# Weekly TMLR digest for Apr 10, 2022

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### TMLR

Apr 9, 2022, 8:00:06 PMApr 9

New submissions
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Title: Margin Calibration for Long-Tailed Visual Recognition

Abstract: The long-tailed visual recognition tasks pose great challenges for neural networks on how to handle the imbalanced predictions between head and tail classes, i.e., models tend to classify tail classes as head classes. While existing research focused on data resampling and loss function engineering, in this paper, we take a different perspective: the classification margins. We study the relationship between the margins and logits (classification scores) and empirically observe that the uncalibrated margins and logits are positively correlated. We propose a simple yet effective MARgin Calibration approach (MARC) to dynamically calibrate the margins to obtain better logits. We validate MARC through extensive experiments on common long-tailed benchmarks including CIFAR-LT, ImageNet-LT, Places-LT, and iNaturalist-LT. Experimental results demonstrate that our MARC achieves favorable results on these benchmarks. In addition, MARC is extremely easy to implement with just three lines of code. We hope this simple approach will motivate people to rethink the uncalibrated margins and logits in long-tailed visual recognition.

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Title: Iterative State Estimation in Non-linear Dynamical Systems Using Approximate Expectation Propagation

Abstract: Bayesian inference in non-linear dynamical systems seeks to find good posterior approximations of a latent state given a sequence of observations. Gaussian filters and smoothers, including the (extended/unscented) Kalman filter/smoother, which are commonly used in engineering applications, yield Gaussian posteriors on the latent state. While they are computationally efficient, they are often criticised for their crude approximation of the posterior state distribution. In this paper, we address this criticism by proposing a message passing scheme for iterative state estimation in non-linear dynamical systems, which yields more informative (Gaussian) posteriors on the latent states. Our message passing scheme is based on expectation propagation (EP). We prove that classical Rauch--Tung--Striebel (RTS) smoothers, such as the extended Kalman smoother (EKS) or the unscented Kalman smoother (UKS), are special cases of our message passing scheme. Running the message passing scheme more than once can lead to significant improvements of the classical RTS smoothers, so that more informative state estimates can be obtained. We address potential convergence issues of EP by generalising our state estimation framework to damped updates and the consideration of general $\alpha$-divergences.

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Title: Algorithm-Agnostic Explainability for Unsupervised Clustering

Abstract: Supervised machine learning explainability has developed rapidly in recent years. However, clustering explainability has lagged behind. Here, we demonstrate the first adaptation of model-agnostic explainability methods to explain unsupervised clustering. We present two novel "algorithm-agnostic" explainability methods – global permutation percent change (G2PC) and local perturbation percent change (L2PC) – that identify feature importance globally to a clustering algorithm and locally to the clustering of individual samples. The methods are (1) easy to implement and (2) broadly applicable across clustering algorithms, which could make them highly impactful. We demonstrate the utility of the methods for explaining five popular clustering methods on low-dimensional synthetic datasets and on high-dimensional functional network connectivity data extracted from a resting-state functional magnetic resonance imaging dataset of 151 individuals with schizophrenia and 160 controls. Our results are consistent with existing literature while also shedding new light on how changes in brain connectivity may lead to schizophrenia symptoms. We further compare the explanations from our methods to an interpretable classifier and find them to be highly similar. Our proposed methods robustly explain multiple clustering algorithms and could facilitate new insights into many applications. We hope this study will greatly accelerate the development of the field of clustering explainability

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Abstract: Policy regularization methods such as maximum entropy regularization are widely used in reinforcement learning to improve the robustness of a learned policy. In this paper, we show how this robustness arises from hedging against worst-case perturbations of the reward function, which are chosen from a limited set by an imagined adversary. Using convex duality, we characterize this robust set of adversarial reward perturbations under KL- and $\alpha$-divergence regularization, which includes Shannon and Tsallis entropy regularization as special cases. Importantly, generalization guarantees can be given within this robust set. We provide detailed discussion of the worst-case reward perturbations, and present intuitive empirical examples to illustrate this robustness and its relationship with generalization. Finally, we discuss how our analysis complements and extends previous results on adversarial reward robustness and path consistency optimality conditions.