Abstract
The multichannel, time-series representation of financial data naturally suggests tensor-based learning algorithms.
这篇文章研究了针对mid-price prediction problem的两种multilinear methods.
在一个有着4 million limit orders的数据集中测试证明， 通过使用tensor representation, multilinear models比其他方式好，包括vector-based 方式。
Introduction
现在介绍一下High-Frequency Trading(HFT)。
A 定义：a form of automated trading that relies on the rapid, subtle changes of the markets to buy or sell assets.
B 特点： high speed and short-term investment horizon. Different from long-term investors, high-frequency traders profit from a low margin of the price changes with large volume within a relatively short time
C 需求： the ability to observe the dynamics of the market to predict prospective changes and act accordingly
目前，越来越多的机器学习模型被引入到 predict financial market behaviors中， 包括egression analysis, multilayer feed forward network, convolutional neural network, recurrent neural network.
大量的数据，市场的不稳定表现，神经网络被广泛应用于学习合适的representation of the data and the corresponding classifiers
优点：
1. Tensor representation offers a natural representation of the time-series data, where time corresponds to one of the tensor orders.
2. 传统vector-based模型中，特征从time-series representation中提取出来，被转换成模型的输入向量。而tensor到vector的representation转换过程会导致the loss of temporal information. 可能会导致分类器无法获取到interactions between spatiotemporal information.
3. 许多神经模型，例如CNN， RNN， 可以直接以tensor的方式学习数据，这也解释了为什么神经网络表现比传统的vectored-based models with hand-crafted features.
与需要heavy tuning of network topology and parameters的神经网络方法不同，tensorbased multilinear techniques is that the objective function is straightforward to interpret and very few parameters are required to tune the model
In this work, we propose to use two multilinear techniques based on the tensor representation of time-series financial data to predict the mid-price movement based on information obtained from Limit Order Book (LOB) data.
本篇论文贡献：
1. investigate the effectiveness of tensor-based discriminant techniques, particularly Multilinear Discriminant Analysis (MDA) in a large-scale prediction problem
of mid-price movement with high-frequency limit order book data.
2. 提出了一个基于tensor representation的简单的回归分类器， 利用了当前及过去的stock limit order book数据来提升vector-based 回归方法的性能。
另外Based on the observation of the learning dynamics of the proposed algorithm, efficient scheme to select the best model’s state is also discussed.
Section 2 回顾了一下the mid-price movement prediction problem given the information collected from LOB as well as related methods that were proposed to tackle this problem
Section 3 呈现了MDA以及作者提出的 tensor regression scheme.
Section 4 性能比较分析
Section 5 结论