Analyzing real estate transaction and pricing data via statistical machine learning

房地产价格估计和预测是加拿大购房者、投资者和政策制定者的关键。到目前为止，加拿大用户可以访问的大多数房地产市场评估都是基于大趋势分析，定性预测或传统的房地产市场指数，导致准确性有限。研究文献提出了大量的参数和非参数模型，以根据同一地区交易的其他物业的销售价格评估个别物业的市场价值。然而，即使使用非参数模型和最新的基于核的回归，现有的方法也具有有限的准确性，并且无法处理具有内部无人居住区域的不规则区域或捕获跨异质区域的价格跳跃。为了克服这些困难，在这个项目中，我们将提出并广泛研究一些新的统计学习工具，用于房地产估价，价格估计和预测，包括有限元分析，空间样条回归，粗糙度和融合LASSO型正则化，低秩矩阵完成和惩罚卡尔曼滤波器的状态空间模型。通过精心设计的结构，我们提出的模型可以使用凸优化进行分解和求解。我们还将研究在具有大量数据的商业房地产市场评估应用中实现更快计算的问题。

Real-estate property price estimation and prediction is key to Canadian home buyers, investors and policy makers. To date, most real-estate market assessments accessible by Canadian users are based on big trend analysis, qualitative prediction or traditional real-estate market indices, leading to a limited accuracy. The research literature has presented a large number of both parametric and non-parametric models to assess the market value of an individual property based on the sold prices of other properties transacted in the same region. However, even with non-parametric models and the latest kernel-based regression, existing approaches have limited accuracy and are unable to handle irregular regions with interior uninhabitated areas or to capture price jumps across heterogeneous areas. To overcome these difficulties, in this project, we will propose and extensively study a number of new statistical learning tools for applications to real-estate valuation, price estimation and prediction, including finite element analysis, spatial spline regression, roughness and fused-LASSO-type regularization, low-rank matrix completion and state-space models with penalized Kalman filters. With carefully designed structures, our proposed models can be decomposed and solved using convex optimization. We will also study the implementation issues for faster computation in commercial real-estate market assessment applications with a large amount of data.