Systems that are based on recursive Bayesian updates for classification limit the cost of evidence collection through certain stopping/termination criteria and accordingly enforce decision making. Conventionally, two termination criteria based on pre-defined thresholds over (i) the maximum of the state posterior distribution; and (ii) the state posterior uncertainty are commonly used. In this paper, we propose a geometric interpretation over the state posterior progression and accordingly we provide a point-by-point analysis over the disadvantages of using such conventional termination criteria. For example, through the proposed geometric interpretation we show that confidence thresholds defined over maximum of the state posteriors suffer from stiffness that results in unnecessary evidence collection whereas uncertainty based thresholding methods are fragile to number of categories and terminate prematurely if some state candidates are already discovered to be unfavorable. Moreover, both types of termination methods neglect the evolution of posterior updates. We then propose a new stopping/termination criterion with a geometrical insight to overcome the limitations of these conventional methods and provide a comparison in terms of decision accuracy and speed. We validate our claims using simulations and using real experimental data obtained through a brain computer interfaced typing system.
Kyushu Institute of Technology（九州工业大学）；The Institute of Statistical Mathematics（统计数理研究所）；RIKEN AIP（理化学研究所革新智能统合研究中心）
Active learning is a framework for supervised learning to improve the predictive performance by adaptively annotating a small number of samples. To realize efficient active learning, both an acquisition function that determines the next datum and a stopping criterion that determines when to stop learning should be considered. In this study, we propose a stopping criterion based on error stability, which guarantees that the change in generalization error upon adding a new sample is bounded by the annotation cost and can be applied to any Bayesian active learning. We demonstrate that the propose…
Kyushu Institute of Technology（九州工业大学）；The Institute of Statistical Mathematics（统计数学研究所）；RIKEN AIP（理化学研究所人工智能研究中心）
Active learning is a framework in which the learning machine can select the samples to be used for training. This technique is promising, particularly when the cost of data acquisition and labeling is high. In active learning, determining the timing at which learning should be stopped is a critical issue. In this study, we propose a criterion for automatically stopping active learning. The proposed stopping criterion is based on the difference in the expected generalization errors and hypothesis testing. We derive a novel upper bound for the difference in expected generalization errors before …
An $(ε,δ)$-accurate level set estimation with a stopping criterion
Kyushu Institute of Technology（九州工业技术大学）；Nagoya University / RIKEN AIP（名古屋大学 / RIKEN AIP）；The Institute of Statistical Mathematics/ RIKEN AIP（统计数学研究所 / RIKEN AIP）
Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the gradient of the data log-likelihood. A simple reconstruction error is often used as a stopping criterion for CD, although several authors \cite{schulz-et-al-Convergence-Contrastive-Divergence-2010-NIPSw, fischer-igel-Divergence-Contrastive-Divergence-2010-ICANN} have raised doubts concerning the feasibility of this procedure. In many cases the evolution curve …
University of Amsterdam（阿姆斯特丹大学）；Google Brain（谷歌大脑）
A common way to avoid overfitting in supervised learning is early stopping, where a held-out set is used for iterative evaluation during training to find a sweet spot in the number of training steps that gives maximum generalization. However, such a method requires a disjoint validation set, thus part of the labeled data from the training set is usually left out for this purpose, which is not ideal when training data is scarce. Furthermore, when the training labels are noisy, the performance of the model over a validation set may not be an accurate proxy for generalization. In this paper, we p…
Cornell University（康奈尔大学）；University of California（加利福尼亚大学）
Sparse Filtering is a popular feature learning algorithm for image classification pipelines. In this paper, we connect the performance of Sparse Filtering with spectral properties of the corresponding feature matrices. This connection provides new insights into Sparse Filtering; in particular, it suggests early stopping of Sparse Filtering. We therefore introduce the Optimal Roundness Criterion (ORC), a novel stopping criterion for Sparse Filtering. We show that this stopping criterion is related with pre-processing procedures such as Statistical Whitening and demonstrate that it can make imag…
Swarm Labs（Swarm实验室）；University of Maryland, College Park（马里兰大学学院市分校）
The general approach taken when training deep learning classifiers is to save the parameters after every few iterations, train until either a human observer or a simple metric-based heuristic decides the network isn't learning anymore, and then backtrack and pick the saved parameters with the best validation accuracy. Simple methods are used to determine if a neural network isn't learning anymore because, as long as it's well after the optimal values are found, the condition doesn't impact the final accuracy of the model. However from a runtime perspective, this is of great significance to the…
University of California, Berkeley（加州大学伯克利分校）；University of Southern California（南加州大学）
We consider the problem of learning an unknown Markov Decision Process (MDP) that is weakly communicating in the infinite horizon setting. We propose a Thompson Sampling-based reinforcement learning algorithm with dynamic episodes (TSDE). At the beginning of each episode, the algorithm generates a sample from the posterior distribution over the unknown model parameters. It then follows the optimal stationary policy for the sampled model for the rest of the episode. The duration of each episode is dynamically determined by two stopping criteria. The first stopping criterion controls the growth …
Université Sorbonne Paris Nord（巴黎北索邦大学）；CNRS（法国国家科学研究中心）；LaMSN, La Maison des Sciences Numériques, USPN（数字科学之家实验室（巴黎北索邦大学））
Collaborative learning has recently achieved very significant results. It still suffers, however, from several issues, including the type of information that needs to be exchanged, the criteria for stopping and how to choose the right collaborators. We aim in this paper to improve the quality of the collaboration and to resolve these issues via a novel approach inspired by Optimal Transport theory. More specifically, the objective function for the exchange of information is based on the Wasserstein distance, with a bidirectional transport of information between collaborators. This formulation …
Politecnico di Torino（都灵理工大学）；University of Bologna（博洛尼亚大学）；ETH Zurich（苏黎世联邦理工学院）
Energy-efficient machine learning models that can run directly on edge devices are of great interest in IoT applications, as they can reduce network pressure and response latency, and improve privacy. An effective way to obtain energy-efficiency with small accuracy drops is to sequentially execute a set of increasingly complex models, early-stopping the procedure for "easy" inputs that can be confidently classified by the smallest models. As a stopping criterion, current methods employ a single threshold on the output probabilities produced by each model. In this work, we show that such a crit…
