Smoothing sparse and unevenly sampled curves using semiparametric mixed models: An application to online auctions

Functional data analysis can be challenging when the functional objects are sampled only very sparsely and unevenly. Most approaches rely on smoothing to recover the underlying functional object from the data which can be difficult if the data is irregularly distributed. In this paper we present a new approach that can overcome this challenge. The approach is based on the ideas of mixed models. Specifically, we propose a semiparametric mixed model with boosting to recover the functional object. While the model can handle sparse and unevenly distributed data, it also results in conceptually more meaningful functional objects. In particular, we motivate our method within the framework of eBay's online auctions. Online auctions produce monotonic increasing price curves that are often correlated across two auctions. The semiparametric mixed model accounts for this correlation in a parsimonious way. It also estimates the underlying increasing trend from the data without imposing model-constraints. Our application shows that the resulting functional objects are conceptually more appealing. Moreover, when used to forecast the outcome of an online auction, our approach also results in more accurate price predictions compared to standard approaches. We illustrate our model on a set of 183 closed auctions for Palm M515 personal digital assistants

Real-Time Bidding by Reinforcement Learning in Display Advertising

The majority of online display ads are served through real-time bidding (RTB) --- each ad display impression is auctioned off in real-time when it is just being generated from a user visit. To place an ad automatically and optimally, it is critical for advertisers to devise a learning algorithm to cleverly bid an ad impression in real-time. Most previous works consider the bid decision as a static optimization problem of either treating the value of each impression independently or setting a bid price to each segment of ad volume. However, the bidding for a given ad campaign would repeatedly happen during its life span before the budget runs out. As such, each bid is strategically correlated by the constrained budget and the overall effectiveness of the campaign (e.g., the rewards from generated clicks), which is only observed after the campaign has completed. Thus, it is of great interest to devise an optimal bidding strategy sequentially so that the campaign budget can be dynamically allocated across all the available impressions on the basis of both the immediate and future rewards. In this paper, we formulate the bid decision process as a reinforcement learning problem, where the state space is represented by the auction information and the campaign's real-time parameters, while an action is the bid price to set. By modeling the state transition via auction competition, we build a Markov Decision Process framework for learning the optimal bidding policy to optimize the advertising performance in the dynamic real-time bidding environment. Furthermore, the scalability problem from the large real-world auction volume and campaign budget is well handled by state value approximation using neural networks.Comment: WSDM 201

Real-time Tactical and Strategic Sales Management for Intelligent Agents Guided By Economic Regimes

Many enterprises that participate in dynamic markets need to make product pricing and inventory resource utilization decisions in real-time. We describe a family of statistical models that address these needs by combining characterization of the economic environment with the ability to predict future economic conditions to make tactical (short-term) decisions, such as product pricing, and strategic (long-term) decisions, such as level of finished goods inventories. Our models characterize economic conditions, called economic regimes, in the form of recurrent statistical patterns that have clear qualitative interpretations. We show how these models can be used to predict prices, price trends, and the probability of receiving a customer order at a given price. These “regime†models are developed using statistical analysis of historical data, and are used in real-time to characterize observed market conditions and predict the evolution of market conditions over multiple time scales. We evaluate our models using a testbed derived from the Trading Agent Competition for Supply Chain Management (TAC SCM), a supply chain environment characterized by competitive procurement and sales markets, and dynamic pricing. We show how regime models can be used to inform both short-term pricing decisions and longterm resource allocation decisions. Results show that our method outperforms more traditional shortand long-term predictive modeling approaches.dynamic pricing;trading agent competition;agent-mediated electronic commerce;dynamic markets;economic regimes;enabling technologies;price forecasting;supply-chain

Statistical Arbitrage Mining for Display Advertising

We study and formulate arbitrage in display advertising. Real-Time Bidding (RTB) mimics stock spot exchanges and utilises computers to algorithmically buy display ads per impression via a real-time auction. Despite the new automation, the ad markets are still informationally inefficient due to the heavily fragmented marketplaces. Two display impressions with similar or identical effectiveness (e.g., measured by conversion or click-through rates for a targeted audience) may sell for quite different prices at different market segments or pricing schemes. In this paper, we propose a novel data mining paradigm called Statistical Arbitrage Mining (SAM) focusing on mining and exploiting price discrepancies between two pricing schemes. In essence, our SAMer is a meta-bidder that hedges advertisers' risk between CPA (cost per action)-based campaigns and CPM (cost per mille impressions)-based ad inventories; it statistically assesses the potential profit and cost for an incoming CPM bid request against a portfolio of CPA campaigns based on the estimated conversion rate, bid landscape and other statistics learned from historical data. In SAM, (i) functional optimisation is utilised to seek for optimal bidding to maximise the expected arbitrage net profit, and (ii) a portfolio-based risk management solution is leveraged to reallocate bid volume and budget across the set of campaigns to make a risk and return trade-off. We propose to jointly optimise both components in an EM fashion with high efficiency to help the meta-bidder successfully catch the transient statistical arbitrage opportunities in RTB. Both the offline experiments on a real-world large-scale dataset and online A/B tests on a commercial platform demonstrate the effectiveness of our proposed solution in exploiting arbitrage in various model settings and market environments.Comment: In the proceedings of the 21st ACM SIGKDD international conference on Knowledge discovery and data mining (KDD 2015

Competition Between Auctions

Even though auctions are capturing an increasing share of commerce, they are typically treated in the theoretical economics literature as isolated. That is, an auction is typically treated as a single seller facing multiple buyers or as a single buyer facing multiple sellers. In this paper, we review the state of the art of competition between auctions. We consider three different types of competition: competition between auctions, competition between formats, and competition between auctioneers vying for auction traffic. We highlight the newest experimental, statistical and analytical methods in the analysis of competition between auctions.auctions, bidding, competition, auction formats, auction houses

Detecting and Forecasting Economic Regimes in Multi-Agent Automated Exchanges

We show how an autonomous agent can use observable market conditions to characterize the microeconomic situation of the market and predict future market trends. The agent can use this information to make both tactical decisions, such as pricing, and strategic decisions, such as product mix and production planning. We develop methods to learn dominant market conditions, such as over-supply or scarcity, from historical data using Gaussian mixture models to construct price density functions. We discuss how this model can be combined with real-time observable information to identify the current dominant market condition and to forecast market changes over a planning horizon. We forecast market changes via both a Markov correction-prediction process and an exponential smoother. Empirical analysis shows that the exponential smoother yields more accurate predictions for the current and the next day (supporting tactical decisions), while the Markov correction-prediction process is better for longer term predictions (supporting strategic decisions). Our approach offers more flexibility than traditional regression based approaches, since it does not assume a fixed functional relationship between dependent and independent variables. We validate our methods by presenting experimental results in a case study, the Trading Agent Competition for Supply Chain Management.dynamic pricing;machine learning;market forecasting;Trading agents

The value of a "free" customer

We study the problem of a firm that faces asymmetric information about the productivity of its potential workers. In our framework, a worker’s productivity is either assigned by nature at birth, or determined by an unobservable initial action of the worker that has persistent effects over time. We provide a characterization of the optimal dynamic compensation scheme that attracts only high productivity workers: consumption –regardless of time period– is ranked according to likelihood ratios of output histories, and the inverse of the marginal utility of consumption satisfies the martingale property derived in Rogerson (1985). However, in the case of i.i.d. output and square root utility we show that, contrary to the features of the optimal contract for a repeated moral hazard problem, the level and the variance of consumption are negatively correlated, due to the influence of early luck into future compensation. Moreover, in this example long-term inequality is lower under persistent private informationCustomer lifetime value, CRM, Dynamic programming, GMM Estimation

Real-time Tactical and Strategic Sales Management for Intelligent Agents Guided By Economic Regimes

Many enterprises that participate in dynamic markets need to make product pricing and inventory resource utilization decisions in real-time. We describe a family of statistical models that address these needs by combining characterization of the economic environment with the ability to predict future economic conditions to make tactical (short-term) decisions, such as product pricing, and strategic (long-term) decisions, such as level of finished goods inventories. Our models characterize economic conditions, called economic regimes, in the form of recurrent statistical patterns that have clear qualitative interpretations. We show how these models can be used to predict prices, price trends, and the probability of receiving a customer order at a given price. These “regime” models are developed using statistical analysis of historical data, and are used in real-time to characterize observed market conditions and predict the evolution of market conditions over multiple time scales. We evaluate our models using a testbed derived from the Trading Agent Competition for Supply Chain Management (TAC SCM), a supply chain environment characterized by competitive procurement and sales markets, and dynamic pricing. We show how regime models can be used to inform both short-term pricing decisions and longterm resource allocation decisions. Results show that our method outperforms more traditional shortand long-term predictive modeling approaches