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Ensuring travelers' safety on roads has become a research challenge in recent years. We introduce a novel safe route planning problem and develop an efficient solution to ensure the travelers' safety on roads. Though few research attempts have been made in this regard, all of them assume that people share their sensitive travel experiences with a centralized entity for finding the safest routes, which is not ideal in practice for privacy reasons. Furthermore, existing works formulate safe route planning in ways that do not meet a traveler's need for safe travel on roads. Our approach finds the safest routes within a user-specified distance threshold based on the personalized travel experience of the knowledgeable crowd without involving any centralized computation. We develop a privacy-preserving model to quantify the travel experience of a user into personalized safety scores. Our algorithms for finding the safest route further enhance user privacy by minimizing the exposure of personalized safety scores with others. Our safe route planner can find the safest routes for individuals and groups by considering both a fixed and a set of flexible destination locations. Extensive experiments using real datasets show that our approach finds the safest route in seconds with 47% less exposure of personalized safety scores.

Many economic and scientific problems involve the analysis of high-dimensional functional time series, where the number of functional variables ($p$) diverges as the number of serially dependent observations ($n$) increases. In this paper, we present a novel functional factor model for high-dimensional functional time series that maintains and makes use of the functional and dynamic structure to achieve great dimension reduction and find the latent factor structure. To estimate the number of functional factors and the factor loadings, we propose a fully functional estimation procedure based on an eigenanalysis for a nonnegative definite matrix. Our proposal involves a weight matrix to improve the estimation efficiency and tackle the issue of heterogeneity, the rationality of which is illustrated by formulating the estimation from a novel regression perspective. Asymptotic properties of the proposed method are studied when $p$ diverges at some polynomial rate as $n$ increases. To provide a parsimonious model and enhance interpretability for near-zero factor loadings, we impose sparsity assumptions on the factor loading space and then develop a regularized estimation procedure with theoretical guarantees when $p$ grows exponentially fast relative to $n.$ Finally, we demonstrate that our proposed estimators significantly outperform the competing methods through both simulations and applications to a U.K. temperature dataset and a Japanese mortality dataset.

We consider the dynamic pricing problem with covariates under a generalized linear demand model: a seller can dynamically adjust the price of a product over a horizon of $T$ time periods, and at each time period $t$, the demand of the product is jointly determined by the price and an observable covariate vector $x_t\in\mathbb{R}^d$ through an unknown generalized linear model. Most of the existing literature assumes the covariate vectors $x_t$'s are independently and identically distributed (i.i.d.); the few papers that relax this assumption either sacrifice model generality or yield sub-optimal regret bounds. In this paper we show that a simple pricing algorithm has an $O(d\sqrt{T}\log T)$ regret upper bound without assuming any statistical structure on the covariates $x_t$ (which can even be arbitrarily chosen). The upper bound on the regret matches the lower bound (even under the i.i.d. assumption) up to logarithmic factors. Our paper thus shows that (i) the i.i.d. assumption is not necessary for obtaining low regret, and (ii) the regret bound can be independent of the (inverse) minimum eigenvalue of the covariance matrix of the $x_t$'s, a quantity present in previous bounds. Furthermore, we discuss a condition under which a better regret is achievable and how a Thompson sampling algorithm can be applied to give an efficient computation of the prices.

In this article, we develop differentially private tools for handling model uncertainty in linear regression models. We introduce hypothesis tests for nested linear models and methods for model averaging and selection. We consider Bayesian approaches based on mixtures of $g$-priors as well as non-Bayesian approaches based on information criteria. The procedures are straightforward to implement with existing software for non-private data and are asymptotically consistent under certain regularity conditions. We address practical issues such as calibrating the tests so that they have adequate type I error rates or quantifying the uncertainty introduced by the privacy mechanisms. Additionally, we provide specific guidelines to maximize the statistical utility of the methods in finite samples.

The combinatorial diameter $\operatorname{diam}(P)$ of a polytope $P$ is the maximum shortest path distance between any pair of vertices. In this paper, we provide upper and lower bounds on the combinatorial diameter of a random "spherical" polytope, which is tight to within one factor of dimension when the number of inequalities is large compared to the dimension. More precisely, for an $n$-dimensional polytope $P$ defined by the intersection of $m$ i.i.d.\ half-spaces whose normals are chosen uniformly from the sphere, we show that $\operatorname{diam}(P)$ is $\Omega(n m^{\frac{1}{n-1}})$ and $O(n^2 m^{\frac{1}{n-1}} + n^5 4^n)$ with high probability when $m \geq 2^{\Omega(n)}$. For the upper bound, we first prove that the number of vertices in any fixed two dimensional projection sharply concentrates around its expectation when $m$ is large, where we rely on the $\Theta(n^2 m^{\frac{1}{n-1}})$ bound on the expectation due to Borgwardt [Math. Oper. Res., 1999]. To obtain the diameter upper bound, we stitch these ``shadows paths'' together over a suitable net using worst-case diameter bounds to connect vertices to the nearest shadow. For the lower bound, we first reduce to lower bounding the diameter of the dual polytope $P^\circ$, corresponding to a random convex hull, by showing the relation $\operatorname{diam}(P) \geq (n-1)(\operatorname{diam}(P^\circ)-2)$. We then prove that the shortest path between any ``nearly'' antipodal pair vertices of $P^\circ$ has length $\Omega(m^{\frac{1}{n-1}})$.

We propose a Doppler velocity-based cluster and velocity estimation algorithm based on the characteristics of FMCW LiDAR which achieves highly accurate, single-scan, and real-time motion state detection and velocity estimation. We prove the continuity of the Doppler velocity on the same object. Based on this principle, we achieve the distinction between moving objects and stationary background via region growing clustering algorithm. The obtained stationary background will be used to estimate the velocity of the FMCW LiDAR by the least-squares method. Then we estimate the velocity of the moving objects using the estimated LiDAR velocity and the Doppler velocity of moving objects obtained by clustering. To ensure real-time processing, we set the appropriate least-squares parameters. Meanwhile, to verify the effectiveness of the algorithm, we create the FMCW LiDAR model on the autonomous driving simulation platform CARLA for spawning data. The results show that our algorithm can process at least a 4.5million points and estimate the velocity of 150 moving objects per second under the arithmetic power of the Ryzen 3600x CPU, with a motion state detection accuracy of over 99% and estimated velocity accuracy of 0.1 m/s.

In this article, we address a class of non convex, integer, non linear mathematical programs using dynamic programming. The mathematical program considered, whose properties are studied in this article, may be used to model the optimal liquidation problem of a single asset portfolio, held in a very large quantity, in a low volatility and perfect memory market, with few market participants. In this context, the Portfolio Manager's selling actions convey information to market participants, which in turn lower bid prices and further penalize the liquidation proceeds we attempt to maximize. We show the problem can be solved exactly using Dynamic Programming (DP) in polynomial time. However, exact resolution is only efficient for small instances. For medium size and large instances, we introduce dedicated heuristics which provide thin admissible solutions, hence tight lower bounds for the initial problem. We also benchmark them against a commercial solver, such as LocalSolver [7]. We are also interested in the continuously relaxed problem, which is non convex. Firstly, we use continuous solutions, obtained by free solver NLopt [26] and transform them into thin admissible solutions of the discrete problem. Secondly, we provide, under some convexity assumptions, an upper bound for the continuous relaxation, and hence for the initial (integer) problem. Numerical experiments confirm the quality of proposed heuristics (lower bounds), which often reach the optimal, or prove very tight, for small and medium size instances, with a very fast CPU time. Our upper bound, however, is not tight.

A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In this paper, we consider the problem of approximating functions by polynomials whose Bernstein coefficients with respect to a given degree satisfy such bounds, which implies such bounds on the approximant. We frame the problem as an inequality-constrained optimization problem and give an algorithm for finding the Bernstein coefficients of the exact solution. Additionally, our method can be modified slightly to include equality constraints such as mass preservation. It also extends naturally to multivariate polynomials over a simplex.

A key challenge of big data analytics is how to collect a large volume of (labeled) data. Crowdsourcing aims to address this challenge via aggregating and estimating high-quality data (e.g., sentiment label for text) from pervasive clients/users. Existing studies on crowdsourcing focus on designing new methods to improve the aggregated data quality from unreliable/noisy clients. However, the security aspects of such crowdsourcing systems remain under-explored to date. We aim to bridge this gap in this work. Specifically, we show that crowdsourcing is vulnerable to data poisoning attacks, in which malicious clients provide carefully crafted data to corrupt the aggregated data. We formulate our proposed data poisoning attacks as an optimization problem that maximizes the error of the aggregated data. Our evaluation results on one synthetic and two real-world benchmark datasets demonstrate that the proposed attacks can substantially increase the estimation errors of the aggregated data. We also propose two defenses to reduce the impact of malicious clients. Our empirical results show that the proposed defenses can substantially reduce the estimation errors of the data poisoning attacks.

In order to answer natural language questions over knowledge graphs, most processing pipelines involve entity and relation linking. Traditionally, entity linking and relation linking has been performed either as dependent sequential tasks or independent parallel tasks. In this paper, we propose a framework called "EARL", which performs entity linking and relation linking as a joint single task. EARL uses a graph connection based solution to the problem. We model the linking task as an instance of the Generalised Travelling Salesman Problem (GTSP) and use GTSP approximate algorithm solutions. We later develop EARL which uses a pair-wise graph-distance based solution to the problem.The system determines the best semantic connection between all keywords of the question by referring to a knowledge graph. This is achieved by exploiting the "connection density" between entity candidates and relation candidates. The "connection density" based solution performs at par with the approximate GTSP solution.We have empirically evaluated the framework on a dataset with 5000 questions. Our system surpasses state-of-the-art scores for entity linking task by reporting an accuracy of 0.65 to 0.40 from the next best entity linker.