance graph, and then trains a Graph Attention Network (GAT) of fixed depth with parameters shared across instances to learn a state representation, which can be decoded to get the policy [sharma et al., 22]. Unfortunately, this approach struggles to learn policies that exploit long-range dependencies – a fact we formally prove in this paper. As a remedy, we first construct a novel influence graph characterized by edges capturing one-step influence (dependence) between nodes based on the transition model. We then define influence distance between two nodes as the shortest path between them in this graph – a feature we exploit to represent long-range dependencies. We show that our architecture, referred to as Symbolic Influence Network (SymNet3.0), with its distance-based features, does not suffer from the representational issues faced by earlier approaches. Extensive experimentation demonstrates that we are competitive with existing baselines on 12 standard IPPC domains, and perform significantly better on six additional domains (including IPPC variants), designed to test a model’s capability in capturing long-range dependencies. Further analysis shows that SymNet3.0 automatically learns to focus on nodes that have key information for representing policies that capture long-range dependencies.

Conducting valid statistical analyses is challenging in the presence of missing-not-at-random (MNAR) data, where the missingness mechanism is dependent on the missing values themselves even conditioned on the observed data. Here, we consider a MNAR model that generalizes several prior popular MNAR models in two ways: first, it is less restrictive in terms of statistical independence assumptions imposed on the underlying joint data distribution, and second, it allows for all variables in the observed sample to have missing values. This MNAR model corresponds to a so-called criss-cross structure considered in the literature on graphical models of missing data that prevents nonparametric identification of the entire missing data model. Nonetheless, part of the complete-data distribution remains nonparametrically identifiable. By exploiting this fact and considering a rich class of exponential family distributions, we establish sufficient conditions for identification of the complete-data distribution as well as the entire missingness mechanism. We then propose methods for testing the independence restrictions encoded in such models using odds ratio as our parameter of interest. We adopt two semiparametric approaches for estimating the odds ratio parameter and establish the corresponding asymptotic theories: one involves maximizing a conditional likelihood with order statistics and the other uses estimating equations. The utility of our methods is illustrated via simulation studies.

Sampling subgraphs for training Graph Neural Networks (GNNs) is receiving much attention from the GNN community. While a variety of methods have been proposed, each method samples the graph according to its own heuristic. However, there has been little work in mixing these heuristics in an end-to-end trainable manner. In this work, we design a generative framework for graph sampling. Our method, SubMix, parameterizes subgraph sampling as a convex combination of heuristics. We show that a continuous relaxation of the discrete sampling process allows us to efficiently obtain analytical gradients for training the sampling parameters. Our experimental results illustrate the usefulness of learning graph sampling in three scenarios: (1) robust training of GNNs by automatically learning to discard noisy edge sources; (2) improving model performance by trainable and online edge subset selection; and (3) by integrating our framework into decoupled GNN models improves their performance on standard benchmarks.

By recursively summing node features over entire neighborhoods, spatial graph convolution operators have been heralded as key to the success of Graph Neural Networks (GNNs). Yet, despite the multiplication of GNN methods across tasks and applications, the effect of this aggregation operation has yet to be analyzed. In fact, while most recent efforts in the GNN community have focused on optimizing the architecture of the neural network, fewer works have attempted to characterize

Certifying the robustness of a graph-based machine learning model poses a critical challenge for safety. Current robustness certificates for graph classifiers guarantee output invariance with respect to the total number of node pair flips (edge addition or edge deletion), which amounts to an {$l_{0}$} ball centred on the adjacency matrix. Although theoretically attractive, this type of isotropic structural noise can be too restrictive in practical scenarios where some node pairs are more critical than others in determining the classifier’s output. The certificate, in this case, gives a pessimistic depiction of the robustness of the graph model. To tackle this issue, we develop a randomised smoothing method based on adding an anisotropic noise distribution to the input graph structure. We show that our process generates structural-aware certificates for our classifiers, whereby the magnitude of robustness certificates can vary across different pre-defined structures of the graph. We demonstrate the benefits of these certificates in both synthetic and real-world experiments.

We consider stochastic graphical bandits, where after pulling an arm, the decision maker observes rewards of not only the chosen arm but also its neighbors in a feedback graph. Most of existing work assumes that the rewards are drawn from bounded or at least sub-Gaussian distributions, which however may be violated in many practical scenarios such as social advertising and financial markets. To settle this issue, we investigate stochastic graphical bandits with heavy-tailed rewards, where the distributions have finite moments of order $1+\epsilon$, for some $\epsilon\in(0, 1]$. Firstly, we develop one UCB-type algorithm, whose expected regret is upper bounded by a sum of gap-based quantities over the

Generative Flow Networks (or GFlowNets for short) are a family of probabilistic agents that learn to sample complex combinatorial structures through the lens of “inference as control”. They have shown great potential in generating high-quality and diverse candidates from a given energy landscape. However, existing GFlowNets can be applied only to deterministic environments, and fail in more general tasks with stochastic dynamics, which can limit their applicability. To overcome this challenge, this paper introduces Stochastic GFlowNets, a new algorithm that extends GFlowNets to stochastic environments. By decomposing state transitions into two steps, Stochastic GFlowNets isolate environmental stochasticity and learn a dynamics model to capture it. Extensive experimental results demonstrate that Stochastic GFlowNets offer significant advantages over standard GFlowNets as well as MCMC- and RL-based approaches, on a variety of standard benchmarks with stochastic dynamics.

We describe a simple two-party protocol in which each party contributes a set as input. The output of the protocol is an estimate of the cardinality of the intersection of the two input sets. We show that our protocol is efficient and secure. We show that the space complexity and communication complexity are constant, the time complexity for each party is proportional to the size of their input set, and that our protocol is differentially private. We also analyze the distribution of the output of the protocol, deriving both its asymptotic distribution and finite-sample bounds on its tail probabilities. These analyses show that, when the input sets are large, our protocol produces accurate set intersection cardinality estimates. We claim that our protocol is an attractive alternative to traditional private set intersection cardinality (PSI-CA) protocols when the input sets are large, exact precision is not required, and differential privacy on its own can provide sufficient protection to the underlying sensitive data.

Multi-model Markov decision process (MMDP) is a promising framework for computing policies that are robust to parameter uncertainty in MDPs. MMDPs aim to find a policy that maximizes the expected return over a distribution of MDP models. Because MMDPs are NP-hard to solve, most methods resort to approximations. In this paper, we derive the policy gradient of MMDPs and propose CADP, which combines a coordinate ascent method and a dynamic programming algorithm for solving MMDPs. The main innovation of CADP compared with earlier algorithms is to take the coordinate ascent perspective to adjust model weights iteratively to guarantee monotone policy improvements to a local maximum. A theoretical analysis of CADP proves that it never performs worse than previous dynamic programming algorithms like WSU. Our numerical results indicate that CADP substantially outperforms existing methods on several benchmark problems.

We investigate the problems of maximizing k-submodular functions over total size constraints and over individual size constraints. k-submodularity is a generalization of submodularity beyond just picking items of a ground set, instead associating one of k types to chosen items. For sensor selection problems, for instance, this enables modeling of which type of sensor to put at a location, not simply whether to put a sensor or not. We propose and analyze threshold-greedy algorithms for both types of constraints. We prove that our proposed algorithms achieve the best known approximation ratios for both constraint types, up to a user-chosen parameter that balances computational complexity and the approximation ratio, while only using a number of function evaluations that depends linearly (up to poly-logarithmic terms) on the number of elements n, the number of types k, and the inverse of the user chosen parameter. Other algorithms that achieve the best-known deterministic approximation ratios require a number of function evaluations that depends linearly on the budget B, while our methods do not. We empirically demonstrate our algorithms’ performance in applications of sensor placement with k types and influence maximization with k topics.

We consider transferability estimation, the problem of estimating how well deep learning models transfer from a source to a target task. We focus on regression tasks, which received little previous attention, and propose two simple and computationally efficient approaches that estimate transferability based on the negative regularized mean squared error of a linear regression model. We prove novel theoretical results connecting our approaches to the actual transferability of the optimal target models obtained from the transfer learning process. Despite their simplicity, our approaches significantly outperform existing state-of-the-art regression transferability estimators in both accuracy and efficiency. On two large-scale keypoint regression benchmarks, our approaches yield 12% to 36% better results on average while being at least 27% faster than previous state-of-the-art methods.

The evolution of many dynamical systems is generically governed by nonlinear partial differential equations (PDEs), whose solution, in a simulation framework, requires vast amounts of computational resources. In this work, we present a novel method that combines a hyper-network solver with a Fourier Neural Operator architecture. Our method treats time and space separately and as a result, it successfully propagates initial conditions in continuous time steps by employing the general composition properties of the partial differential operators. Following previous works, supervision is provided at a specific time point. We test our method on various time evolution PDEs, including nonlinear fluid flows in one, two, or three spatial dimensions. The results show that the new method improves the learning accuracy at the time of the supervision point, and can interpolate the solutions to any intermediate time.

Distributions on integers are ubiquitous in probabilistic modeling but remain challenging for many of today’s probabilistic programming languages (PPLs). The core challenge comes from discrete structure: many of today’s PPL inference strategies rely on enumeration, sampling, or differentiation in order to scale, which fail for high-dimensional complex discrete distributions involving integers. Our insight is that there is structure in arithmetic that these approaches are not using. We present a binary encoding strategy for discrete distributions that exploits the rich logical structure of integer operations like summation and comparison. We leverage this structured encoding with knowledge compilation to perform exact probabilistic inference, and show that this approach scales to much larger integer distributions with arithmetic.

Learning and understanding heterogeneous patterns in complex spatio-temporal data is an important and challenging task across domains in science and engineering. In this work, we develop a model for learning heterogeneous and dynamic patterns of velocity field data, motivated by applications in the transportation domain. We draw from basic nonparametric Bayesian modeling elements such as the infinite hidden Markov model and Gaussian process and focus on making the learning of such a stochastic model scalable for voluminous and streaming data. This is achieved by employing sequential MAP estimates from the infinite HMM model, an efficient sequential sparse GP posterior computation, and refinement of the estimates using the Viterbi algorithm, which is shown to work effectively on a careful simulation study. We demonstrate the efficacy of our techniques to the NGSIM dataset of complex multi-vehicle interactions.

Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is hindered by prevalent large data sizes, missing entries, and corruption with outliers. In this work, we propose a scalable and robust TR decomposition algorithm capable of handling large-scale tensor data with missing entries and gross corruptions. We first develop a novel auto-weighted steepest descent method that can adaptively fill the missing entries and identify the outliers during the decomposition process. Further, taking advantage of the tensor ring model, we develop a novel fast Gram matrix computation (FGMC) approach and a randomized subtensor sketching (RStS) strategy which yield significant reduction in storage and computational complexity. Experimental results demonstrate that the proposed method outperforms existing TR decomposition methods in the presence of outliers, and runs significantly faster than existing robust tensor completion algorithms.

Ensemble methods are a very diverse family of algorithms with a wide range of applications. One of the most commonly used is boosting, with the prominent Adaboost. Adaboost relies on greedily learning base classifiers that rectify the error from previous iterations. Then, it combines them through a weighted majority vote, based on their quality on the entire learning set. In this paper, we propose a supervised binary classification framework that propagates the local knowledge acquired during the boosting iterations to the prediction function. Based on this general framework, we introduce SamBA, an interpretable greedy ensemble method designed for fat datasets, with a large number of dimensions and a small number of samples. SamBA learns local classifiers and combines them, using a similarity function, to optimize its efficiency in data extraction. We provide a theoretical analysis of SamBA, yielding convergence and generalization guarantees. In addition, we highlight SamBA’s empirical behavior in an extensive experimental analysis on both real biological and generated datasets, comparing it to state-of-the-art ensemble methods and similarity-based approaches.

The pre-training and fine-tuning paradigm has contributed to a number of breakthroughs in Natural Language Processing (NLP). Instead of directly training on a downstream task, language models are first pre-trained on large datasets with cross-domain knowledge (e.g., Pile, MassiveText, etc.) and then fine-tuned on task-specific data (e.g., natural language generation, text summarization, etc.). Scaling the model and dataset size has helped improve the performance of LLMs, but unfortunately, this also lead to highly prohibitive computational costs. Pre-training LLMs often require orders of magnitude more FLOPs than fine-tuning and the model capacity often remains the same between the two phases. To achieve training efficiency w.r.t training FLOPs, we propose to decouple the model capacity between the two phases and introduce Sparse Pre-training and Dense Fine-tuning (SPDF). In this work, we show the benefits of using unstructured weight sparsity to train only a subset of weights during pre-training (Sparse Pre-training) and then recover the representational capacity by allowing the zeroed weights to learn (Dense Fine-tuning). We demonstrate that we can induce up to 75% sparsity into a 1.3B parameter GPT-3 XL model resulting in a 2.5x reduction in pre-training FLOPs, without a significant loss in accuracy on the downstream tasks relative to the dense baseline. By rigorously evaluating multiple downstream tasks, we also establish a relationship between sparsity, task complexity and dataset size. Our work presents a promising direction to train large GPT models at a fraction of the training FLOPs using weight sparsity, while retaining the benefits of pre-trained textual representations for downstream tasks.

Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to exploit the entire information encoded in them properly. We address this problem by considering an order based on (sets of) expectations of random variables mapping into such non-standard spaces. This order contains stochastic dominance and expectation order as extreme cases when no, or respectively perfect, cardinal structure is given. We derive a (regularized) statistical test for our proposed generalized stochastic dominance (GSD) order, operationalize it by linear optimization, and robustify it by imprecise probability models. Our findings are illustrated with data from multidimensional poverty measurement, finance, and medicine.

Knowledge distillation is a popular technique that has been shown to produce remarkable gains in average accuracy. However, recent work has shown that these gains are not uniform across subgroups in the data, and can often come at the cost of accuracy on rare subgroups and classes. Robust optimization is a common remedy to improve worst-class accuracy in standard learning settings, but in distillation it is unknown whether it is best to apply robust objectives when training the teacher, the student, or both. This work studies the interplay between robust objectives for the teacher and student. Empirically, we show that that jointly modifying the teacher and student objectives can lead to better worst-class student performance and even Pareto improvement in the trade-off between worst-class and overall performance. Theoretically, we show that the