Regressing the vector field of a dynamical system from a finite number of observed states is a natural way to learn surrogate models for such systems. We present variants of cross-validation (Kernel Flows \cite{Owhadi19} and its variants based on Maximum Mean Discrepancy and Lyapunov exponents) as simple approaches for learning the kernel used in these emulators.
An effective approach in meta-learning is to utilize multiple "train tasks" to learn a good initialization for model parameters that can help solve unseen "test tasks" with very few samples by fine-tuning from this initialization. Although successful in practice, theoretical understanding of such methods is limited. This work studies an important aspect of these methods: splitting the data from each task into train (support) and validation (query) sets during meta-training. Inspired by recent work (Raghu et al., 2020), we view such meta-learning methods through the lens of representation learn…
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Imperial College London（帝国理工学院）；Zhejiang Zhelixin Credit Investigation Co., Ltd.（浙江浙里信征信有限公司）；Caltech（加州理工学院）；Johns Hopkins University（约翰斯·霍普金斯大学）
Regressing the vector field of a dynamical system from a finite number of observed states is a natural way to learn surrogate models for such systems. A simple and interpretable way to learn a dynamical system from data is to interpolate its vector-field with a data-adapted kernel which can be learned by using Kernel Flows. The method of Kernel Flows is a trainable machine learning method that learns the optimal parameters of a kernel based on the premise that a kernel is good if there is no significant loss in accuracy if half of the data is used. The objective function could be a short-term …
National University of Singapore（新加坡国立大学）；Peking University（北京大学）
We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for universal approximation using continuous-time deep residual networks, which can also be understood as approximation theories in $L^p$ using flow maps of dynamical systems. In specific cases, rates of approximation in terms of the time horizon are also established. Overall, these results reveal that composition function approximation through flow maps present…
The Lipschitz constant of neural networks has been established as a key quantity to enforce the robustness to adversarial examples. In this paper, we tackle the problem of building $1$-Lipschitz Neural Networks. By studying Residual Networks from a continuous time dynamical system perspective, we provide a generic method to build $1$-Lipschitz Neural Networks and show that some previous approaches are special cases of this framework. Then, we extend this reasoning and show that ResNet flows derived from convex potentials define $1$-Lipschitz transformations, that lead us to define the {\em Con…
To study users' travel behaviour and travel time between origin and destination, researchers employ travel surveys. Although there is consensus in the field about the potential, after over ten years of research and field experimentation, Smartphone-based travel surveys still did not take off to a large scale. Here, computer intelligence algorithms take the role that operators have in Traditional Travel Surveys; since we train each algorithm on data, performances rest on the data quality, thus on the ground truth. Inaccurate validations affect negatively: labels, algorithms' training, travel di…
The evaluation of recommender systems from a practical perspective is a topic of ongoing discourse within the research community. While many current evaluation methods reduce performance to a single value metric as an easy way to compare models, it relies on the assumption that the methods' performance remains constant over time. In this study, we examine this assumption and propose the Cross-Validation Thought Time (CVTT) technique as a more comprehensive evaluation method, focusing on model performance over time. By utilizing the proposed technique, we conduct an in-depth analysis of the per…
Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align existing branches of deep learning theory through the lens of dynamical system and optimal control. By viewing deep neural networks as discrete-time nonlinear dynamical systems, we can analyze how information propagates through layers using mean field theory. When optimization algorithms are further recast as controllers, the ultimate goal of training processes…
Swiss Federal Institute of Technology, ETH Zurich（苏黎世联邦理工学院）
Model selection in clustering requires (i) to specify a suitable clustering principle and (ii) to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an information theoretic perspective where the uncertainty in the measurements quantizes the set of data partitionings and, thereby, induces uncertainty in the solution space of clusterings. A clustering model, which can tolerate a higher level of fluctuations in the measurements than alternative models, is considered to be superior provided that the clustering sol…
RWTH Aachen University（亚琛工业大学）；Institute for Automotive Engineering（汽车工程研究所）
Scenario-based testing for the safety validation of highly automated vehicles is a promising approach that is being examined in research and industry. This approach heavily relies on data from real-world scenarios to derive the necessary scenario information for testing. Measurement data should be collected at a reasonable effort, contain naturalistic behavior of road users and include all data relevant for a description of the identified scenarios in sufficient quality. However, the current measurement methods fail to meet at least one of the requirements. Thus, we propose a novel method to m…
Machine learning decision systems are getting omnipresent in our lives. From dating apps to rating loan seekers, algorithms affect both our well-being and future. Typically, however, these systems are not infallible. Moreover, complex predictive models are really eager to learn social biases present in historical data that can lead to increasing discrimination. If we want to create models responsibly then we need tools for in-depth validation of models also from the perspective of potential discrimination. This article introduces an R package fairmodels that helps to validate fairness and elim…
A roadmap to fair and trustworthy prediction model validation in healthcare
Duke-NUS Medical School（杜克-国大医学院）；Erasmus MC University Medical Center（伊拉斯姆斯大学医学中心）；Singapore Health Services（新加坡保健服务集团）；Singapore General Hospital（新加坡中央医院）；Duke University（杜克大学）；National University of Singapore（新加坡国立大学）
