Ping Li

Miao Fan, Jizhou Huang, An Zhuo et al. · baidu

The value assessment of private properties is an attractive but challenging task which is widely concerned by a majority of people around the world. A prolonged topic among us is ``\textit{how much is my house worth?}''. To answer this question, most experienced agencies would like to price a property given the factors of its attributes as well as the demographics and the public facilities around it. However, no one knows the exact prices of these factors, especially the values of public facilities which may help assess private properties. In this paper, we introduce our newly launched project ``Monopoly'' (named after a classic board game) in which we propose a distributed approach for revaluing private properties by learning to price public facilities (such as hospitals etc.) with the large-scale urban data we have accumulated via Baidu Maps. To be specific, our method organizes many points of interest (POIs) into an undirected weighted graph and formulates multiple factors including the virtual prices of surrounding public facilities as adaptive variables to parallelly estimate the housing prices we know. Then the prices of both public facilities and private properties can be iteratively updated according to the loss of prediction until convergence. We have conducted extensive experiments with the large-scale urban data of several metropolises in China. Results show that our approach outperforms several mainstream methods with significant margins. Further insights from more in-depth discussions demonstrate that the ``Monopoly'' is an innovative application in the interdisciplinary field of business intelligence and urban computing, and it will be beneficial to tens of millions of our users for investments and to the governments for urban planning as well as taxation.

Fan Zhou, Ping Li

Let $\mathbf{x}_j = \mathbfθ + \mathbfε_j$, $j=1,\dots,n$ be i.i.d. copies of a Gaussian random vector $\mathbf{x}\sim\mathcal{N}(\mathbfθ,\mathbfΣ)$ with unknown mean $\mathbfθ \in \mathbb{R}^d$ and unknown covariance matrix $\mathbfΣ\in \mathbb{R}^{d\times d}$. The goal of this article is to study the estimation of $f(\mathbfθ)$ where $f$ is a given smooth function of which smoothness is characterized by a Besov-type norm. The problem of interest resides in the high dimensional regime where the intrinsic dimension can grow with the sample size $n$. Inspired by the classical work of A. N. Kolmogorov on unbiased estimation and Littlewood-Paley theory, we develop a new estimator based on a Fourier analytical approach that achieves effective bias reduction. Asymptotic normality and efficiency are proved when the smoothness index of $f$ is above certain threshold which was discovered recently by Koltchinskii et. al. (2018) for a Hölder type class. Numerical simulations are presented to validate our analysis. The simplicity of implementation and its superiority over the plug-in approach indicate the new estimator can be applied to a broad range of real world applications.

Ping Li

The method of 1-bit ("sign-sign") random projections has been a popular tool for efficient search and machine learning on large datasets. Given two $D$-dim data vectors $u$, $v\in\mathbb{R}^D$, one can generate $x = \sum_{i=1}^D u_i r_i$, and $y = \sum_{i=1}^D v_i r_i$, where $r_i\sim N(0,1)$ iid. The "collision probability" is ${Pr}\left(sgn(x)=sgn(y)\right) = 1-\frac{\cos^{-1}ρ}π$, where $ρ= ρ(u,v)$ is the cosine similarity. We develop "sign-full" random projections by estimating $ρ$ from (e.g.,) the expectation $E(sgn(x)y)=\sqrt{\frac{2}π} ρ$, which can be further substantially improved by normalizing $y$. For nonnegative data, we recommend an interesting estimator based on $E\left(y_- 1_{x\geq 0} + y_+ 1_{x<0}\right)$ and its normalized version. The recommended estimator almost matches the accuracy of the (computationally expensive) maximum likelihood estimator. At high similarity ($ρ\rightarrow1$), the asymptotic variance of recommended estimator is only $\frac{4}{3π} \approx 0.4$ of the estimator for sign-sign projections. At small $k$ and high similarity, the improvement would be even much more substantial.