Predicting future values in multivariate time series is vital across various
domains. This work explores the use of large language models (LLMs) for this
task. However, LLMs typically handle one-dimensional data. We introduce
MultiCast, a zero-shot LLM-based approach for multivariate time series
forecasting. It allows LLMs to receive multivariate time series as input,
through three novel token multiplexing solutions that effectively reduce
dimensionality while preserving key repetitive patterns. Additionally, a
quantization scheme helps LLMs to better learn these patterns, while
significantly reducing token use for practical applications. We showcase the
performance of our approach in terms of RMSE and execution time against
state-of-the-art approaches on three real-world datasets.

使用大型语言模型（LLMs）和 MultiCast 方法，可以通过三种新型的令牌复用解决方案，将多变量时间序列预测问题映射为一维数据的处理，提高预测准确性并减少令牌使用量。在三个真实数据集中，MultiCast 方法在 RMSE 和执行时间方面表现出与现有方法相比的优势。

MultiCast：使用 LLM 进行零样本多元时间序列预测

MultiCast: Zero-Shot Multivariate Time Series Forecasting Using LLMs

We analyse the effectiveness of RMSE, PSNR, SSIM and FOM for evaluating edge
detection algorithms used for automated coastline detection. Typically, the
accuracy of detected coastlines is assessed visually. This can be impractical
on a large scale leading to the need for objective evaluation metrics. Hence,
we conduct an experiment to find reliable metrics. We apply Canny edge
detection to 95 coastline satellite images across 49 testing locations. We vary
the Hysteresis thresholds and compare metric values to a visual analysis of
detected edges. We found that FOM was the most reliable metric for selecting
the best threshold. It could select a better threshold 92.6% of the time and
the best threshold 66.3% of the time. This is compared RMSE, PSNR and SSIM
which could select the best threshold 6.3%, 6.3% and 11.6% of the time
respectively. We provide a reason for these results by reformulating RMSE, PSNR
and SSIM in terms of confusion matrix measures. This suggests these metrics not
only fail for this experiment but are not useful for evaluating edge detection
in general.

我们分析了用于自动海岸线检测的边缘检测算法的有效性，通过评估 RMSE、PSNR、SSIM 和 FOM 等评估指标，发现 FOM 是选择最佳阈值的最可靠指标。相对于 RMSE、PSNR 和 SSIM，在这次实验中，FOM 在 92.6% 的时间内选择到更好的阈值，在 66.3% 的时间内选择到最佳阈值。而 RMSE、PSNR 和 SSIM 的选择率分别仅为 6.3%、6.3% 和 11.6%。通过重新解释 RMSE、PSNR 和 SSIM 的混淆矩阵度量，我们提出了对这些结果的解释，这表明这些评估指标不仅在这次实验中效果不好，而且在一般的边缘检测评估中也不实用。

自动海岸线检测的边缘检测评估指标的有效性

The Effectiveness of Edge Detection Evaluation Metrics for Automated  Coastline Detection

This paper discusses predictive performance and processes undertaken on
flight pricing data utilizing r2(r-square) and RMSE that leverages a large
dataset, originally from Expedia.com, consisting of approximately 20 million
records or 4.68 gigabytes. The project aims to determine the best models usable
in the real world to predict airline ticket fares for non-stop flights across
the US. Therefore, good generalization capability and optimized processing
times are important measures for the model.
We will discover key business insights utilizing feature importance and
discuss the process and tools used for our analysis. Four regression machine
learning algorithms were utilized: Random Forest, Gradient Boost Tree, Decision
Tree, and Factorization Machines utilizing Cross Validator and Training
Validator functions for assessing performance and generalization capability.

本论文通过利用 r2（确定系数）和 RMSE 研究了航班定价数据的预测性能和过程，结合了从 Expedia.com 获取的大型数据集，包含约 2000 万条记录或 4.68GB。该项目旨在确定在真实世界中用于预测美国境内直达航班机票价格的最佳模型。因此，良好的泛化能力和优化的处理时间是衡量模型的重要指标。通过特征重要性发现了关键业务洞见，并讨论了我们分析所使用的过程和工具。使用了四种回归机器学习算法：随机森林、梯度提升树、决策树和分解机，利用交叉验证和训练验证函数来评估性能和泛化能力。

使用 Spark 机器学习模型对航班票价数据进行预测分析

Using Spark Machine Learning Models to Perform Predictive Analysis on  Flight Ticket Pricing Data

Let M be a random (alpha n) x n matrix of rank r<<n, and assume that a
uniformly random subset E of its entries is observed. We describe an efficient
algorithm that reconstructs M from |E| = O(rn) observed entries with relative
root mean square error RMSE <= C(rn/|E|)^0.5 . Further, if r=O(1), M can be
reconstructed exactly from |E| = O(n log(n)) entries. These results apply
beyond random matrices to general low-rank incoherent matrices.
This settles (in the case of bounded rank) a question left open by Candes and
Recht and improves over the guarantees for their reconstruction algorithm. The
complexity of our algorithm is O(|E|r log(n)), which opens the way to its use
for massive data sets. In the process of proving these statements, we obtain a
generalization of a celebrated result by Friedman-Kahn-Szemeredi and Feige-Ofek
on the spectrum of sparse random matrices.

本文研究如何从观测到的随机稀疏矩阵子集中重建一个秩较低的随机矩阵，提供相应的算法并给出一些误差保证以及时间复杂度估计，并得到一些稀疏随机矩阵谱的推广结果。