Through constant improvements in recent years radar sensors have become a viable alternative to lidar as the main distancing sensor of an autonomous vehicle. Although robust and with the possibility to directly measure the radial velocity, it brings it's own set of challenges, for which existing algorithms need to be adapted. One core algorithm of a perception system is dynamic occupancy grid mapping, which has traditionally relied on lidar. In this paper we present a dual-weight particle filter as an extension for a Bayesian occupancy grid mapping framework to allow to operate it with radar as its main sensors. It uses two separate particle weights that are computed differently to compensate that a radial velocity measurement in many situations is not able to capture the actual velocity of an object. We evaluate the method extensively with simulated data and show the advantages over existing single weight solutions.

This paper approaches the unsupervised learning problem by gradient descent in the space of probability density functions. A main result shows that along the gradient flow induced by a distribution-dependent ordinary differential equation (ODE), the unknown data distribution emerges as the long-time limit. That is, one can uncover the data distribution by simulating the distribution-dependent ODE. Intriguingly, the simulation of the ODE is shown equivalent to the training of generative adversarial networks (GANs). This equivalence provides a new "cooperative" view of GANs and, more importantly, sheds new light on the divergence of GANs. In particular, it reveals that the GAN algorithm implicitly minimizes the mean squared error (MSE) between two sets of samples, and this MSE fitting alone can cause GANs to diverge. To construct a solution to the distribution-dependent ODE, we first show that the associated nonlinear Fokker-Planck equation has a unique weak solution, by the Crandall-Liggett theorem for differential equations in Banach spaces. Based on this solution to the Fokker-Planck equation, we construct a unique solution to the ODE, using Trevisan's superposition principle. The convergence of the induced gradient flow to the data distribution is obtained by analyzing the Fokker-Planck equation.

The constraints ensure that the interaction term can be nonzero only if the corresponding main term is nonzero. Even though the idea is still young, it has been applied in different areas, for example to multinomial logistic regression (Asenso et al., 2022b), Cox's proportional hazards model (Du and Tibshirani, 2018) and support vector machines (Asenso et al., 2022a). However, in all the above studies, the block-wise coordinate descent procedure was used in solving the problem which includes overlapping groups. The algorithm involves multiple "if" statements and a generalized gradient at the final stage. This implies that extending the model to a multi-response case would require rigorous computations like the case of Li et al. 2015, which might be difficult to handle. In this paper, we introduce the alternating direction method of multipliers (ADMM) to handle this problem and extend the results from the single response model to a multi-response problem. We provide a publicly available software package MAD-MMplasso (Asenso and Zucknick, 2022) implemented in R. We present a brief review on the ADMM algorithm in what follows.

Massive rumors usually appear along with breaking news or trending topics, seriously hindering the truth. Existing rumor detection methods are mostly focused on the same domain, and thus have poor performance in cross-domain scenarios due to domain shift. In this work, we propose an end-to-end instance-wise and prototype-wise contrastive learning model with a cross-attention mechanism for cross-domain rumor detection. The model not only performs cross-domain feature alignment but also enforces target samples to align with the corresponding prototypes of a given source domain. Since target labels in a target domain are unavailable, we use a clustering-based approach with carefully initialized centers by a batch of source domain samples to produce pseudo labels. Moreover, we use a cross-attention mechanism on a pair of source data and target data with the same labels to learn domain-invariant representations. Because the samples in a domain pair tend to express similar semantic patterns, especially on the people's attitudes (e.g., supporting or denying) towards the same category of rumors, the discrepancy between a pair of the source domain and target domain will be decreased. We conduct experiments on four groups of cross-domain datasets and show that our proposed model achieves state-of-the-art performance.

In today's data-driven world, predictive analytics has become an integral part of businesses to anticipate future trends and gain a competitive advantage. Machine learning models have made it easier to analyze and interpret data and make informed decisions. This article will discuss the 10 powerful machine learning models for predictive analytics that businesses can utilize to improve their operations. Predictive analytics is the process of analyzing historical data to make predictions about future events. Machine learning models have made it possible to predict these events accurately by analyzing large volumes of data.

Abstract: It is well known that the finite step-size (h) in Gradient Descent (GD) implicitly regularizes solutions to flatter minima. A natural question to ask is "Does the momentum parameter β play a role in implicit regularization in Heavy-ball (H.B) momentum accelerated gradient descent (GD M)?". To answer this question, first, we show that the discrete H.B momentum update (GD M) follows a continuous trajectory induced by a modified loss, which consists of an original loss and an implicit regularizer. Then, we show that this implicit regularizer for (GD M) is stronger than that of (GD) by factor of (1 β1 β), thus explaining why (GD M) shows better generalization performance and higher test accuracy than (GD). Furthermore, we extend our analysis to the stochastic version of gradient descent with momentum (SGD M) and characterize the continuous trajectory of the update of (SGD M) in a pointwise sense. Abstract: When training Convolutional Neural Networks (CNNs) there is a large emphasis on creating efficient optimization algorithms and highly accurate networks.

Physics-Informed Neural Networks (PINNs) are a powerful tool for simulating complex physical systems. Unlike traditional machine learning models, PINNs can effectively utilize limited data by incorporating the underlying physics of the studied system. In scientific and engineering applications, acquiring large labeled datasets can be difficult due to the high cost and limited experimental or simulated data availability. Traditional machine learning models, such as decision trees or support vector machines, require large amounts of labeled data for effective training. However, PINNs can leverage the governing laws and constraints of the studied problem to achieve accurate results with minimal training data.

Citation-based Information Retrieval (IR) methods for scientific documents have proven effective for IR applications, such as Plagiarism Detection or Literature Recommender Systems in academic disciplines that use many references. In science, technology, engineering, and mathematics, researchers often employ mathematical concepts through formula notation to refer to prior knowledge. Our long-term goal is to generalize citation-based IR methods and apply this generalized method to both classical references and mathematical concepts. In this paper, we suggest how mathematical formulas could be cited and define a Formula Concept Retrieval task with two subtasks: Formula Concept Discovery (FCD) and Formula Concept Recognition (FCR). While FCD aims at the definition and exploration of a 'Formula Concept' that names bundled equivalent representations of a formula, FCR is designed to match a given formula to a prior assigned unique mathematical concept identifier. We present machine learning-based approaches to address the FCD and FCR tasks. We then evaluate these approaches on a standardized test collection (NTCIR arXiv dataset). Our FCD approach yields a precision of 68% for retrieving equivalent representations of frequent formulas and a recall of 72% for extracting the formula name from the surrounding text. FCD and FCR enable the citation of formulas within mathematical documents and facilitate semantic search and question answering as well as document similarity assessments for plagiarism detection or recommender systems.

Our study focuses on determining the best weight windows for a weighted moving average smoother under squared loss. We show that there exists an optimal weight window that is symmetrical around its center. We study the class of tapered weight windows, which decrease in weight as they move away from the center. We formulate the corresponding least squares problem as a quadratic program and finally as a projection of the origin onto a convex polytope. Additionally, we provide some analytical solutions to the best window when some conditions are met on the input data.

Safe deployment of deep neural networks in high-stake real-world applications requires theoretically sound uncertainty quantification. Conformal prediction (CP) is a principled framework for uncertainty quantification of deep models in the form of prediction set for classification tasks with a user-specified coverage (i.e., true class label is contained with high probability). This paper proposes a novel algorithm referred to as Neighborhood Conformal Prediction (NCP) to improve the efficiency of uncertainty quantification from CP for deep classifiers (i.e., reduce prediction set size). The key idea behind NCP is to use the learned representation of the neural network to identify k nearest-neighbors calibration examples for a given testing input and assign them importance weights proportional to their distance to create adaptive prediction sets. We theoretically show that if the learned data representation of the neural network satisfies some mild conditions, NCP will produce smaller prediction sets than traditional CP algorithms. Our comprehensive experiments on CIFAR-10, CIFAR-100, and ImageNet datasets using diverse deep neural networks strongly demonstrate that NCP leads to significant reduction in prediction set size over prior CP methods.