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The International Conference on Machine Learning (ICML) Outstanding Paper awards are given to papers from the current conference that are *“strong representatives of solid theoretical and empirical work in the field”*. This year, there were 10 awards. The accolades went to:

**Solving Stackelberg prediction game with least squares loss via spherically constrained least squares reformulation**

*Jiali Wang, Wen Huang, Rujun Jiang, Xudong Li, Alex L. Wang*

*Abstract:* The Stackelberg prediction game (SPG) is popular in characterizing strategic interactions between a learner and an attacker. As an important special case, the SPG with least squares loss (SPG-LS) has recently received much research attention. Although initially formulated as a difficult bi-level optimization problem, SPG-LS admits tractable reformulations which can be polynomially globally solved by semidefinite programming or second order cone programming. However, all the available approaches are not well-suited for handling large-scale datasets, especially those with huge numbers of features. In this paper, we explore an alternative reformulation of the SPG-LS. By a novel nonlinear change of variables, we rewrite the SPG-LS as a spherically constrained least squares (SCLS) problem. Theoretically, we show that an ϵ optimal solution to the SCLS (and the SPG-LS) can be achieved in Õ(N/√ϵ) floating-point operations, where N is the number of nonzero entries in the data matrix. Practically, we apply two well-known methods for solving this new reformulation, i.e., the Krylov subspace method and the Riemannian trust region method. Both algorithms are factorization free so that they are suitable for solving large scale problems. Numerical results on both synthetic and real-world datasets indicate that the SPG-LS, equipped with the SCLS reformulation, can be solved orders of magnitude faster than the state of the art.

Read the full paper here.

**Stable conformal prediction sets**

*Eugene Ndiaye*

*Abstract:* When one observes a sequence of variables (x_{1},y_{1}),…,(x_{n},y_{n}), conformal prediction is a methodology that allows to estimate a confidence set for y_{n+1} given x_{n+1} by merely assuming that the distribution of the data is exchangeable. While appealing, the computation of such set turns out to be infeasible in general, e.g. when the unknown variable yn+1 is continuous. In this paper, we combine conformal prediction techniques with algorithmic stability bounds to derive a prediction set computable with a single model fit. We perform some numerical experiments that illustrate the tightness of our estimation when the sample size is sufficiently large.

Read the full paper here.

**Do differentiable simulators give better policy gradients?**

*H.J. Terry Suh, Max Simchowitz, Kaiqing Zhang, Russ Tedrake*

*Abstract:* Differentiable simulators promise faster computation time for reinforcement learning by replacing zeroth-order gradient estimates of a stochastic objective with an estimate based on first-order gradients. However, it is yet unclear what factors decide the performance of the two estimators on complex landscapes that involve long-horizon planning and control on physical systems, despite the crucial relevance of this question for the utility of differentiable simulators. We show that characteristics of certain physical systems, such as stiffness or discontinuities, may compromise the efficacy of the first-order estimator, and analyze this phenomenon through the lens of bias and variance. We additionally propose an α-order gradient estimator, with α∈[0,1], which correctly utilizes exact gradients to combine the efficiency of first-order estimates with the robustness of zero-order methods. We demonstrate the pitfalls of traditional estimators and the advantages of the α-order estimator on some numerical examples.

Read the full paper here.

**Learning mixtures of linear dynamical systems**

*Yanxi Chen, H. Vincent Poor*

*Abstract:* We study the problem of learning a mixture of multiple linear dynamical systems (LDSs) from unlabeled short sample trajectories, each generated by one of the LDS models. Despite the wide applicability of mixture models for time-series data, learning algorithms that come with end-to-end performance guarantees are largely absent from existing literature. There are multiple sources of technical challenges, including but not limited to (1) the presence of latent variables (i.e. the unknown labels of trajectories); (2) the possibility that the sample trajectories might have lengths much smaller than the dimension d of the LDS models; and (3) the complicated temporal dependence inherent to time-series data. To tackle these challenges, we develop a two-stage meta-algorithm, which is guaranteed to efficiently recover each ground-truth LDS model up to error Õ(√(d/T)), where T is the total sample size. We validate our theoretical studies with numerical experiments, confirming the efficacy of the proposed algorithm.

Read the full paper here.

**Causal conceptions of fairness and their consequences**

*Hamed Nilforoshan, Johann Gaebler, Ravi Shroff, Sharad Goel*

*Abstract:* Recent work highlights the role of causality in designing equitable decision-making algorithms. It is not immediately clear, however, how existing causal conceptions of fairness relate to one another, or what the consequences are of using these definitions as design principles. Here, we first assemble and categorize popular causal definitions of algorithmic fairness into two broad families: (1) those that constrain the effects of decisions on counterfactual disparities; and (2) those that constrain the effects of legally protected characteristics, like race and gender, on decisions. We then show, analytically and empirically, that both families of definitions \emph{almost always} — in a measure theoretic sense — result in strongly Pareto dominated decision policies, meaning there is an alternative, unconstrained policy favored by every stakeholder with preferences drawn from a large, natural class. For example, in the case of college admissions decisions, policies constrained to satisfy causal fairness definitions would be disfavored by every stakeholder with neutral or positive preferences for both academic preparedness and diversity. Indeed, under a prominent definition of causal fairness, we prove the resulting policies require admitting all students with the same probability, regardless of academic qualifications or group membership. Our results highlight formal limitations and potential adverse consequences of common mathematical notions of causal fairness.

Read the full paper here.

**Privacy for free: How does dataset condensation help privacy?**

*Tian Dong, Bo Zhao, Lingjuan Lyu*

*Abstract:* To prevent unintentional data leakage, research community has resorted to data generators that can produce differentially private data for model training. However, for the sake of the data privacy, existing solutions suffer from either expensive training cost or poor generalization performance. Therefore, we raise the question whether training efficiency and privacy can be achieved simultaneously. In this work, we for the first time identify that dataset condensation (DC) which is originally designed for improving training efficiency is also a better solution to replace the traditional data generators for private data generation, thus providing privacy for free. To demonstrate the privacy benefit of DC, we build a connection between DC and differential privacy, and theoretically prove on linear feature extractors (and then extended to non-linear feature extractors) that the existence of one sample has limited impact (O(m/n)) on the parameter distribution of networks trained on m samples synthesized from n(n≫m) raw samples by DC. We also empirically validate the visual privacy and membership privacy of DC-synthesized data by launching both the loss-based and the state-of-the-art likelihood-based membership inference attacks. We envision this work as a milestone for data-efficient and privacy-preserving machine learning.

Read the full paper here.

**Understanding dataset difficulty with V-usable information**

*Kawin Ethayarajh, Yejin Choi, Swabha Swayamdipta*

*Abstract:* Estimating the difficulty of a dataset typically involves comparing state-of-the-art models to humans; the bigger the performance gap, the harder the dataset is said to be. However, this comparison provides little understanding of how difficult each instance in a given distribution is, or what attributes make the dataset difficult for a given model. To address these questions, we frame dataset difficulty—w.r.t. a model V—as the lack of V-usable information (Xu et al., 2019), where a lower value indicates a more difficult dataset for V. We further introduce pointwise V-information (PVI) for measuring the difficulty of individual instances w.r.t. a given distribution. While standard evaluation metrics typically only compare different models for the same dataset, V-usable information and PVI also permit the converse: for a given model V, we can compare different datasets, as well as different instances/slices of the same dataset. Furthermore, our framework allows for the interpretability of different input attributes via transformations of the input, which we use to discover annotation artefacts in widely-used NLP benchmarks.

Read the full paper here.

**G-Mixup: Graph data augmentation for graph classification**

*Xiaotian Han, Zhimeng Jiang, Ninghao Liu, Xia Hu*

*Abstract:* This work develops *mixup for graph data*. Mixup has shown superiority in improving the generalization and robustness of neural networks by interpolating features and labels between two random samples. Traditionally, Mixup can work on regular, grid-like, and Euclidean data such as image or tabular data. However, it is challenging to directly adopt Mixup to augment graph data because different graphs typically: 1) have different numbers of nodes; 2) are not readily aligned; and 3) have unique typologies in non-Euclidean space. To this end, we propose G-Mixup to augment graphs for graph classification by interpolating the generator (i.e., graphon) of different classes of graphs. Specifically, we first use graphs within the same class to estimate a graphon. Then, instead of directly manipulating graphs, we interpolate graphons of different classes in the Euclidean space to get mixed graphons, where the synthetic graphs are generated through sampling based on the mixed graphons. Extensive experiments show that G-Mixup substantially improves the generalization and robustness of GNNs.

Read the full paper here.

**The importance of non-Markovianity in maximum state entropy exploration**

*Mirco Mutti, Riccardo De Santi, Marcello Restelli*

*Abstract:* In the maximum state entropy exploration framework, an agent interacts with a reward-free environment to learn a policy that maximizes the entropy of the expected state visitations it is inducing. Hazan et al. (2019) noted that the class of Markovian stochastic policies is sufficient for the maximum state entropy objective, and exploiting non-Markovianity is generally considered pointless in this setting. In this paper, we argue that non-Markovianity is instead paramount for maximum state entropy exploration in a finite-sample regime. Especially, we recast the objective to target the expected entropy of the induced state visitations in a single trial. Then, we show that the class of non-Markovian deterministic policies is sufficient for the introduced objective, while Markovian policies suffer non-zero regret in general. However, we prove that the problem of finding an optimal non-Markovian policy is NP-hard. Despite this negative result, we discuss avenues to address the problem in a tractable way and how non-Markovian exploration could benefit the sample efficiency of online reinforcement learning in future works.

Read the full paper here.

**Bayesian model selection, the marginal likelihood, and generalization**

*Sanae Lotfi, Pavel Izmailov, Gregory Benton, Micah Goldblum, Andrew Gordon Wilson*

*Abstract:* How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive approach to this foundational question, automatically encoding Occam’s razor. Although it has been observed that the marginal likelihood can overfit and is sensitive to prior assumptions, its limitations for hyperparameter learning and discrete model comparison have not been thoroughly investigated. We first revisit the appealing properties of the marginal likelihood for learning constraints and hypothesis testing. We then highlight the conceptual and practical issues in using the marginal likelihood as a proxy for generalization. Namely, we show how marginal likelihood can be negatively correlated with generalization, with implications for neural architecture search, and can lead to both underfitting and overfitting in hyperparameter learning. We provide a partial remedy through a conditional marginal likelihood, which we show is more aligned with generalization, and practically valuable for large-scale hyperparameter learning, such as in deep kernel learning.

Read the full paper here.

*Note: This article has been amended since publication on 21 July. There was a bug on the ICML webpage that initially listed 15 winners of the outstanding paper award. The list on the ICML page has now been reduced to 10 winners. We’ve updated this article to reflect that change. *

tags: ICML, ICML2022

Lucy Smith
, Managing Editor for AIhub.

Lucy Smith
, Managing Editor for AIhub.

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