Much of the field of Machine Learning exhibits a prominent set of failure modes, including vulnerability to adversarial examples, poor out-of-distribution (OoD) detection, miscalibration, and willingness to memorize random labelings of datasets. We characterize these as failures of robust generalization, which extends the traditional measure of generalization as accuracy or related metrics on a held-out set. We hypothesize that these failures to robustly generalize are due to the learning systems retaining too much information about the training data. To test this hypothesis, we propose the Minimum Necessary Information (MNI) criterion for evaluating the quality of a model. In order to train models that perform well with respect to the MNI criterion, we present a new objective function, the Conditional Entropy Bottleneck (CEB), which is closely related to the Information Bottleneck (IB). We experimentally test our hypothesis by comparing the performance of CEB models with deterministic models and Variational Information Bottleneck (VIB) models on a variety of different datasets and robustness challenges. We find strong empirical evidence supporting our hypothesis that MNI models improve on these problems of robust generalization.
University of Florida（佛罗里达大学）；NEC Laboratories Europe（NEC欧洲实验室）
We introduce the matrix-based Renyi's $α$-order entropy functional to parameterize Tishby et al. information bottleneck (IB) principle with a neural network. We term our methodology Deep Deterministic Information Bottleneck (DIB), as it avoids variational inference and distribution assumption. We show that deep neural networks trained with DIB outperform the variational objective counterpart and those that are trained with other forms of regularization, in terms of generalization performance and robustness to adversarial attack.Code available at https://github.com/yuxi120407/DIB
We introduce a new framework for training deep generative models for high-dimensional conditional density estimation. The Bottleneck Conditional Density Estimator (BCDE) is a variant of the conditional variational autoencoder (CVAE) that employs layer(s) of stochastic variables as the bottleneck between the input $x$ and target $y$, where both are high-dimensional. Crucially, we propose a new hybrid training method that blends the conditional generative model with a joint generative model. Hybrid blending is the key to effective training of the BCDE, which avoids overfitting and provides a nov…
Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the conditional density itself is preferable, but conditional density estimation (CDE) is challenging in high-dimensional space. A naive approach to coping with high-dimensionality is to first perform dimensionality reduction (DR) and then execute CDE. However, such a two-step process does not perform well in practice because the error incurred in the first DR step can be mag…
Jagiellonian University（雅盖隆大学）；Technical University of Munich（慕尼黑工业大学）
In this paper, we propose a semi-supervised clustering method, CEC-IB, that models data with a set of Gaussian distributions and that retrieves clusters based on a partial labeling provided by the user (partition-level side information). By combining the ideas from cross-entropy clustering (CEC) with those from the information bottleneck method (IB), our method trades between three conflicting goals: the accuracy with which the data set is modeled, the simplicity of the model, and the consistency of the clustering with side information. Experiments demonstrate that CEC-IB has a performance com…
We introduce the HSIC (Hilbert-Schmidt independence criterion) bottleneck for training deep neural networks. The HSIC bottleneck is an alternative to the conventional cross-entropy loss and backpropagation that has a number of distinct advantages. It mitigates exploding and vanishing gradients, resulting in the ability to learn very deep networks without skip connections. There is no requirement for symmetric feedback or update locking. We find that the HSIC bottleneck provides performance on MNIST/FashionMNIST/CIFAR10 classification comparable to backpropagation with a cross-entropy target, e…
In this draft, which reports on work in progress, we 1) adapt the information bottleneck functional by replacing the compression term by class-conditional compression, 2) relax this functional using a variational bound related to class-conditional disentanglement, 3) consider this functional as a training objective for stochastic neural networks, and 4) show that the latent representations are learned such that they can be used in a naive Bayes classifier. We continue by suggesting a series of experiments along the lines of Nonlinear In-formation Bottleneck [Kolchinsky et al., 2018], Deep Vari…
Microsoft Research（微软研究院）；University of California at Irvine（加州大学欧文分校）；University of California at Berkeley（加州大学伯克利分校）
There is a rapidly increasing interest in crowdsourcing for data labeling. By crowdsourcing, a large number of labels can be often quickly gathered at low cost. However, the labels provided by the crowdsourcing workers are usually not of high quality. In this paper, we propose a minimax conditional entropy principle to infer ground truth from noisy crowdsourced labels. Under this principle, we derive a unique probabilistic labeling model jointly parameterized by worker ability and item difficulty. We also propose an objective measurement principle, and show that our method is the only method w…
Istituto Italiano di Tecnologia（意大利理工学院）；Dept. of Neurobiology, Harvard Medical School（哈佛医学院神经生物学系）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Max Planck ETH Center for Learning Systems（马克斯·普朗克-ETH学习系统中心）；Max Planck Institute for Biological Cybernetics（马克斯·普朗克生物控制论研究所）
The inference of causal relationships using observational data from partially observed multivariate systems with hidden variables is a fundamental question in many scientific domains. Methods extracting causal information from conditional independencies between variables of a system are common tools for this purpose, but are limited in the lack of independencies. To surmount this limitation, we capitalize on the fact that the laws governing the generative mechanisms of a system often result in substructures embodied in the generative functional equation of a variable, which act as sufficient s…
Many policy gradient methods are variants of Actor-Critic (AC), where a value function (critic) is learned to facilitate updating the parameterized policy (actor). The update to the actor involves a log-likelihood update weighted by the action-values, with the addition of entropy regularization for soft variants. In this work, we explore an alternative update for the actor, based on an extension of the cross entropy method (CEM) to condition on inputs (states). The idea is to start with a broader policy and slowly concentrate around maximal actions, using a maximum likelihood update towards ac…
Mila - Quebec AI institute（米拉-魁北克人工智能研究所）；McGill University（麦吉尔大学）；Université de Montréal（蒙特利尔大学）；BIOS Health Ltd.（BIOS健康有限公司）；CIFAR（加拿大高等研究院）；Montreal Neurological Institute（蒙特利尔神经学研究所）
When presented with a data stream of two statistically dependent variables, predicting the future of one of the variables (the target stream) can benefit from information about both its history and the history of the other variable (the source stream). For example, fluctuations in temperature at a weather station can be predicted using both temperatures and barometric readings. However, a challenge when modelling such data is that it is easy for a neural network to rely on the greatest joint correlations within the target stream, which may ignore a crucial but small information transfer from t…
Which bits went where? Past and future transfer entropy decomposition with the information bottleneck
University of Pennsylvania（宾夕法尼亚大学）；Perelman School of Medicine, University of Pennsylvania（宾夕法尼亚大学佩雷尔曼医学院）；The Santa Fe Institute（圣塔菲研究所）；Montreal Neurological Institute, McGill University（麦吉尔大学蒙特利尔神经学研究所）
Opening the Black Box of Classifier-Free Guidance via Information Bottleneck
Shanghai Jiao Tong University（上海交通大学）；vivo Mobile Communication Co., Ltd.（维沃移动通信有限公司）；Stanford University（斯坦福大学）；University of British Columbia（不列颠哥伦比亚大学）
This article offers a modification of Chow and Liu's learning algorithm in the context of handwritten digit recognition. The modified algorithm directs the user to group digits into several classes consisting of digits that are hard to distinguish and then constructing an optimal conditional tree representation for each class of digits instead of for each single digit as done by Chow and Liu (1968). Advantages and extensions of the new method are discussed. Related works of Wong and Wang (1977) and Wong and Poon (1989) which offer a different entropy-based learning algorithm are shown to rest …
Invariance-principle-based methods such as Invariant Risk Minimization (IRM), have recently emerged as promising approaches for Domain Generalization (DG). Despite promising theory, such approaches fail in common classification tasks due to the mixing of true invariant features and spurious invariant features. To address this, we propose a framework based on the conditional entropy minimization (CEM) principle to filter-out the spurious invariant features leading to a new algorithm with a better generalization capability. We show that our proposed approach is closely related to the well-known …
Domain Adaptation (DA) is a typical problem in machine learning that aims to transfer the model trained on source domain to target domain with different distribution. Causal DA is a special case of DA that solves the problem from the view of causality. It embeds the probabilistic relationships in multiple domains in a larger causal structure network of a system and tries to find the causal source (or intervention) on the system as the reason of distribution drifts of the system states across domains. In this sense, causal DA is transformed as a causal discovery problem that finds invariant rep…
End-to-end deep trainable models are about to exceed the performance of the traditional handcrafted compression techniques on videos and images. The core idea is to learn a non-linear transformation, modeled as a deep neural network, mapping input image into latent space, jointly with an entropy model of the latent distribution. The decoder is also learned as a deep trainable network, and the reconstructed image measures the distortion. These methods enforce the latent to follow some prior distributions. Since these priors are learned by optimization over the entire training set, the performan…
This paper discusses the application of L1-regularized maximum entropy modeling or SL1-Max [9] to multiclass categorization problems. A new modification to the SL1-Max fast sequential learning algorithm is proposed to handle conditional distributions. Furthermore, unlike most previous studies, the present research goes beyond a single type of conditional distribution. It describes and compares a variety of modeling assumptions about the class distribution (independent or exclusive) and various types of joint or conditional distributions. It results in a new methodology for combining binary reg…
Statistical independence and conditional independence are two fundamental concepts in statistics and machine learning. Copula Entropy is a mathematical concept defined by Ma and Sun for multivariate statistical independence measuring and testing, and also proved to be closely related to conditional independence (or transfer entropy). As the unified framework for measuring both independence and causality, CE has been applied to solve several related statistical or machine learning problems, including association discovery, structure learning, variable selection, and causal discovery. The nonpar…
