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Balancing Molecular Information and Empirical Data in the Prediction of Physico-Chemical Properties

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arXiv 2024年

作者： Zenn, Johannes Gond, Dominik Jirasek, Fabian Bamler, Robert AI Center Tübingen Germany University of Tübingen Germany IMPRS-IS Germany RPTU Kaiserslautern United States

Predicting the physico-chemical properties of pure substances and mixtures is a central task in thermodynamics. Established prediction methods range from fully physics-based ab-initio calculations, which are only feasible for very simple systems, over descriptor-based methods that use some information on the molecules to be modeled together with fitted model parameters (e.g., quantitative-structure-property relationship methods or classical group contribution methods), to representation-learning methods, which may, in extreme cases, completely ignore molecular descriptors and extrapolate only from existing data on the property to be modeled (e.g., matrix completion methods). In this work, we propose a general method for combining molecular descriptors with representation learning using the so-called expectation maximization algorithm from the probabilistic machine-learning literature, which uses uncertainty estimates to trade off between the two approaches. The proposed hybrid model exploits chemical structure information using graph neural networks, but it automatically detects cases where structure-based predictions are unreliable, in which case it corrects them by representation-learning based predictions that can better specialize to unusual cases. The effectiveness of the proposed method is demonstrated using the prediction of activity coefficients in binary mixtures as an example. The results are compelling, as the method significantly improves predictive accuracy over the current state of the art, showcasing its potential to advance the prediction of physico-chemical properties in general. © 2024, CC BY.

关键词： expectation maximization algorithm

PixOOD: Pixel-Level Out-of-Distribution Detection

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arXiv 2024年

作者： Vojíř, Tomáš Šochman, Jan Matas, Jiří Czech Technical University in Prague Faculty of Electrical Engineering Department of Cybernetics Visual Recognition Group Czech Republic

We propose a pixel-level out-of-distribution detection algorithm, called PixOOD, which does not require training on samples of anomalous data and is not designed for a specific application which avoids traditional training biases. In order to model the complex intra-class variability of the in-distribution data at the pixel level, we propose an online data condensation algorithm which is more robust than standard K-means and is easily trainable through SGD. We evaluate PixOOD on a wide range of problems. It achieved state-of-the-art results on four out of seven datasets, while being competitive on the rest. The source code is available at https://***/vojirt/PixOOD. © 2024, CC BY-NC-SA.

关键词： expectation maximization algorithm

A general statistical approach to quantum algorithms in a circuit model based on the expectation and standard deviation of each gate separately

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arXiv 2024年

作者： Shushi, Tomer Center for Quantum Science and Technology Department of Business Administration Guilford Glazer Faculty of Business and Management Ben-Gurion University of the Negev Beer-Sheva Israel

Recently, there has been a growing literature exploring the generalization of quantum algorithms, such that different quantum algorithms are special examples of a more fundamental structure. In this short paper, we provide a general approach to describe quantum algorithms as a quantum state with amplitudes that are constructed from the expected value and standard deviation of each quantum gate or a sub-sequence of gates in the algorithm. The proposed statistical-based description relies on the celebrated Aharonov-Vaidman identity. We present a more fundamental identity that, unlike the previous one, allows us to switch the basis of the states into a desired form. © 2024, CC BY.

关键词： expectation maximization algorithm

Mixed Noise and Posterior Estimation with Conditional DeepGEM

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arXiv 2024年

作者： Hagemann, Paul Hertrich, Johannes Casfor, Maren Heidenreich, Sebastian Steidl, Gabriele Institute of Mathematics TU Berlin Straße des 17. Juni 136 BerlinD-10623 Germany University College London United Kingdom Physikalisch Technische Bundesanstalt Germany

We develop an algorithm for jointly estimating the posterior and the noise parameters in Bayesian inverse problems, which is motivated by indirect measurements and applications from nanometrology with a mixed noise model. We propose to solve the problem by an expectation maximization algorithm. Based on the current noise parameters, we learn in the E-step a conditional normalizing flow that approximates the posterior. In the M-step, we propose to find the noise parameter updates again by an expectation maximization algorithm, which has analytical formulas. We compare the training of the conditional normalizing flow with the forward and reverse Kullback-Leibler divergence, and show that our model is able to incorporate information from many measurements, unlike previous approaches. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Matching prior pairs connecting Maximum A Posteriori estimation and posterior expectation

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arXiv 2023年

作者： Okudo, Michiko Yano, Keisuke Department of Mathematical Informatics Graduate School of Information Science and Technology The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan The Institute of Statistical Mathematics 10-3 Midori cho Tokyo Tachikawa190-8562 Japan

Bayesian statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We derive an asymptotic condition for a pair of prior densities under which the posterior mean based on one prior coincides with the MAP estimate based on the other prior. A sufficient condition for the existence of this prior pair relates to α-flatness of the statistical model in information geometry. We also construct a matching prior pair using α-parallel priors. Our result elucidates an interesting connection between regularization in generalized linear regression models and posterior expectation. Copyright © 2023, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Causal Bayesian Optimization via Exogenous Distribution Learning

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arXiv 2024年

作者： Ren, Shaogang Qian, Xiaoning Department of Computer Science and Engineering University of Tennessee at Chattanooga United States Department of Electrical and Computer Engineering Texas A&M University United States

Maximizing a target variable as an operational objective in a structural causal model is an important problem. Causal Bayesian Optimization (CBO) methods either rely on interventions that alter the causal structure to maximize the reward;or introduce action nodes to endogenous variables so that the data generation mechanisms are adjusted to achieve the objective. This paper introduces a novel method to learn the distribution of exogenous variables, which is typically marginalized through expectation or ignored by existing CBO methods. Exogenous distribution learning improves the approximation accuracy of structural causal models in a surrogate model that is usually trained with limited observational data. Moreover, the learned exogenous distribution extends existing CBO to general causal schemes beyond simple Additive Noise Models (ANMs). The recovery of exogenous variables allows us to use a more flexible prior for noise or unobserved hidden variables. We develop a new CBO method by leveraging the learned exogenous distribution. Experiments on different datasets and applications show the benefits of our proposed method. © 2024, CC BY-NC-ND.

关键词： expectation maximization algorithm

Extended target tracking with mobility based on GPR-AUKF

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Heliyon 2024年第23期10卷 e40506页

作者： Zhang, Renli Zhang, Yan Chen, Jintao Sun, Ziwen Li, Jing Tan, Zhuangbin Jiao, Zhongxing School of Aeronautics and Astronautics Sun Yat-sen University Shenzhen 518107 China School of Electronics and Communication Engineering Sun Yat-sen University Shenzhen 518107 China

Simultaneously estimating the kinematic state and extent of extended targets is a nonlinear and high-dimensional problem. While the extended Kalman filter (EKF) is widely employed to achieve this goal, it may not be sufficient for mobility targets. To address this issue, this paper first proposes to embed unscented Kalman filter (UKF) into Gaussian process regression (GPR) since the superiority of UKF to high nonlinear. Furthermore, given the widely-existed environment with time-varying noise, it is crucial to study the change of measurement noise covariance caused by time-varying noise for high-precision tracking of extended targets. However, traditional UKF filter considers measurement noise covariance as constant value. To this end, an adaptive unscented Kalman filter (AUKF) algorithm combining with GPR model (GPR-AUKF) is proposed to address the issue. Specifically, the GPR-AUKF algorithm is built based on expectation maximization (EM) algorithm to track the target state and covariance, and which updates the measurement noise covariance in real-time. Experimental results show that GPR-AUKF is more accurate and robust than other methods for tracking extended targets. © 2024

关键词： Adaptive unscented Kalman filter expectation maximization algorithm Extended target Gaussian process regression Time-varying noise

First-Person Indoor Navigation via Vision-Inertial Data Fusion

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First-Person Indoor Navigation via Vision-Inertial Data Fusi...

IEEE/ION Position, Location and Navigation Symposium

作者： Amirreza Farnoosh Mohsen Nabian Pau Closas Sarah Ostadabbas Electrical and Computer Engineering Department Northeastern University Boston MA USA

In this paper, we aim to enhance the first-person indoor navigation and scene understanding experience by fusing inertial data collected from a smartphone carried by the user with the vision information obtained through the phone's camera. We employed the concept of vanishing directions together with the orthogonality constraints of the man-made environments in an expectation maximization framework to estimate person's orientation with respect to the known indoor coordinates from video frames. This framework allows to include prior information about camera rotation axis for better estimations as well as to select candidate edge-lines for estimation of hallways' depth and width from monocular video frames, and 3D modeling of the scene. Our proposed algorithm concurrently combines the vision-based estimated orientation with the inertial data using a Kalman filter in order to refine estimations and remove substantial measurement drift from inertial sensors. We evaluated the performance of our vision-inertial data fusion method on an IMU-augmented video recorded from a rotary hallway in which a participant completed a full lap. We demonstrated that this fusion provides virtually drift-free instantaneous information about the person's relative orientation. We were able to estimate hallways' depth and width, and generate a closed-path map from the rotary hallway over a roughly 60-meter lap.

关键词： Computer vision Data fusion expectation maximization algorithm In-door navigation Simultaneous localization and mapping (SLAM)

Unsupervised algorithm for Radiographic Image Segmentation Based on the Gaussian Mixture Model

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Unsupervised Algorithm for Radiographic Image Segmentation B...

EUROCON 2007 - The International Conference on " Computer as a Tool" (EUROCON 2007), vol.3

作者： Faiza Mekhalfa Nafaa Nacereddine Aicha Baya Goumeidane Image and Signal Processing Laboratory Welding and NDT Research Center Cheraga Algeria

In this paper we study an unsupervised algorithm for radiographic image segmentation, based on the Gaussian mixture models (GMMs). Gaussian mixture models constitute a well-known type of probabilistic neural networks. One of their many successful applications is in image segmentation. Mixture model parameters have been trained using the expectation maximization (EM) algorithm. Numerical experiments using radiographic images illustrate the superior performance of EM method in term of segmentation accuracy compared to fuzzy c-means algorithm.

关键词： Weld defect Radiographic images Image segmentation Gaussian mixture model expectation maximization algorithm Fuzzy C-means algorithm