**4. Conclusions**

In this paper we have implemented a machine learning algorithm, RF, to predict houses price with an application to UK real estate data. In particular, we have analyzed the average house price of the center of London, taking in consideration urban explicative variables of the demand and supply of the houses. The point of view offered is different and complementary with respect to the literature on the field, which considers features attaining the buildings like size and location, and is based on an urban perspective to explain the evolution of the local real estate market. This is the main reason our data set has been selected. Despite the dataset size being small, the numerical results show a better prediction improvement by RF with respect to the traditional regression approach based on GLM. The use of RF in small datasets is common among data scientists as the bootstrapping, on which RF is based, allows the algorithm to perform well anyway. RF is relatively easy to build and does not require expensive hyperparameters tuning. Besides, to avoid overfitting that generally affects the models trained on small datasets, we control both the number of trees and the maximum depth. This improves the model's ability to do not see patterns that do not exist. As regard to the importance of variables, the algorithm selects the local population as the most predictive variable. This result confirms that the

demand size is the main driver of the real estate market. The space for further works is twofold: on one hand the model presented is flexible and can be easily extended to combine variables related to supply and demand with others attaining to the physical features of the house, on the other hand, different machine learning algorithms, like that deals with the problem of the endogeneity of predictors and the bias of results, can be implemented and compared. The research conducted can be reproduced for the analysis of other real estate dataset. A more accurate forecast of the evolution of real estate market prices must exploit not only variables relating to local characteristics of the market, but also combine them with different information sources such as macroeconomic ones. The improvements achieved can show practical feedback for the whole society. As population and urbanization grow, the need for models able to catch the possible evolution of the real estate market concerns more stakeholders, from homeowners to real estate companies to insurance companies and so on. In modern society we are witnessing the growth of the elderly "cash poor house rich", those who own a home but have retirement incomes so low that they cannot ensure a decent survival and the necessary medical care. Faced with this phenomenon, the insurance market of Reverse Mortgage is developing considerably. In this context, the role that data play will be at the core of the forecasting of assets future value in terms of real-world evaluation and of the cost of insurance contracts related to house valuation.

**Author Contributions:** The authors have equally contributed to the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
