UAI 2022 Papers

We propose a neural network architecture that enables non-parametric calibration and generation of multivariate extreme value distributions (MEVs). MEVs arise from Extreme Value Theory (EVT) as the necessary class of models when extrapolating a distributional fit over large spatial and temporal scales based on data observed in intermediate scales. In turn, EVT dictates that $d$-max-decreasing, a stronger form of convexity, is an essential shape constraint in the characterization of MEVs. As far as we know, our proposed architecture provides the first class of non-parametric estimators for MEVs that preserve these essential shape constraints. We show that the architecture approximates the dependence structure encoded by MEVs at parametric rate. Moreover, we present a new method for sampling high-dimensional MEVs using a generative model. We demonstrate our methodology on a wide range of experimental settings, ranging from environmental sciences to financial mathematics and verify that the structural properties of MEVs are retained compared to existing methods.

Increasing interest in privacy-preserving machine learning has led to new and evolved approaches for generating private synthetic data from undisclosed real data. However, mechanisms of privacy preservation can significantly reduce the utility of synthetic data, which in turn impacts downstream tasks such as learning predictive models or inference. We propose several re-weighting strategies using privatised likelihood ratios that not only mitigate statistical bias of downstream estimators but also have general applicability to differentially private generative models. Through large-scale empirical evaluation, we show that private importance weighting provides simple and effective privacy-compliant augmentation for general applications of synthetic data.

Existing meta-learning works assume that each task has available training and testing data. However, there are many available pre-trained models without accessing their training data in practice. We often need a single model to solve different tasks simultaneously as this is much more convenient to deploy the models. Our work aims to meta-learn a model initialization from these pre-trained models without using corresponding training data. We name this challenging problem setting as Data-Free Learning To Learn (DFL2L). We propose a distributionally robust optimization (DRO) framework to learn a black-box model to fuse and compress all the pre-trained models into a single network to address this problem. To encourage good generalization to the unseen new tasks, the proposed DRO framework diversifies the learned task embedding associated with each pre-trained model to cover the diversity in the underlying training task distributions. A model initialization is sampled from the black-box network during meta-testing as the meta learned initialization. Extensive experiments on offline and online DFL2L settings and several real image datasets demonstrate the effectiveness of the proposed methods.

We consider the problem of learning the behavioral preferences of an expert engaged in a task from noisy and partially-observable demonstrations. This is motivated by real-world applications such as a line robot learning from observing a human worker, where some observations are occluded by environmental elements. Furthermore, robotic perception tends to be imperfect and noisy. Previous techniques for inverse reinforcement learning (IRL) take the approach of either omitting the missing portions or inferring it as part of expectation-maximization, which tends to be slow and prone to local optima. We present a new method that generalizes the well-known Bayesian maximum-a-posteriori (MAP) IRL method by marginalizing the occluded portions of the trajectory. This is then extended with an observation model to account for perception noise. This novel application of marginal MAP (MMAP) to IRL significantly improves on the previous IRL technique under occlusion in both formative evaluations on a toy problem and in a summative evaluation on a produce sorting line task by a physical robot.

Low precision arithmetic has had a transformative effect on the training of neural networks, reducing computation, memory and energy requirements. However, despite their promise, low precision operations have received little attention for Gaussian process (GP) training, largely because GPs require sophisticated linear algebra routines that are unstable in low precision. We study the different failure modes that can occur when training GPs in half-precision. To circumvent these failure modes, we propose a multi-faceted approach involving conjugate gradients with re-orthogonalization, mixed precision, compact kernels, and preconditioners. Our approach significantly improves the numerical stability and practical performance of conjugate gradients in low precision over a wide range of settings, and reduces the runtime of 1.8 million data points to 10 hours on a single GPU, without requiring any sparse approximations.

Probabilistic classifiers output confidence scores along with their predictions, and these confidence scores should be calibrated, i.e., they should reflect the reliability of the prediction. Confidence scores that minimize standard metrics such as the expected calibration error (ECE) accurately measure the reliability \textit{on average} across the entire population. However, it is in general impossible to measure the reliability of an \textit{individual} prediction. In this work, we propose the local calibration error (LCE) to span the gap between average and individual reliability. For each individual prediction, the LCE measures the average reliability of a set of similar predictions, where similarity is quantified by a kernel function on a pretrained feature space and by a binning scheme over predicted model confidences. We show theoretically that the LCE can be estimated sample-efficiently from data, and empirically find that it reveals miscalibration modes that are more fine-grained than the ECE can detect. Our key result is a novel {\textbf{lo}cal \textbf{re}calibration} method \method{}, to improve confidence scores for individual predictions and decrease the LCE. Experimentally, we show that our recalibration method produces more accurate confidence scores, which improves downstream fairness and decision making on classification tasks with both image and tabular data.

In many real-world applications of multi-armed bandit problems, both rewards and contexts are often influenced by confounding latent variables which evolve stochastically over time. While the observed contexts and rewards are nonlinearly related, we show that prior knowledge of latent causal structure can be used to reduce the problem to the linear bandit setting. We develop two algorithms, Latent Linear Thompson Sampling (L2TS) and Latent Linear UCB (L2UCB), which use online EM algorithms for hidden Markov models to learn the latent transition model and maintain a posterior belief over the latent state, and then use the resulting posteriors as context features in a linear bandit problem. We upper bound the error in reward estimation in the presence of a dynamical latent state, and derive a novel problem-dependent regret bound for linear Thompson sampling with non-stationarity and unconstrained reward distributions, which we apply to L2TS under certain conditions. Finally, we demonstrate the superiority of our algorithms over related bandit algorithms through experiments.

A decentralised partially observable Markov decision problem (DecPOMDP) formalises collaborative multi-agent decision making. A solution to a DecPOMDP is a joint policy for the agents, fulfilling an optimality criterion such as maximum expected utility. A crux is that the problem is intractable regarding the number of agents. Inspired by lifted inference, this paper examines symmetries within the agent set for a potential tractability. Specifically, this paper contributes (i) specifications of counting and isomorphic symmetries, (ii) a compact encoding of symmetric DecPOMDPs as partitioned DecPOMDPs, and (iii) a formal analysis of complexity and tractability. This works allows tractability in terms of agent numbers and a new query type for isomorphic DecPOMDPs.

This paper deals with preference elicitation within Choquet Expected Utility (CEU) theory for decision making under uncertainty. We consider the Savage’s framework with a finite set of states and assume that preferences of the Decision Maker over acts are observable. The CEU model involves two parameters that must be tuned to the value system of the decision maker: a set function (capacity) modeling weights attached to events, of size exponential in the number of states, and a utility function defined on the space of outcomes. Our aim is to learn a sparse representation of the CEU model from preference data. We propose and test a preference learning approach based on a spline representation of utilities and the sparse learning of capacities to obtain CEU models achieving a good tradeoff between the aim of sparsity and the expressivity required by preference data.

Complex systems often contain feedback loops that can be described as cyclic causal models. Intervening in such systems may lead to counterintuitive effects, which cannot be inferred directly from the graph structure. After establishing a framework for differentiable soft interventions based on Lie groups, we take advantage of modern automatic differentiation techniques and their application to implicit functions in order to optimize interventions in cyclic causal models. We illustrate the use of this framework by investigating scenarios of transition to sustainable economies.

In the context of graphical causal discovery, we adapt the versatile framework of linear non-Gaussian acyclic models (LiNGAMs) to propose new algorithms to efficiently learn graphs that are polytrees. Our approach combines the Chow–Liu algorithm, which first learns the undirected tree structure, with novel schemes to orient the edges. The orientation schemes assess algebraic relations among moments of the data-generating distribution and are computationally inexpensive. We establish high-dimensional consistency results for our approach and compare different algorithmic versions in numerical experiments.

We propose a new score-based algorithm for learning the structure of a Bayesian Network (BN). It is the first algorithm that simultaneously supports the requirements of (i) learning a BN of bounded treewidth, (ii) satisfying expert constraints, including positive and negative ancestry properties between nodes, and (iii) scaling up to BNs with several thousand nodes. The algorithm operates in two phases. In Phase 1, we utilize a modified version of an existing BN structure learning algorithm, modified to generate an initial Directed Acyclic Graph (DAG) that supports a portion of the given constraints. In Phase 2, we follow the BN-SLIM framework, introduced by Peruvemba Ramaswamy and Szeider (AAAI 2021). We improve the initial DAG by repeatedly running a MaxSAT solver on selected local parts. The MaxSAT encoding entails local versions of the expert constraints as hard constraints. We evaluate a prototype implementation of our algorithm on several standard benchmark sets. The encouraging results demonstrate the power and flexibility of the BN-SLIM framework. It boosts the score while increasing the number of satisfied expert constraints.

Assumptions about invariances or symmetries in data can significantly increase the predictive power of statistical models. Many commonly used machine learning models are constraint to respect certain symmetries, such as translation equivariance in convolutional neural networks, and incorporating other symmetry types is actively being studied. Yet, learning invariances from the data itself remains an open research problem. It has been shown that the marginal likelihood offers a principled way to learn invariances in Gaussian Processes. We propose a weight-space equivalent to this approach, by minimizing a lower bound on the marginal likelihood to learn invariances in neural networks, resulting in naturally higher performing models.

In this paper, we study the learning problem in two-player general-sum Markov Games. We consider the online setting where we control a single player, playing against an arbitrary opponent to minimize the regret. Previous works only consider the zero-sum Markov Games setting, in which the two agents are completely adversarial. However, in some cases, the two agents may have different reward functions without having conflicting objectives. This involves a stronger notion of regret than the one used in previous works. This class of games, called general-sum Markov Games is far to be well understood and studied. We show that the new regret minimization problem is significantly harder than in standard Markov Decision Processes and zero-sum Markov Games. To do this, we derive a lower bound on the expected regret of any “good” learning strategy which shows the constant dependencies with the number of deterministic policies, which is not present in zerosum Markov Games and Markov Decision Processes. Then we propose a novel optimistic algorithm that nearly matches the proposed lower bound. Proving these results requires overcoming several new challenges that are not present in Markov Decision Processes or zero-sum Markov Games.

We propose a general deep architecture for learning functions on multiple permutation-invariant sets. We also show how to generalize this architecture to sets of elements of any dimension by dimension equivariance. We demonstrate that our architecture is a universal approximator of these functions, and show superior results to existing methods on a variety of tasks including counting tasks, alignment tasks, distinguishability tasks and statistical distance measurements. This last task is quite important in Machine Learning. Although our approach is quite general, we demonstrate that it can generate approximate estimates of KL divergence and mutual information that are more accurate than previous techniques that are specifically designed to approximate those statistical distances.

Templated graphical models (TGMs) encode model structure using rules that capture recurring relationships between multiple random variables. While the rules in TGMs are interpretable, it is not clear how they can be used to generate explanations for the individual predictions of the model. Further, learning these rules from data comes with high computational costs: it typically requires an expensive combinatorial search over the space of rules and repeated optimization over rule weights. In this work, we propose a new structure learning algorithm, Explainable Structured Model Search (ESMS), that learns a templated graphical model and an explanation framework for its predictions. ESMS uses a novel search procedure to efficiently search the space of models and discover models that trade-off predictive accuracy and explainability. We introduce the notion of relational stability and prove that our proposed explanation framework is stable. Further, our proposed piecewise pseudolikelihood (PPLL) objective does not require re-optimizing the rule weights across models during each iteration of the search. In our empirical evaluation on three realworld datasets, we show that our proposed approach not only discovers models that are explainable, but also significantly outperforms existing state-out-the-art structure learning approaches.

Network games are a natural modeling framework for strategic interactions of agents whose actions have local impact on others. Recently, a multi-scale network game model has been proposed to capture local effects at multiple network scales, such as among both individuals and groups. We propose a framework to learn the utility functions of binary multi-scale games from agents’ behavioral data. Departing from much prior work in this area, we model agent behavior as following logit-response dynamics, rather than acting according to a Nash equilibrium. This defines a generative time-series model of joint behavior of both agents and groups, which enables us to naturally cast the learning problem as maximum likelihood estimation (MLE). We show that in the important special case of multi-scale linear-quadratic games, this MLE problem is convex. Extensive experiments using both synthetic and real data demonstrate that our proposed modeling and learning approach is effective in both game parameter estimation as well as prediction of future behavior, even when we learn the game from only a single behavior time series. Furthermore, we show how to use our framework to develop a statistical test for the existence of multi-scale structure in the game, and use it to demonstrate that real time-series data indeed exhibits such structure.

Multi-objective optimization (MOO) problems require balancing competing objectives, often under constraints. The Pareto optimal solution set defines all possible optimal trade-offs over such objectives. In this work, we present a novel method for Pareto-front learning: inducing the full Pareto manifold at train-time so users can pick any desired optimal trade-off point at run-time. Our key insight is to exploit Fritz-John Conditions for a novel guided double gradient descent strategy. Evaluation on synthetic benchmark problems allows us to vary MOO problem difficulty in controlled fashion and measure accuracy \vs known analytic solutions. We further test scalability and generalization in learning optimal neural model parameterizations for Multi-Task Learning (MTL) on image classification. Results show consistent improvement in accuracy and efficiency over prior MTL methods as well as techniques from operations research.

Gaussian process state-space models describe time series data in a probabilistic and non-parametric manner using a Gaussian process transition function. As inference is intractable, recent methods use variational inference and either rely on simplifying independence assumptions on the approximate posterior or learn the temporal states iteratively. The latter hampers optimization since the posterior over the presence can only be learned once the posterior governing the past has converged. We present a novel inference scheme that applies stochastic variational inference for the Gaussian process posterior and the Laplace approximation on the temporal states. This approach respects the conditional dependencies in the model and, through the Laplace approximation, treats the temporal states jointly, thereby avoiding their sequential learning. Our method is computationally efficient and leads to better calibrated predictions compared to state-of-the art alternatives on synthetic data and on a range of benchmark datasets.