We propose a recommendation system, based on a modified language model in the class of Mixture Transition Distribution (MTD) models, to recommend optimized and near-optimized time series of promotional rewards. The historical data of our application domain, loyalty program, are low count, non-Gaussian, sparse and bursty time series. These are significantly more challenging to model than Gaussian time series. Our contribution is the first time series-based recommendation system based on a language model and based on MTD models. This proposed recommendation system is essentially a hierarchical model for the reward-response time series pair. As timeliness of promotional rewards is important, we estimate probable churn off time by a simple technique using a related time series of visits of the loyalty program customers to the business location. We also propose a novel human in the loop technique to fabricate a future response time series using the estimated churn time. Using Viterbi algorithm, an optimized future reward series is estimated for recommendation, given the future response time series as input. During the evaluation process, the real response series was used as input instead. We also propose a constraint-based modification of Viterbi algorithm called Hopefulness procedure (HP). HP was proposed as a constraint based optimization method for achieving trade-offs between user retention and the likelihood of the future reward series. We also proposed three new evaluation metrics. To assess the degree of user retention that can likely be achieved using the future reward sequence, we used MAE (generally used for sequence matching) and recall, their two proposed modifications, and a proposed metric goodrec. We used three different types of correlated user engagement time series data recorded for an year for a set of users. The evaluation showed that the lower bound of the expected performance of HP algorithm is better than the Viterbi algorithm in generating a future reward series for user retention.

The main focus of this work is to discover naturally occurring clusters in behavioral time series, and then associate a numerical representation with every cluster, which could be used to further study and control cluster properties. We presented a higher order but parsimonious model similar to HMM to do predictive analysis on time series. We revised the modeling assumptions of an unpublished large language model [1] to make it more suitable to our problem, which practically transformed it into a new model, which is based on mixture transition distribution [2]. This work is the first application of this modified language model [1] in the area of finance, and in the area of customer(user) behavior study and user group discovery. The broader class of this kind of models [2], [3] has very few applications in finance at all.Our user behavior dataset, which is a collection of low count non-Gaussian time series, is collected from a loyalty program marketing company. This non-Gaussian time series data set contains bursts and flat stretches, hence it is already hard to model. But, it also poses significant modeling challenges, because it is not annotated, and is unaligned. Moreover, these time series are of short length and of unequal length. As a result, our work involved extensive pre-processing of raw data, including merging several time series using aggregate data at the data processing level to create longer time series for better estimation of parameters. We derived numerical representation of every time series from estimated parameters by learning the proposed model, and then clustered these representations. After clustering we derived a numerical representation of every cluster. We used three algorithms for clustering and three metrics to evaluate the clusters. We used cluster quality evaluation scores as measures of goodness of fit of the models that we experimented with. Although we used two other baseline models for our work, we see that the best well-separated dense latent clusters have been discovered when we used the numerical representation learned from our model. Hence, we find that our proposed model performed better than or equally well with the baseline models.

This paper addresses the problem of sampling of training examples as a "fair" subset of raw data, where the raw training data is assumed to consist of several distinct clusters, differently skewed with respect to target class ratio. We have treated class imbalance, as well as, error-rate imbalance as a cluster-level property of the data, and we established the connection between variation of this property over the clusters and fairness of the sampling process. This work can be seen as the Bayesian version of the Kleinberg’s [1] Equalized odds idea. We added a few fairness related decision rules defined in terms of FP and FN errors to the Bayesian balance framework. We also added a few fairness measures in terms of FP and FN errors in the framework. We incorporated a Bayesian version of relaxation for Equalized odds to accommodate the impossibility result. We used three datasets for experiment and implemented a Bayesian technique of fair sampling by measuring fairness with explicit measure of its uncertainty. We proved that a Bayesian approach to fairness is better than the state-of-the-art non-Bayesian approach.

An algorithm is proposed in this paper to identify the latent groups among users based on similar behavior pattern and to generate group-profile for every latent group discovered. The behavior history of every user is represented by a sequence of zeros and positive numbers. Our goal is to create a hierarchical Bayesian model of the sequence data and soft-assign the sequences to a number of clusters. Profiles representative of each cluster are generated by the data model. This model is a mixture model where every user's sequence is effectively a mixture of the distributions for each cluster. However, the novelty of this algorithm is that it is not required to assume a Gaussian mixture as is the case with EM, instead it could be any distribution that fits the data. In this paper Poisson distribution is used to model individual users sequence. The data used in this paper are real industrial data, collected from a collaborating marketing company, which promotes businesses through loyalty programs. Loyalty program helps businesses engage users by sending weekly rewards, coupons etc and the number of rewards redeemed per week for a period of two years forms the users sequence, where every entry in the sequence represents number of redemptions every week. The similarity in the real-life motivators such as schedules, locations, tastes, and expectations gives rise to similar pattern in redemption of these rewards. Based on this inherent similarity the latent groups evolve in the data.