Class (philosophy)

About: Class (philosophy) is a research topic. Over the lifetime, 821 publications have been published within this topic receiving 28000 citations.

What does a vector field know about volume

Abstract: This note provides an affirmative answer to a question of Viterbo concerning the existence of nondiffeomorphic contact forms that share the same Reeb vector field. Starting from an observation by Croke-Kleiner and Abbondandolo that such contact forms define the same total volume, we discuss various related issues for the wider class of geodesible vector fields. In particular, we define an Euler class of a geodesible vector field in the associated basic cohomology and give a topological characterisation of vector fields with vanishing Euler class. We prove the theorems of Gauss-Bonnet and Poincare-Hopf for closed, oriented 2-dimensional orbifolds using global surfaces of section and the volume determined by a geodesible vector field. This volume is computed for Seifert fibred 3-manifolds and for some transversely holomorphic flows.

Optimistic MLE: A Generic Model-Based Algorithm for Partially Observable Sequential Decision Making

Abstract: This paper introduces a simple efficient learning algorithms for general sequential decision making. The algorithm combines Optimism for exploration with Maximum Likelihood Estimation for model estimation, which is thus named OMLE. We prove that OMLE learns the near-optimal policies of an enormously rich class of sequential decision making problems in a polynomial number of samples. This rich class includes not only a majority of known tractable model-based Reinforcement Learning (RL) problems (such as tabular MDPs, factored MDPs, low witness rank problems, tabular weakly-revealing/observable POMDPs and multi-step decodable POMDPs ), but also many new challenging RL problems especially in the partially observable setting that were not previously known to be tractable. Notably, the new problems addressed by this paper include (1) observable POMDPs with continuous observation and function approximation, where we achieve the first sample complexity that is completely independent of the size of observation space; (2) well-conditioned low-rank sequential decision making problems (also known as Predictive State Representations (PSRs)), which include and generalize all known tractable POMDP examples under a more intrinsic representation; (3) general sequential decision making problems under SAIL condition, which unifies our existing understandings of model-based RL in both fully observable and partially observable settings. SAIL condition is identified by this paper, which can be viewed as a natural generalization of Bellman/witness rank to address partial observability. This paper also presents a reward-free variant of OMLE algorithm, which learns approximate dynamic models that enable the computation of near-optimal policies for all reward functions simultaneously.

Continual learning with Bayesian model based on a fixed pre-trained feature extractor

Abstract: Abstract Deep learning has shown its human-level performance in various applications. However, current deep learning models are characterized by catastrophic forgetting of old knowledge when learning new classes. This poses a challenge such as in intelligent diagnosis systems where initially only training data of a limited number of diseases are available. In this case, updating the intelligent system with data of new diseases would inevitably downgrade its performance on previously learned diseases. Inspired by the process of learning new knowledge in human brains, we propose a Bayesian generative model for continual learning built on a fixed pre-trained feature extractor. In this model, knowledge of each old class can be compactly represented by a collection of statistical distributions, e.g., with Gaussian mixture models, and naturally kept from forgetting in continual learning over time. Unlike existing class-incremental learning methods, the proposed approach is not sensitive to the continual learning process and can be additionally well applied to the data-incremental learning scenario. Experiments on multiple medical and natural image classification tasks reveal that the proposed approach outperforms state-of-the-art approaches that even keep some images of old classes during continual learning of new classes.

Reference Class Forecasting and Machine Learning for Improved Offshore Oil and Gas Megaproject Planning: Methods and Application

Abstract: This article develops and describes rigorous oil and gas project forecasting methods. First, it builds a theoretical foundation by mapping megaproject performance literature to these projects. Second, it draws on heuristics and biases literature, using a questionnaire to demonstrate forecasting-related biases and principal-agent issues among industry project professionals. Third, it uses methodically collected project performance data to demonstrate that overrun distributions are non-normal and fat-tailed. Fourth, reference-class forecasting is demonstrated for cost and schedule uplifts. Finally, a predictive approach using machine learning (ML) considers project-specific factors to forecast the most likely cost and schedule overruns in a project.