Guillermo Gallego

Zi Yang, Haojin Yang, Soumajit Majumder et al.

Previous studies have demonstrated that not each sample in a dataset is of equal importance during training. Data pruning aims to remove less important or informative samples while still achieving comparable results as training on the original (untruncated) dataset, thereby reducing storage and training costs. However, the majority of data pruning methods are applied to image classification tasks. To our knowledge, this work is the first to explore the feasibility of these pruning methods applied to object re-identification (ReID) tasks, while also presenting a more comprehensive data pruning approach. By fully leveraging the logit history during training, our approach offers a more accurate and comprehensive metric for quantifying sample importance, as well as correcting mislabeled samples and recognizing outliers. Furthermore, our approach is highly efficient, reducing the cost of importance score estimation by 10 times compared to existing methods. Our approach is a plug-and-play, architecture-agnostic framework that can eliminate/reduce 35%, 30%, and 5% of samples/training time on the VeRi, MSMT17 and Market1501 datasets, respectively, with negligible loss in accuracy (< 0.1%). The lists of important, mislabeled, and outlier samples from these ReID datasets are available at https://github.com/Zi-Y/data-pruning-reid.

Ningyuan Chen, Guillermo Gallego, Zhuodong Tang

Problem definition. In retailing, discrete choice models (DCMs) are commonly used to capture the choice behavior of customers when offered an assortment of products. When estimating DCMs using transaction data, flexible models (such as machine learning models or nonparametric models) are typically not interpretable and hard to estimate, while tractable models (such as the multinomial logit model) tend to misspecify the complex behavior represeted in the data. Methodology/results. In this study, we use a forest of binary decision trees to represent DCMs. This approach is based on random forests, a popular machine learning algorithm. The resulting model is interpretable: the decision trees can explain the decision-making process of customers during the purchase. We show that our approach can predict the choice probability of any DCM consistently and thus never suffers from misspecification. Moreover, our algorithm predicts assortments unseen in the training data. The mechanism and errors can be theoretically analyzed. We also prove that the random forest can recover preference rankings of customers thanks to the splitting criterion such as the Gini index and information gain ratio. Managerial implications. The framework has unique practical advantages. It can capture customers' behavioral patterns such as irrationality or sequential searches when purchasing a product. It handles nonstandard formats of training data that result from aggregation. It can measure product importance based on how frequently a random customer would make decisions depending on the presence of the product. It can also incorporate price information and customer features. Our numerical experiments using synthetic and real data show that using random forests to estimate customer choices can outperform existing methods.

Ningyuan Chen, Guillermo Gallego

We consider the problem of a firm seeking to use personalized pricing to sell an exogenously given stock of a product over a finite selling horizon to different consumer types. We assume that the type of an arriving consumer can be observed but the demand function associated with each type is initially unknown. The firm sets personalized prices dynamically for each type and attempts to maximize the revenue over the season. We provide a learning algorithm that is near-optimal when the demand and capacity scale in proportion. The algorithm utilizes the primal-dual formulation of the problem and learns the dual optimal solution explicitly. It allows the algorithm to overcome the curse of dimensionality (the rate of regret is independent of the number of types) and sheds light on novel algorithmic designs for learning problems with resource constraints.

Ningyuan Chen, Guillermo Gallego

Personalized pricing analytics is becoming an essential tool in retailing. Upon observing the personalized information of each arriving customer, the firm needs to set a price accordingly based on the covariates such as income, education background, past purchasing history to extract more revenue. For new entrants of the business, the lack of historical data may severely limit the power and profitability of personalized pricing. We propose a nonparametric pricing policy to simultaneously learn the preference of customers based on the covariates and maximize the expected revenue over a finite horizon. The policy does not depend on any prior assumptions on how the personalized information affects consumers' preferences (such as linear models). It is adaptively splits the covariate space into smaller bins (hyper-rectangles) and clusters customers based on their covariates and preferences, offering similar prices for customers who belong to the same cluster trading off granularity and accuracy. We show that the algorithm achieves a regret of order $O(\log(T)^2 T^{(2+d)/(4+d)})$, where $T$ is the length of the horizon and $d$ is the dimension of the covariate. It improves the current regret in the literature \citep{slivkins2014contextual}, under mild technical conditions in the pricing context (smoothness and local concavity). We also prove that no policy can achieve a regret less than $O(T^{(2+d)/(4+d)})$ for a particular instance and thus demonstrate the near optimality of the proposed policy.