UAI 2023 Papers

In this paper, we present FLASH, a framework which addresses for the first time the central AutoML problem of Combined Algorithm Selection and HyperParameter (HP) Optimization (CASH) in the context of Federated Learning (FL). To limit training cost, FLASH incrementally adapts the set of algorithms to train based on their projected loss rates, while supporting decentralized (federated) implementation of the embedded hyper-parameter optimization (HPO), model selection and loss calculation problems. We provide a theoretical analysis of the training and validation loss under FLASH, and their tradeoff with the training cost measured as the data wasted in training sub-optimal algorithms. The bounds depend on the degree of dissimilarity between the datasets of the clients, a result of FL restriction that client datasets remain private. Through extensive experimental investigation on several datasets, we evaluate three variants of FLASH, and show that FLASH performs close to centralized CASH methods.

This paper studies a cooperative multi-agent bandit scenario in which the rewards observed by agents are heterogeneous—one agent’s meat can be another agent’s poison. Specifically, the total reward observed by each agent is the sum of two values: an arm-specific reward, capturing the intrinsic value of the arm, and a privately-known agent-specific reward, which captures the personal preference/limitations of the agent. This heterogeneity in total reward leads to different local optimal arms for agents but creates an opportunity for \textit{free exploration} in a cooperative setting—an agent can freely explore its local optimal arm with no regret and share this free observation with some other agents who would suffer regrets if they pull this arm since the arm is not optimal for them. We first characterize a regret lower bound that captures free exploration, i.e., arms that can be freely explored have no contribution to the regret lower bound. Then, we present a cooperative bandit algorithm that takes advantage of free exploration and achieves a near-optimal regret upper bound which tightly matches the regret lower bound up to a constant factor. Lastly, we run numerical simulations to compare our algorithm with various baselines without free exploration.

Neural Processes (NPs) are appealing due to their ability to perform fast adaptation based on a context set. This set is encoded by a latent variable, which is often assumed to follow a simple distribution. However, in real-word settings, the context set may be drawn from richer distributions having multiple modes, heavy tails, etc. In this work, we provide a framework that allows NPs’ latent variable to be given a rich prior defined by a graphical model. These distributional assumptions directly translate into an appropriate aggregation strategy for the context set. Moreover, we describe a message-passing procedure that still allows for end-to-end optimization with stochastic gradients. We demonstrate the generality of our framework by using mixture and Student-t assumptions that yield improvements in function modelling and test-time robustness.

Despite their incredible performance, it is well reported that deep neural networks tend to be overoptimistic about their prediction confidence. Finding effective and efficient calibration methods for neural networks is therefore an important endeavour towards better uncertainty quantification in deep learning. In this manuscript, we introduce a novel calibration technique named expectation consistency (EC), consisting of a post-training rescaling of the last layer weights by enforcing that the average validation confidence coincides with the average proportion of correct labels. First, we show that the EC method achieves similar calibration performance to temperature scaling (TS) across different neural network architectures and data sets, all while requiring similar validation samples and computational resources. However, we argue that EC provides a principled method grounded on a Bayesian optimality principle known as the Nishimori identity. Next, we provide an asymptotic characterization of both TS and EC in a synthetic setting and show that their performance crucially depends on the target function. In particular, we discuss examples where EC significantly outperforms TS.

Classic learning theory suggests that proper regularization is the key to good generalization and robustness. In classification, current training schemes only target the complexity of the classifier itself, which can be misleading and ineffective. Instead, we advocate directly measuring the complexity of the decision boundary. Existing literature is limited in this area with few well-established definitions of boundary complexity. As a proof of concept, we start by analyzing ReLU neural networks, whose boundary complexity can be conveniently characterized by the number of affine pieces. With the help of tropical geometry, we develop a novel method that can explicitly count the exact number of boundary pieces, and as a by-product, the exact number of total affine pieces. Numerical experiments are conducted and distinctive properties of our boundary complexity are uncovered. First, the boundary piece count appears largely independent of other measures, e.g., total piece count, and $l_2$ norm of weights, during the training process. Second, the boundary piece count is negatively correlated with robustness, where popular robust training techniques, e.g., adversarial training or random noise injection, are found to reduce the number of boundary pieces.

We present a new, efficient procedure to establish Markov equivalence between directed graphs that may or may not contain cycles. It is based on the Cyclic Equivalence Theorem (CET) in the seminal works on cyclic models by Thomas Richardson in the mid ’90s, but now rephrased from an ancestral perspective. The resulting characterization leads to a procedure for establishing Markov equivalence between graphs that no longer requires explicit tests for $d$-separation, leading to a significantly reduced algorithmic complexity. The conceptually simplified characterization may help to reinvigorate theoretical research towards sound and complete cyclic discovery in the presence of latent confounders.

Randomized experiments (REs) are the cornerstone for treatment effect evaluation. However, due to practical considerations, REs may encounter difficulty recruiting sufficient patients. External controls (ECs) can supplement REs to boost estimation efficiency. Yet, there may be incomparability between ECs and concurrent controls (CCs), resulting in misleading treatment effect evaluation. We introduce a novel bias function to measure the difference in the outcome mean functions between ECs and CCs. We show that the ANCOVA model augmented by the bias function for ECs renders a consistent estimator of the average treatment effect, regardless of whether or not the ANCOVA model is correct. To accommodate possibly different structures of the ANCOVA model and the bias function, we propose a double penalty integration estimator (DPIE) with different penalization terms for the two functions. With an appropriate choice of penalty parameters, our DPIE ensures consistency, oracle property, and asymptotic normality even in the presence of model misspecification. DPIE is at least as efficient as the estimator derived from REs alone, validated through theoretical and experimental results.

In real-world applications, handling partial observability is a common requirement for reinforcement learning algorithms, which is not captured by a Markov decision process (MDP). Although partially observable Markov decision processes (POMDPs) have been specifically designed to address this requirement, they present significant computational and statistical challenges in learning and planning. In this work, we introduce the

Computational efficiency is a major bottleneck in using classic graph-based approaches for semi-supervised learning on datasets with a large number of unlabeled examples. Known techniques to improve efficiency typically involve an approximation of the graph regularization objective, but suffer two major drawbacks - first the graph is assumed to be known or constructed with heuristic hyperparameter values, second they do not provide a principled approximation guarantee for learning over the full unlabeled dataset. Building on recent work on learning graphs for semi-supervised learning from multiple datasets for problems from the same domain, and leveraging techniques for fast approximations for solving linear systems in the graph Laplacian matrix, we propose algorithms that overcome both the above limitations. We show a formal separation in the learning-theoretic complexity of sparse and dense graph families. We further show how to approximately learn the best graphs from the sparse families efficiently using the conjugate gradient method. Our approach can also be used to learn the graph efficiently online with sub-linear regret, under mild smoothness assumptions. Our online learning results are stated generally, and may be useful for approximate and efficient parameter tuning in other problems. We implement our approach and demonstrate significant ($\sim$10-100x) speedups over prior work on semi-supervised learning with learned graphs on benchmark datasets.

While many solutions for privacy-preserving convex empirical risk minimization (ERM) have been developed, privacy-preserving nonconvex ERM remains a challenge. We study nonconvex ERM, which takes the form of minimizing a finite-sum of nonconvex loss functions over a training set. We propose a new differentially private stochastic gradient descent algorithm for nonconvex ERM that achieves strong privacy guarantees efficiently, and provide a tight analysis of its privacy and utility guarantees, as well as its gradient complexity. Our algorithm reduces gradient complexity while matching the best-known utility guarantee. Our experiments on benchmark nonconvex ERM problems demonstrate superior performance in terms of both training cost and utility gains compared with previous differentially private methods using the same privacy budgets.

High-dimensional data is common in multiple areas, such as health care and genomics, where the number of features can be tens of thousands. In such scenarios, the large number of features often leads to inefficient learning. Constraint generation methods have recently enabled efficient learning of L1-regularized support vector machines (SVMs). In this paper, we leverage such methods to obtain an efficient learning algorithm for the recently proposed minimax risk classifiers (MRCs). The proposed iterative algorithm also provides a sequence of worst-case error probabilities and performs feature selection. Experiments on multiple high-dimensional datasets show that the proposed algorithm is efficient in high-dimensional scenarios. In addition, the worst-case error probability provides useful information about the classifier performance, and the features selected by the algorithm are competitive with the state-of-the-art.

Given a (machine learning) classifier and a collection of unlabeled data, how can we efficiently identify misclassification patterns presented in this dataset? To address this problem, we propose a human-machine collaborative framework that consists of a team of human annotators and a sequential recommendation algorithm. The recommendation algorithm is conceptualized as a stochastic sampler that, in each round, queries the annotators a subset of samples for their true labels and obtains the feedback information on whether the samples are misclassified. The sampling mechanism needs to balance between discovering new patterns of misclassification (exploration) and confirming the potential patterns of classification (exploitation). We construct a determinantal point process, whose intensity balances the exploration-exploitation trade-off through the weighted update of the posterior at each round to form the generator of the stochastic sampler. The numerical results empirically demonstrate the competitive performance of our framework on multiple datasets at various signal-to-noise ratios.

Stochastic Heavy Ball (SHB) and Nesterov’s Accelerated Stochastic Gradient (ASG) are popular momentum methods in optimization. While the benefits of these acceleration ideas in deterministic settings are well understood, their advantages in stochastic optimization are unclear. Several works have recently claimed that SHB and ASG always help in stochastic optimization. Our work shows that i.) these claims are either flawed or one-sided (e.g., consider only the bias term but not the variance), and ii.) when both these terms are accounted for, SHB and ASG do not always help. Specifically, for

Equivalence classes of DAGs (represented by CPDAGs) may be too large to provide useful causal information. Here, we address incorporating tiered background knowledge yielding restricted equivalence classes represented by ‘tiered MPDAGs’. Tiered knowledge leads to considerable gains in informativeness and computational efficiency: We show that construction of tiered MPDAGs only requires application of Meeks 1st rule, and that tiered MPDAGs (unlike general MPDAGs) are chain graphs with chordal components. This entails simplifications e.g. of determining valid adjustment sets for causal effect estimation. Further, we characterise when one tiered ordering is more informative than another, providing insights into useful aspects of background knowledge.

Ensemble methods combine multiple individual models for prediction, which have demonstrated their effectiveness in accurate uncertainty quantification (UQ) and strong robustness. Obtaining a diverse ensemble set of model parameters results in better model averaging performance and better approximation of the true posterior distribution of these parameters. In this paper, we propose the diversity-enhanced probabilistic ensemble method with the adaptive uncertainty-guided ensemble learning strategy for better quantifying uncertainty and further improving the model robustness. Specifically, we construct the probabilistic ensemble model by building a Gaussian distribution of the model parameters for each ensemble component using Laplacian approximation in a post-processing manner. Then a mixture of Gaussian model is established with learnable and refinable parameters in an EM-like algorithm. During ensemble training, we leverage the uncertainty estimated from previous models as guidance when training the next one such that the new model will focus more on the less explored regions by previous models. Various experiments including out-of-distribution detection and image classification under distributional shifts have demonstrated better uncertainty estimation and improved model generalization ability of our proposed method.

Probabilistic, hierarchically coherent forecasting is a key problem in many practical forecasting applications – the goal is to obtain coherent probabilistic predictions for a large number of time series arranged in a pre-specified tree hierarchy. In this paper, we present an end-to-end deep probabilistic model for hierarchical forecasting that is motivated by a classical top-down strategy. It jointly learns the distribution of the root time series, and the (dirichlet) proportions according to which each parent time-series is split among its children at any point in time. The resulting forecasts are naturally coherent, and provide probabilistic predictions over all time series in the hierarchy. We experiment on several public datasets and demonstrate significant improvements of up to 26% on most datasets compared to state-of-the-art baselines. Finally, we also provide theoretical justification for the superiority of our top-down approach compared to the more traditional bottom-up modeling.

Creation of a synthetic dataset that faithfully represents the data distribution and simultaneously preserves privacy is a major research challenge. Many space partitioning based approaches have emerged in recent years for answering statistical queries in a differentially private manner. However, for synthetic data generation problem, recent research has been mainly focused on deep generative models. In contrast, we exploit space partitioning techniques together with noise perturbation and thus achieve intuitive and transparent algorithms. We propose both data independent and data dependent algorithms for $\epsilon$-differentially private synthetic data generation whose kernel density resembles that of the real dataset. Additionally, we provide theoretical results on the utility-privacy trade-offs and show how our data dependent approach overcomes the curse of dimensionality and leads to a scalable algorithm. We show empirical utility improvements over the prior work, and discuss performance of our algorithm on a downstream classification task on a real dataset.

In this paper, we revisit the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) in Euclidean and general $\ell_p^d$ spaces. Specifically, we focus on three settings that are still far from well understood: (1) DP-SCO over a constrained and bounded (convex) set in Euclidean space; (2) unconstrained DP-SCO in $\ell_p^d$ space; (3) DP-SCO with heavy-tailed data over a constrained and bounded set in $\ell_p^d$ space. For problem (1), for both convex and strongly convex loss functions, we propose methods whose outputs could achieve (expected) excess population risks that are only dependent on the Gaussian width of the constraint set, rather than the dimension of the space. Moreover, we also show the bound for strongly convex functions is optimal up to a logarithmic factor. For problems (2) and (3), we propose several novel algorithms and provide the first theoretical results for both cases when $1

Privacy-aware multiagent systems must protect agents’ sensitive data while simultaneously ensuring that agents accomplish their shared objectives. Towards this goal, we propose a framework to privatize inter-agent communications in cooperative multiagent decision-making problems. We study sequential decision-making problems formulated as cooperative Markov games with reach-avoid objectives. We apply a differential privacy mechanism to privatize agents’ communicated symbolic state trajectories, and analyze tradeoffs between the strength of privacy and the team’s performance. For a given level of privacy, this tradeoff is shown to depend critically upon the total correlation among agents’ state-action processes. We synthesize policies that are robust to privacy by reducing the value of the total correlation. Numerical experiments demonstrate that the team’s performance under these policies decreases by only 6 percent when comparing private versus non-private implementations of communication. By contrast, the team’s performance decreases by 88 percent when using baseline policies that ignore total correlation and only optimize team performance.