Likelihood adjusted semidefinite programs for clustering heterogeneous data

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxima even in the special case of the standard Gaussian mixture model with common isotropic covariance matrices. On the other hand, recent studies reveal that the unique global solution of a semidefinite programming (SDP) relaxed $K$-means achieves the information-theoretically sharp threshold for perfectly recovering the cluster labels under the standard Gaussian mixture model. In this paper, we extend the SDP approach to a general setting by integrating cluster labels as model parameters and propose an iterative likelihood adjusted SDP (iLA-SDP) method that directly maximizes the \emph{exact} observed likelihood in the presence of data heterogeneity. By lifting the cluster assignment to group-specific membership matrices, iLA-SDP avoids centroids estimation -- a key feature that allows exact recovery under well-separateness of centroids without being trapped by their adversarial configurations. Thus iLA-SDP is less sensitive than EM to initialization and more stable on high-dimensional data. Our numeric experiments demonstrate that iLA-SDP can achieve lower mis-clustering errors over several widely used clustering methods including $K$-means, SDP and EM algorithms

Cognitive Grounding and Its Adaptability to Chinese Noun Studies

Cognitive Grammar is a linguistic theory represented by the symbolic thesis and the usage-based thesis. Cognitive grounding theory is a newly fledged theory in CG. Studies related to grounding have been in their infancy, exhibiting a typological vigor. There have been so far no systematic studies devoted to the grounding system of the Chinese language. Chinese grammar studies applying modern Western linguistic theories have long been the pursuit of scholars from generation to generation. This paper is devoted to introduce grounding theory and then focus on its adaptability to Chinese noun studies. It is concluded that (1) grounding is a cognitive process in which the construal of entities becomes more subjective, and in which a type concept is changed into instances that are singled out by the interlocutors; (2) grounding theory and Chinese noun studies have high adaptability, so Chinese noun studies can be approached from the perspective of Chinese nominal grounding

THE IMPACT OF PRODUCT PHOTO ON ONLINE CONSUMER PURCHASE INTENTION: AN IMAGE-PROCESSING ENABLED EMPIRICAL STUDY

Determinants of online consumer’s purchase decisions are of long-term interest to researchers and practitioners. Since product photos directly aid consumers’ understanding of products, retailers often put a lot of effort into polishing them. However, there is limited research on the impact of product photos on purchase decisions. Most previous studies took an experiment-based approach, which delivered strict theories on some aspects of product photos. This research takes advantage of image-processing techniques to study product photos’ impact. These techniques allow us to investigate a large set of photo characteristics simultaneously in an empirical study. To rule out possible confounding factors, we collect a dataset from a social shopping Website, which has a simple interface allowing users to judge products mainly based on their photos. We examine product photo characteristics from the aspects of information, emotion, aesthetics, and social presence. We found that consumers prefer product photos with a larger key object, lower entropy on key objects, a warmer color, a higher contrast, a higher depth-of-field, and more social presences. This research introduces a Big Data-based approach to study the impact of e-commerce systems’ visual features on consumers

Augmenting Black-box LLMs with Medical Textbooks for Clinical Question Answering

Large-scale language models (LLMs), such as ChatGPT, are capable of generating human-like responses for various downstream tasks, such as task-oriented dialogues and question answering. However, applying LLMs to medical domains remains challenging due to their inability to leverage domain-specific knowledge. In this study, we present the Large-scale Language Models Augmented with Medical Textbooks (LLM-AMT), which integrates authoritative medical textbooks as the cornerstone of its design, enhancing its proficiency in the specialized domain through plug-and-play modules, comprised of a Hybrid Textbook Retriever, supplemented by the Query Augmenter and the LLM Reader. Experimental evaluation on three open-domain medical question-answering tasks reveals a substantial enhancement in both the professionalism and accuracy of the LLM responses when utilizing LLM-AMT, exhibiting an improvement ranging from 11.4% to 13.2%. Despite being 100 times smaller, we found that medical textbooks as the retrieval corpus serves as a more valuable external knowledge source than Wikipedia in the medical domain. Our experiments show that textbook augmentation results in a performance improvement ranging from 9.7% to 12.2% over Wikipedia augmentation

Estudio de la influencia y efectos de la Pandemia COVID-19 en la gestión urbanística moderna: comparativa entre los casos de China y España

[ES] La gestión urbanística desde el levantamiento de las primeras civilizaciones ha enfrentado problemas relacionados con la salud, en la actualidad siendo una actividad relacionada con la arquitectura, la ingeniería y el desarrollo de las infraestructuras que conforman las grandes y pequeñas ciudades del mundo, el urbanismo está enfrentando en el primer cuarto del siglo XXI una situación que requiere el uso de los recursos con los que se han desarrollado ciudades que tienen más de 100 años de desarrollo y que no habían enfrentado una situación como la que ha sido causada por la pandemia generada por el virus del Covid-19. En este sentido, la llegada de este virus ha cambiado el panorama urbano y la manera en la que las personas se comportan ya que es necesario preservar la integridad de la sociedad desde la salud hasta el resto de los aspectos como el económico, cultural y en relación a la gestión urbana por parte de los gobiernos del mundo. De este modo, dentro de ciudades ya construidas y desarrolladas se genera una situación en la que se requieren espacios para contener una enfermedad que ataca con rapidez y con una gran tasa de contagio, poniendo en riesgo la vida de las personas más vulnerables lo que genera una acción urbana basada en los recursos existentes. Esta investigación explora la gestión, desde un enfoque urbanístico, realizada por China el país donde estalló la pandemia por primera vez y España uno de los países más afectados, teniendo en cuenta los requerimientos sanitarios como enfoque principal en las gestiones realizadas por estos gobiernos para mantener a raya la crisis pandémica y mejorar la situación generada por esta.[EN] Urban management since the rise of the first civilizations has faced problems related to health, currently being an activity related to architecture, engineering and the development of infrastructures that make up the large and small cities of the world, urban planning is facing in the first quarter of the 21st century a situation that requires the use of the resources with which cities that have been developed for more than 100 years and that had not faced a situation such as that caused by the pandemic generated by the Covid-19 virus. In this sense, the arrival of this virus has changed the urban landscape and the way in which people behave since it is necessary to preserve the integrity of society from health to other aspects such as economic, cultural and in relation to urban management by the governments of the world. In this way, within already built and developed cities a situation is generated in which spaces are required to contain a disease that attacks quickly and with a high rate of contagion, putting the lives of the most vulnerable people at risk, which generates an urban action based on existing resources. This research explores the management, from an urban approach, carried out by China at the country where the pandemic first broke out and Spain, one of the most affected countries, taking into account health requirements as the main focus in the efforts made by these governments to keep the crisis at bay. pandemic and improve the situation generated by it.Chen, Y. (2020). Estudio de la influencia y efectos de la Pandemia COVID-19 en la gestión urbanística moderna: comparativa entre los casos de China y España. Universitat Politècnica de València. http://hdl.handle.net/10251/162390TFG

Monotone methods for a discrete boundary problem

AbstractThis paper is motivated by recent interests in space discrete Nagumo equations and is concerned with the existence of solutions of a nonlinear discrete boundary value problem. Monotone methods are used to derive the existence theorems. These methods, as is well known, provide constructive schemes for calculating the solutions

Journey to the Center of the Knowledge Neurons: Discoveries of Language-Independent Knowledge Neurons and Degenerate Knowledge Neurons

Pre-trained language models (PLMs) contain vast amounts of factual knowledge, but how the knowledge is stored in the parameters remains unclear. This paper delves into the complex task of understanding how factual knowledge is stored in multilingual PLMs, and introduces the Architecture-adapted Multilingual Integrated Gradients method, which successfully localizes knowledge neurons more precisely compared to current methods, and is more universal across various architectures and languages. Moreover, we conduct an in-depth exploration of knowledge neurons, leading to the following two important discoveries: (1) The discovery of Language-Independent Knowledge Neurons, which store factual knowledge in a form that transcends language. We design cross-lingual knowledge editing experiments, demonstrating that the PLMs can accomplish this task based on language-independent neurons; (2) The discovery of Degenerate Knowledge Neurons, a novel type of neuron showing that different knowledge neurons can store the same fact. Its property of functional overlap endows the PLMs with a robust mastery of factual knowledge. We design fact-checking experiments, proving that the degenerate knowledge neurons can help the PLMs to detect wrong facts. Experiments corroborate these findings, shedding light on the mechanisms of factual knowledge storage in multilingual PLMs, and contribute valuable insights to the field. The code is available at https://github.com/heng840/AMIG.Comment: Accepted in the 38th AAAI Conference on Artificial Intelligence (AAAI 2024