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APPROXIMATION THEORY, COMPUTING, AND DEEP learning ON THE WASSERSTEIN SPACE

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arXiv 2023年

作者： Fornasier, Massimo Heid, Pascal Sodini, Giacomo Enrico TUM School of Computation Information Technlogy Department of Mathematics Boltzmannstrasse 3 Garching bei München85748 Germany TUM Institute for Advanced Studies Germany Munich Data Science Institute Germany Munich Center for Machine Learning Germany Institut für Mathematik Fakultät für Mathematik Universität Wien Oskar-Morgenstern-Platz 1 Wien1090 Austria

The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. In this study, we delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on probability spaces. Our particular focus centers on the Wasserstein distance function, which serves as a relevant example. In contrast to the existing body of literature focused on approximating efficiently pointwise evaluations, we chart a new course to define functional approximants by adopting three machine learning-based approaches: 1. Solving a finite number of optimal transport problems and computing the corresponding Wasserstein potentials. 2. Employing empirical risk minimization with Tikhonov regularization in Wasserstein Sobolev spaces. 3. Addressing the problem through the saddle point formulation that characterizes the weak form of the Tikhonov functional’s Euler-Lagrange equation. As a theoretical contribution, we furnish explicit and quantitative bounds on generalization errors for each of these solutions. In the proofs, we leverage the theory of metric Sobolev spaces and we combine it with techniques of optimal transport, variational calculus, and large deviation bounds. In our numerical implementation, we harness appropriately designed neural networks to serve as basis functions. These networks undergo training using diverse methodologies. This approach allows us to obtain approximating functions that can be rapidly evaluated after training. Consequently, our constructive solutions significantly enhance at equal accuracy the evaluation speed, surpassing that of state-of-the-art methods by several orders of magnitude. This allows evaluations over large datasets several times faster, including training, than traditional optimal transport algorithms. Moreover, our analytically designed deep learning architecture slightly outperforms the test error of state-of-the-art CNN architectures on datasets of ***

关键词： Sobolev spaces

Less is More: Facial Landmarks can Recognize a Spontaneous Smile 022

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arXiv 2022年

作者： Tushar, Tahrim Faroque Yang, Yan Hossain, Zakir Naim, Sheikh Motahar Mohammed, Nabeel Rahman, Shafin Department of Electrical and Computer Engineering North South University Bangladesh Biological Data Science Institute The Australian National University Canberra Australia CSIRO Agriculture & Food Canberra Australia CSIRO Machine Learning & Artificial Intelligence Future Science Platform Canberra Australia Amazon Web Services United States

Smile veracity classification is a task of interpreting social interactions. Broadly, it distinguishes between spontaneous and posed smiles. Previous approaches used hand-engineered features from facial landmarks or considered raw smile videos in an end-to-end manner to perform smile classification tasks. Feature-based methods require intervention from human experts on feature engineering and heavy pre-processing steps. On the contrary, raw smile video inputs fed into end-to-end models bring more automation to the process with the cost of considering many redundant facial features (beyond landmark locations) that are mainly irrelevant to smile veracity classification. It remains unclear to establish discriminative features from landmarks in an end-to-end manner. We present a MeshSmileNet framework, a transformer architecture, to address the above limitations. To eliminate redundant facial features, our landmarks input is extracted from Attention Mesh, a pre-trained landmark detector. Again, to discover discriminative features, we consider the relativity and trajectory of the landmarks. For the relativity, we aggregate facial landmark that conceptually formats a curve at each frame to establish local spatial features. For the trajectory, we estimate the movements of landmark composed features across time by self-attention mechanism, which captures pairwise dependency on the trajectory of the same landmark. This idea allows us to achieve state-of-the-art performances on UVA-NEMO, BBC, MMI Facial Expression, and SPOS datasets. © 2022, CC BY-NC-ND.

关键词： Relativity

Convergence of Multiscale Reinforcement Q-learning Algorithms for Mean Field Game and Control Problems

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arXiv 2023年

作者： Angiuli, Andrea Fouque, Jean-Pierre Laurière, Mathieu Zhang, Mengrui Prime Machine Learning Team Amazon. 320 Westlake Ave N SEA83 SeattleWA98109 United States Department of Statistics and Applied Probability South Hall University of California Santa BarbaraCA93106 United States Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai NYU Shanghai 567 West Yangsi Road Shanghai200126 China

We establish the convergence of the unified two-timescale Reinforcement learning (RL) algorithm presented in [Angiuli et al., 2022]. This algorithm provides solutions to Mean Field Game (MFG) or Mean Field Control (MFC) problems depending on the ratio of two learning rates, one for the value function and the other for the mean field term. Our proof of convergence highlights the fact that in the case of MFC several mean field distributions need to be updated and for this reason we present two separate algorithms, one for MFG and one for MFC. We focus on a setting with finite state and action spaces, discrete time and infinite horizon. The proofs of convergence rely on a generalization of the two-timescale approach of [Borkar, 1997]. The accuracy of approximation to the true solutions depends on the smoothing of the policies. We provide a numerical example illustrating the convergence. © 2023, CC BY.

关键词： Reinforcement learning

Even order contributions to relative energies vanish for antisymmetric perturbations

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arXiv 2023年

作者： von Lilienfeld, O. Anatole Domenichini, Giorgio Vector Institute for Artificial Intelligence TorontoONM5S 1M1 Canada Departments of Chemistry Materials Science and Engineering and Physics University of Toronto St. George Campus TorontoON Canada Machine Learning Group Technische Universität Berlin Institute for the Foundations of Learning and Data Berlin10587 Germany University of Vienna Faculty of Physics Kolingasse 14-16 ViennaAT-1090 Austria University of Vienna Vienna Doctoral School in Physics Boltzmanngasse 5 ViennaAT-1090 Austria

We show that even order contributions to energy differences between any two iso-electronic compounds vanish when using perturbation theory around an averaged electronic reference Hamiltonian. This finding generalizes the previously introduced alchemical chirality concept [von Rudorff, von Lilienfeld, science Advances, 7 2021] by lifting the symmetry requirements for transmutating atoms in the iso-electronic reference system. The leading order term corresponds to twice the Hellmann-Feynman derivative evaluated using the electron density of the averaged Hamiltonian. Analogous analysis reveals Mel Levy's formula for relative energies [J. Chem. Phys. 70, 1573 (1979)] to include the first order contribution while overestimating the higher odd order energy contributions by a factor linearly increasing in order. Using density functional theory, we illustrate the predictive power of the leading order term for estimating relative energies among diatomics in the charge-neutral iso-electronic 14 proton series N2, CO, BF, BeNe, LiNa, HeMg, HAl, and the united atom, Si. The framework's potential for the simultaneous exploration of multiple dimensions in chemical space is demonstrated for toluene by evaluating relative energies between all the possible 35 antisymmetric BN doped isomers (dubbed "alchemical diastereomers"). Based solely on toluene's electron density, necessary to evaluate all the respective Hellmann-Feynman derivatives, mean absolute errors of predicted total potential energy differences between the alchemical diastereomers are on the scale of mHa. © 2023, CC0.

关键词： Carrier concentration

Modeling non-genetic information dynamics in cells using reservoir computing

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arXiv 2023年

作者： Niraula, Dipesh Naqa, Issam El Tuszynski, Jack Adam Gatenby, Robert A. Department of Machine Learning Moffitt Cancer Center TampaFL United States Departments of Physics and Oncology University of Alberta EdmontonAB Canada Department of Data Science and Engineering The Silesian University of Technology Gliwice44-100 Poland Department of Mechanical and Aerospace Engineering Politecnico di Torino TurinI-10129 Italy Departments of Radiology and Integrated Mathematical Oncology Moffitt Cancer Center TampaFL United States

Virtually all cells use energy and ion-specific membrane pumps to maintain large transmembrane gradients of Na+, K+, Cl−, Mg++, and Ca++. Although they consume up to 1/3 of a cell’s energy budget, the corresponding evolutionary benefit of transmembrane ion gradients remain unclear. Here, we propose that ion gradients enable a dynamic and versatile biological system that acquires, analyzes, and responds to environmental information. We hypothesize environmental signals are transmitted into the cell by ion fluxes along pre-existing gradients through gated ion-specific membrane channels. The consequent changes of cytoplasmic ion concentration can generate a local response and orchestrate global or regional responses through wire-like ion fluxes along preexisting and self-assembling cytoskeleton to engage the endoplasmic reticulum, mitochondria, and nucleus. Here, we frame our hypothesis through a quasi-physical (Cell-Reservoir) model that treats intra-cellular ion-based information dynamics as a sub-cellular process permitting spatiotemporally resolved cellular response that is also capable of learning complex nonlinear dynamical cellular behavior. We demonstrate the proposed ion dynamics permits rapid dissemination of response to information extrinsic perturbations that is consistent with experimental observations. © 2023, CC BY.

关键词： Ions

AutoMS: automatic model selection for novelty detection with error rate control 22

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AutoMS: automatic model selection for novelty detection with...

Proceedings of the 36th International Conference on Neural Information Processing Systems

作者： Yifan Zhang Haiyan Jiang Haojie Ren Changliang Zou Dejing Dou School of Statistics and Data Sciences LPMC KLMDASR and LEBPS Nankai University Tianjin China Machine Learning Department MBZUAI Abu Dhabi UAE and Baidu Research Baidu Inc. Beijing China School of Mathematical Science Shanghai Jiao Tong University Shanghai China Baidu Research Baidu Inc. Beijing China

ISBN: (纸本)9781713871088

Given an unsupervised novelty detection task on a new dataset, how can we automatically select a "best" detection model while simultaneously controlling the error rate of the best model? For novelty detection analysis, numerous detectors have been proposed to detect outliers on a new unseen dataset based on a score function trained on available clean data. However, due to the absence of labeled anomalous data for model evaluation and comparison, there is a lack of systematic approaches that are able to select the "best" model/detector (i.e., the algorithm as well as its hyperparameters) and achieve certain error rate control simultaneously. In this paper, we introduce a unified data-driven procedure to address this issue. The key idea is to maximize the number of detected outliers while controlling the false discovery rate (FDR) with the help of Jackknife prediction. We establish non-asymptotic bounds for the false discovery proportions and show that the proposed procedure yields valid FDR control under some mild conditions. Numerical experiments on both synthetic and real data validate the theoretical results and demonstrate the effectiveness of our proposed AutoMS method.

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The Role of Blockchain Technology in Supply chain Management for data Security

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The Role of Blockchain Technology in Supply chain Management...

Blockchain and Distributed Systems Security (ICBDS), IEEE International Conference on

作者： Dipika R. Birari Vijay U. Rathod Aarti Dandavate Nilesh Shelke Ranjit Kumar Masira M. S Kulkarni Department of Information Technology Army Institute of Technology Pune Department of Artificial Intelligent and Machine Learning G H Raisoni College of Engineering and Management Wagholi Pune Department of Computer Engineering Dhole Patil College of Engineering Pune Department of Computer Science and Engineering Symbiosis Institute of Technology Nagpur Campus Symbiosis International Deemed University Pune India Department of Computer Engineering Ajeenkya D Y Patil University Pune Department of Cyber Security and Data Science G H Raisoni College of Engineering and Management Wagholi Pune

ISBN: (数字)9798350354348

ISBN: (纸本)9798350354355

In a traditional supply chain system, the process of producing raw materials so that a product may be delivered to a customer is a manual operation with insufficient data and transaction security. The entire process is time consuming and requires a lot of effort. The undivided process is generally ineffective and unreliable for consumers. The data security, authenticity, the inclusion of will significantly improve the time management and transaction procedures of conventional supply chain management systems. data is shielded from illegal access via the ground-breaking, decentralized technology known as blockchain. After smart contracts are put into place, the complete supply chain management (SCM) will be satisfied with the customer. When the mediator is contracted, which is possible in various ways, the plan becomes more reliable. This article places particular emphasis on lowering third party involvement in the supply chain system and enhancing data security. Conventional supply chain management techniques have several serious shortcomings. Some of them include a lack of traceability, difficulties maintaining product safety and quality, a failure to track and manage inventories in stores and warehouses, escalating supply chain costs, and so on. The reduction of third-party involvement in the supply chain system and the improvement of data security are the main goals of this article. This enhances process accessibility, effectiveness, and timeliness overall. They will feel safer throughout the payment procedure, which is the main benefit. Yet in this investigation, a smart contract and a peer-to-peer encrypted system were both used. There are a few additional features as well.

关键词： Supply chain management Costs Supply chains Smart contracts Reliability engineering Raw materials Blockchains Peer-to-peer computing Product safety

MCBench: A Benchmark Suite for Monte Carlo Sampling Algorithms

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arXiv 2025年

作者： Ding, Zeyu Grunwald, Cornelius Ickstadt, Katja Kröninger, Kevin La Cagnina, Salvatore Department of Statistics TU Dortmund University Vogelpothsweg 87 Dortmund44227 Germany Department of Physics TU Dortmund University Otto-Hahn-Straße 4 Dortmund44227 Germany Lamarr-Institute for Machine Learning and Artificial Intelligence Joseph-von-Fraunhofer-Straße 25 Dortmund44227 Germany TU Dortmund - Center for Data Science and Simulation TU Dortmund University August-Schmidt-Straße 4 Dortmund44227 Germany

In this paper, we present MCBench, a benchmark suite designed to assess the quality of Monte Carlo (MC) samples. The benchmark suite enables quantitative comparisons of samples by applying different metrics, including basic statistical metrics as well as more complex measures, in particular the sliced Wasserstein distance and the maximum mean discrepancy. We apply these metrics to point clouds of both independent and identically distributed (IID) samples and correlated samples generated by MC techniques, such as Markov Chain Monte Carlo or Nested Sampling. Through repeated comparisons, we evaluate test statistics of the metrics, allowing to evaluate the quality of the MC sampling algorithms. Our benchmark suite offers a variety of target functions with different complexities and dimensionalities, providing a versatile platform for testing the capabilities of sampling algorithms. Implemented as a Julia package, MCBench enables users to easily select test cases and metrics from the provided collections, which can be extended as needed. Users can run external sampling algorithms of their choice on these test functions and input the resulting samples to obtain detailed metrics. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov chains

RBGNet: Ray-based Grouping for 3D Object Detection

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arXiv 2022年

作者： Wang, Haiyang Shi, Shaoshuai Yang, Ze Fang, Rongyao Qian, Qi Li, Hongsheng Schiele, Bernt Wang, Liwei Center for Data Science Peking University China Max Planck Institute for Informatics Germany University of Toronto Canada The Chinese University of Hong Kong Hong Kong Alibaba Group China Key Laboratory of Machine Perception MOE School of Artificial Intelligence Peking University China International Center for Machine Learning Research Peking University China

As a fundamental problem in computer vision, 3D object detection is experiencing rapid growth. To extract the point-wise features from the irregularly and sparsely distributed points, previous methods usually take a feature grouping module to aggregate the point features to an object candidate. However, these methods have not yet leveraged the surface geometry of foreground objects to enhance grouping and 3D box generation. In this paper, we propose the RBGNet framework, a voting-based 3D detector for accurate 3D object detection from point clouds. In order to learn better representations of object shape to enhance cluster features for predicting 3D boxes, we propose a ray-based feature grouping module, which aggregates the point-wise features on object surfaces using a group of determined rays uniformly emitted from cluster centers. Considering the fact that foreground points are more meaningful for box estimation, we design a novel foreground biased sampling strategy in downsample process to sample more points on object surfaces and further boost the detection performance. Our model achieves state-of-the-art 3D detection performance on ScanNet V2 and SUN RGB-D with remarkable performance gains. Code will be available at https://***/Haiyang-W/RBGNet. Copyright © 2022, The Authors. All rights reserved.

关键词： Object recognition