Multivariate time series (MTS) forecasting has shown great importance in numerous industries.

The recent coronavirus disease (Covid-19) has become a pandemic and has affected the entire globe. During the pandemic, we have observed a spike in cases related to mental health, such as anxiety, stress, and depression. Depression significantly influences most diseases worldwide, making it difficult to detect mental health conditions in people due to unawareness and unwillingness to consult a doctor. However, nowadays, people extensively use online social media platforms to express their emotions and thoughts. Hence, social media platforms are now becoming a large data source that can be utilized for detecting depression and mental illness. However, existing approaches often overlook data sparsity in tweets and the multimodal aspects of social media. In this paper, we propose a novel multimodal framework that combines textual, user-specific, and image analysis to detect depression among social media users. To provide enough context about the user's emotional state, we propose (i) an extrinsic feature by harnessing the URLs present in tweets and (ii) extracting textual content present in images posted in tweets. We also extract five sets of features belonging to different modalities to describe a user. Additionally, we introduce a Deep Learning model, the Visual Neural Network (VNN), to generate embeddings of user-posted images, which are used to create the visual feature vector for prediction. We contribute a curated Covid-19 dataset of depressed and non-depressed users for research purposes and demonstrate the effectiveness of our model in detecting depression during the Covid-19 outbreak. Our model outperforms existing state-of-the-art methods over a benchmark dataset by 2%-8% and produces promising results on the Covid-19 dataset. Our analysis highlights the impact of each modality and provides valuable insights into users' mental and emotional states.

Multivariate time series (MTS) forecasting has shown great importance in numerous industries.

We provide all missing proofs in this section. We prove the statement by contradiction. Next we show the proof for the second half. Now we show the last piece of the statement by construction. We prove the statement via three main steps.

C.1 Datasets Detailed data description is as follows: 15 Figure 1: Illustration of 0-and 1-dimensional ZFCs for COVID-19 dataset on Texas (TX).

Bayesian phylogenetics requires accurate and efficient approximation of posterior distributions over trees. In this work, we develop a variational Bayesian approach for ultrametric phylogenetic trees. We present a novel variational family based on coalescent times of a single-linkage clustering and derive a closed-form density of the resulting distribution over trees. Unlike existing methods for ultrametric trees, our method performs inference over all of tree space, it does not require any Markov chain Monte Carlo subroutines, and our variational family is differentiable. Through experiments on benchmark genomic datasets and an application to SARS-CoV-2, we demonstrate that our method achieves competitive accuracy while requiring significantly fewer gradient evaluations than existing state-of-the-art techniques.

With their advanced capabilities, Large Language Models (LLMs) can generate highly convincing and contextually relevant fake news, which can contribute to disseminating misinformation. Though there is much research on fake news detection for human-written text, the field of detecting LLM-generated fake news is still under-explored. This research measures the efficacy of detectors in identifying LLM-paraphrased fake news, in particular, determining whether adding a paraphrase step in the detection pipeline helps or impedes detection. This study contributes: (1) Detectors struggle to detect LLM-paraphrased fake news more than human-written text, (2) We find which models excel at which tasks (evading detection, paraphrasing to evade detection, and paraphrasing for semantic similarity). (3) Via LIME explanations, we discovered a possible reason for detection failures: sentiment shift. (4) We discover a worrisome trend for paraphrase quality measurement: samples that exhibit sentiment shift despite a high BERTSCORE. (5) We provide a pair of datasets augmenting existing datasets with paraphrase outputs and scores. The dataset is available on GitHub

Recent advances in healthcare technologies have led to the availability of large amounts of biological samples across several techniques and applications. In particular, in the last few years, Raman spectroscopy analysis of biological samples has been successfully applied for early-stage diagnosis. However, spectra' inherent complexity and variability make the manual analysis challenging, even for domain experts. For the same reason, the use of traditional Statistical and Machine Learning (ML) techniques could not guarantee for accurate and reliable results. ML models, combined with robust optimization techniques, offer the possibility to improve the classification accuracy and enhance the resilience of predictive models. In this paper, we investigate the performance of a novel robust formulation for Support Vector Machine (SVM) in classifying COVID-19 samples obtained from Raman Spectroscopy. Given the noisy and perturbed nature of biological samples, we protect the classification process against uncertainty through the application of robust optimization techniques. Specifically, we derive robust counterpart models of deterministic formulations using bounded-by-norm uncertainty sets around each observation. We explore the cases of both linear and kernel-induced classifiers to address binary and multiclass classification tasks. The effectiveness of our approach is validated on real-world COVID-19 datasets provided by Italian hospitals by comparing the results of our simulations with a state-of-the-art classifier.