In this paper, we study a bi-criterion framework for assessing scoring functions in the context of binary classification. The positive and negative predictive values (ppv and npv, respectively) are conditional probabilities of the true label matching a classifier's predicted label. The usual classification error rate is a linear combination of these probabilities, and therefore, concentration inequalities for the error rate do not yield confidence intervals for the two separate predictive values. We study generalization properties of scoring functions with respect to predictive values by deriving new distribution-free large deviation and uniform convergence bounds. The latter bound is stated in terms of a measure of function class complexity that we call the order coefficient; we relate this combinatorial quantity to the VC-subgraph dimension.
We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example). A mixture of learnable processes need not be learnable itself, and certainly its generalization error need not decay at the same rate. In this paper, we argue that it is natural in predictive PAC to condition not on the past observations but on the mixture component of the sample path. This definition not only matches what a realistic learner might demand, but also allows us to sidestep sev…
The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task. Predictive sparse coding algorithms recently have demonstrated impressive performance on a variety of supervised tasks, but their generalization properties have not been studied. We establish the first generalization error bounds for predictive sparse coding, covering two settings: 1) the overcomplete setting, where the number of features k exceeds the origin…
In traditional machine learning techniques, the degree of closeness between true and predicted values generally measures the quality of predictions. However, these learning algorithms do not consider prescription problems where the predicted values will be used as input to decision problems. In this paper, we efficiently leverage feature variables, and we propose a new framework directly integrating predictive tasks under prescriptive tasks in order to prescribe consistent decisions. We train the parameters of predictive algorithm within a prescription problem via bilevel optimization techniqu…
Acceleration of machine learning research in healthcare is challenged by lack of large annotated and balanced datasets. Furthermore, dealing with measurement inaccuracies and exploiting unsupervised data are considered to be central to improving existing solutions. In particular, a primary objective in predictive modeling is to generalize well to both unseen variations within the observed classes, and unseen classes. In this work, we consider such a challenging problem in machine learning driven diagnosis: detecting a gamut of cardiovascular conditions (e.g. infarction, dysrhythmia etc.) from …
On Cold Posteriors of Probabilistic Neural Networks: Understanding the Cold Posterior Effect and A New Way to Learn Cold Posteriors with Tight Generalization Guarantees
Recent years have seen a substantial development of quantitative methods, mostly led by the computer science community with the goal of developing better machine learning applications, mainly focused on predictive modeling. However, economic, management, and technology forecasting research has so far been hesitant to apply predictive modeling techniques and workflows. In this paper, we introduce a machine learning (ML) approach to quantitative analysis geared towards optimizing the predictive performance, contrasting it with standard practices inferential statistics, which focus on producing g…
University of Almería（阿尔梅里亚大学）；University of Copenhagen（哥本哈根大学）
Virtually any model we use in machine learning to make predictions does not perfectly represent reality. So, most of the learning happens under model misspecification. In this work, we present a novel analysis of the generalization performance of Bayesian model averaging under model misspecification and i.i.d. data using a new family of second-order PAC-Bayes bounds. This analysis shows, in simple and intuitive terms, that Bayesian model averaging provides suboptimal generalization performance when the model is misspecified. In consequence, we provide strong theoretical arguments showing that …
Indian Institute of Technology, Madras（马德拉斯印度理工学院）
Deep Neural Networks can generalize despite being significantly overparametrized. Recent research has tried to examine this phenomenon from various view points and to provide bounds on the generalization error or measures predictive of the generalization gap based on these viewpoints, such as norm-based, PAC-Bayes based, and margin-based analysis. In this work, we provide an interpretation of generalization from the perspective of quality of internal representations of deep neural networks, based on neuroscientific theories of how the human visual system creates invariant and untangled object …
From the statistical learning perspective, complexity control via explicit regularization is a necessity for improving the generalization of over-parameterized models. However, the impressive generalization performance of neural networks with only implicit regularization may be at odds with this conventional wisdom. In this work, we revisit the importance of explicit regularization for obtaining well-calibrated predictive uncertainty. Specifically, we introduce a probabilistic measure of calibration performance, which is lower bounded by the log-likelihood. We then explore explicit regularizat…
Prior design is one of the most important problems in both statistics and machine learning. The cross validation (CV) and the widely applicable information criterion (WAIC) are predictive measures of the Bayesian estimation, however, it has been difficult to apply them to find the optimal prior because their mathematical properties in prior evaluation have been unknown and the region of the hyperparameters is too wide to be examined. In this paper, we derive a new formula by which the theoretical relation among CV, WAIC, and the generalization loss is clarified and the optimal hyperparameter c…
A general class of models is proposed that is able to estimate the whole predictive distribution of a dependent variable $Y$ given a vector of explanatory variables $\xb$. The models exploit that the strength of explanatory variables to distinguish between low and high values of the dependent variable may vary across the thresholds that are used to define low and high. Simple linear versions of the models are generalizations of classical linear regression models but also of widely used ordinal regression models. They allow to visualize the effect of explanatory variables in the form of paramet…
Motion planning in environments with multiple agents is critical to many important autonomous applications such as autonomous vehicles and assistive robots. This paper considers the problem of motion planning, where the controlled agent shares the environment with multiple uncontrolled agents. First, a predictive model of the uncontrolled agents is trained to predict all possible trajectories within a short horizon based on the scenario. The prediction is then fed to a motion planning module based on model predictive control. We proved generalization bound for the predictive model using three …
Robert Bosch GmbH, Automated Driving Research（罗伯特·博世有限公司，自动驾驶研究）；University of Lübeck, Institute of Signal Processing（吕贝克大学，信号处理研究所）
Deep Neural Networks (DNNs) achieve state-of-the-art performance on numerous applications. However, it is difficult to tell beforehand if a DNN receiving an input will deliver the correct output since their decision criteria are usually nontransparent. A DNN delivers the correct output if the input is within the area enclosed by its generalization envelope. In this case, the information contained in the input sample is processed reasonably by the network. It is of large practical importance to assess at inference time if a DNN generalizes correctly. Currently, the approaches to achieve this go…
German Research Center for Artificial Intelligence（德国人工智能研究中心）
Estimating predictive uncertainty is crucial for many computer vision tasks, from image classification to autonomous driving systems. Hamiltonian Monte Carlo (HMC) is an sampling method for performing Bayesian inference. On the other hand, Dropout regularization has been proposed as an approximate model averaging technique that tends to improve generalization in large scale models such as deep neural networks. Although, HMC provides convergence guarantees for most standard Bayesian models, it does not handle discrete parameters arising from Dropout regularization. In this paper, we present a r…
The Bayesian posterior minimizes the "inferential risk" which itself bounds the "predictive risk". This bound is tight when the likelihood and prior are well-specified. However since misspecification induces a gap, the Bayesian posterior predictive distribution may have poor generalization performance. This work develops a multi-sample loss (PAC$^m$) which can close the gap by spanning a trade-off between the two risks. The loss is computationally favorable and offers PAC generalization guarantees. Empirical study demonstrates improvement to the predictive distribution.
ETH Zürich（苏黎世联邦理工学院）；MPI Tübingen（蒂宾根马克斯·普朗克研究所）；University of Copenhagen（哥本哈根大学）
Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called CausalKinetiX, that identifies structure from discrete time, noisy observations, generated from heterogeneous experiments. The algorithm assumes the existence of an underlying, invariant kinetic model, a key criterion for reproducible research. Results on both simulated and real-world examples suggest that learning the structure of kinetic systems benefits …
University of Southern California（南加利福尼亚大学）；Google Brain（谷歌大脑）
Simulation-to-real transfer is an important strategy for making reinforcement learning practical with real robots. Successful sim-to-real transfer systems have difficulty producing policies which generalize across tasks, despite training for thousands of hours equivalent real robot time. To address this shortcoming, we present a novel approach to efficiently learning new robotic skills directly on a real robot, based on model-predictive control (MPC) and an algorithm for learning task representations. In short, we show how to reuse the simulation from the pre-training step of sim-to-real metho…
It has been recently demonstrated that multi-generational self-distillation can improve generalization. Despite this intriguing observation, reasons for the enhancement remain poorly understood. In this paper, we first demonstrate experimentally that the improved performance of multi-generational self-distillation is in part associated with the increasing diversity in teacher predictions. With this in mind, we offer a new interpretation for teacher-student training as amortized MAP estimation, such that teacher predictions enable instance-specific regularization. Our framework allows us to the…
Variational mutual information (MI) estimators are widely used in unsupervised representation learning methods such as contrastive predictive coding (CPC). A lower bound on MI can be obtained from a multi-class classification problem, where a critic attempts to distinguish a positive sample drawn from the underlying joint distribution from $(m-1)$ negative samples drawn from a suitable proposal distribution. Using this approach, MI estimates are bounded above by $\log m$, and could thus severely underestimate unless $m$ is very large. To overcome this limitation, we introduce a novel estimator…
Jožef Stefan Institute（约瑟夫·斯特凡研究所）；Jožef Stefan International Postgraduate School（约瑟夫·斯特凡国际研究生院）
Predictive clustering trees (PCTs) are a well established generalization of standard decision trees, which can be used to solve a variety of predictive modeling tasks, including structured output prediction. Combining them into ensembles yields state-of-the-art performance. Furthermore, the ensembles of PCTs can be interpreted by calculating feature importance scores from the learned models. However, their learning time scales poorly with the dimensionality of the output space. This is often problematic, especially in (hierarchical) multi-label classification, where the output can consist of h…
University of California, Berkeley（加州大学伯克利分校）；University of California, San Diego（加州大学圣地亚哥分校）
In this paper, we propose Test-Time Training, a general approach for improving the performance of predictive models when training and test data come from different distributions. We turn a single unlabeled test sample into a self-supervised learning problem, on which we update the model parameters before making a prediction. This also extends naturally to data in an online stream. Our simple approach leads to improvements on diverse image classification benchmarks aimed at evaluating robustness to distribution shifts.
Undetected overfitting can occur when there are significant redundancies between training and validation data. We describe AVE, a new measure of training-validation redundancy for ligand-based classification problems that accounts for the similarity amongst inactive molecules as well as active. We investigated seven widely-used benchmarks for virtual screening and classification, and show that the amount of AVE bias strongly correlates with the performance of ligand-based predictive methods irrespective of the predicted property, chemical fingerprint, similarity measure, or previously-applied …
Korea Advanced Institute of Science and Technology（韩国科学技术院）；University of California, Berkeley（加州大学伯克利分校）
Deep neural networks with millions of parameters may suffer from poor generalization due to overfitting. To mitigate the issue, we propose a new regularization method that penalizes the predictive distribution between similar samples. In particular, we distill the predictive distribution between different samples of the same label during training. This results in regularizing the dark knowledge (i.e., the knowledge on wrong predictions) of a single network (i.e., a self-knowledge distillation) by forcing it to produce more meaningful and consistent predictions in a class-wise manner. Consequen…
We introduce Supersparse Linear Integer Models (SLIM) as a tool to create scoring systems for binary classification. We derive theoretical bounds on the true risk of SLIM scoring systems, and present experimental results to show that SLIM scoring systems are accurate, sparse, and interpretable classification models.
