The promised benefits of the Internet of Things (IoT) are predicated on the notion that better decisions will be enabled through a multitude of autonomous sensors (often deployed by different companies) providing real-time knowledge of the state of things. This knowledge will be imperfect, however, due to sensor quality limitations. A sensor can improve its estimation quality by soliciting a state estimate from other sensors operating in its general environment.

Operational decision making in service systems often depends largely on the characterization of the random fluctuations involved. Exogenous arrivals represent a primary source of uncertainty and their stochastic behavior needs to be modeled carefully. In this talk, we will first argue that the conventional approach to arrival modeling which focuses on the microstructure, e.g., the distribution of the inter-arrival times, may be inadequate.

We derive a generalized likelihood ratio method to estimate any distribution sensitivity in a unified form. Then, the distribution sensitivities are used to in a gradient-based simulated maximum likelihood estimation (GSMLE) to estimate unknown parameters in a stochastic model without assuming that the likelihoods of the observations are available in closed form. GSMLE can direct fit the underlying stochastic model to the output data, which opens the possibility of extending data-driven ideas to complex (causal) stochastic models.

News arrive randomly and the resulting sentiment, after quantification, behaves like a stochastic process. We propose a sentiment-driven stochastic volatility model to characterize the evolution of sentiment and its interplay with price and volatility process. Specifically, we propose a mean-reverting (Ornstein-Uhlenbeck) sentiment stochastic process to push over-optimistic/pessmistic sentiment back to neutral mood. Using the high-frequency news from Nasdaq news platform, we quantify news and model sentiment in the continuous time fashion.

Assortment rotation -- the retailing practice of changing the assortment of products offered to customers -- has recently been used as a competitive advantage for both brick-and-mortar and online retailers. We focus on product categories where consumers typically purchase multiple products during a season and investigate a new reason why frequent assortment rotations can be valuable to a retailer.

A prevalent yet little understood phenomenon of customer reward programs is the use of finite reward expiration term. We develop a theoretical framework to investigate the economic rationale behind this phenomenon, and the tradeoff between short and long expiration terms. In our model, a monopolistic firm interacts with consumers over an infinite horizon, and simultaneously sets the expiration term along with the price and reward size. Consumers are heterogeneous in shopping probabilities and product valuations, and forward-looking in making purchase decisions.

Recently, there has been a rapid rise of on-demand ride-hailing platforms, such as Uber and Didi, which allow passengers with smartphones to submit trip requests and match them to drivers based on their locations and drivers' availability. With the rapid rise, there have been questions about how such a new matching mechanism will affect the efficiency of the transportation system, in particular, whether it will help reduce passenger's average waiting time compared to that under a traditional street hailing system.

Minimization with respect to a matrix X subject to orthogonality constraints X'X = I has wide applications in polynomial optimization, combinatorial optimization, eigenvalue problems, the total energy minimization in electronic structure calculation, sparse principal component analysis, community detection and matrix rank minimization, etc. These problems are generally difficult because the constraints are not only non-convex but also numerically expensive to preserve during iterations. This talk will present a few recent advance for solving these problems.

We provide a theory that unifies the long tail and blockbuster phenomena. Specifically, we analyze a three-stage game where, first, a large number of potential firms make entry decisions, then those who stay in the market decide on the investment in its product, and lastly customers with heterogeneous preferences arrive sequentially to make purchase decisions based on product quality and historic sales under the network effect.

I will give a very broad history of efforts to find a method for discovering causal relations, from Aristotle to contemporary work in "artificial intelligence." I will also talk about some of the open problems and difficulties that remain.