Travel providers such as airlines and on-line travel agents are becoming more and more interested in understanding how passengers choose among alternative itineraries when searching for flights. This knowledge helps them better display and adapt their offer, taking into account market conditions and customer needs. Some common applications are not only filtering and sorting alternatives, but also changing certain attributes in real-time (e.g., changing the price). In this paper, we concentrate with the problem of modeling air passenger choices of flight itineraries. This problem has historically been tackled using classical Discrete Choice Modelling techniques. Traditional statistical approaches, in particular the Multinomial Logit model (MNL), is widely used in industrial applications due to its simplicity and general good performance. However, MNL models present several shortcomings and assumptions that might not hold in real applications. To overcome these difficulties, we present a new choice model based on Pointer Networks. Given an input sequence, this type of deep neural architecture combines Recurrent Neural Networks with the Attention Mechanism to learn the conditional probability of an output whose values correspond to positions in an input sequence. Therefore, given a sequence of different alternatives presented to a customer, the model can learn to point to the one most likely to be chosen by the customer. The proposed method was evaluated on a real dataset that combines on-line user search logs and airline flight bookings. Experimental results show that the proposed model outperforms the traditional MNL model on several metrics.
Moreover, @cite_4 propose a Markov chain based choice model, where the substitution from one product to another is modeled as a state transition of a Markov chain. The chain's parameters are estimated with a data-driven procedure.
@cite_4
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Markov chains with Labelled Transitions can be used to generate test cases in a model-based approach. These test cases are generated by random walks on the model according to probabilities associated with transitions. When these probabilities correspond to a usage profile, reliability may be estimated. However, in early stages of development, such probabilities are not easy to determine, thus default profiles must be considered. In such a case it may be interesting to target some coverage criteria rather to use classical uniform probability generation approach. In this paper we enrich an existing industrial tool based on usage profile with 3 possibilities to create default profiles that improve transition coverage. We report experiments that compare the improvement of the coverage rates by our approaches with respect to uniform probabilities on transitions from a given state, which is the current default profile. Assortment planning is an important problem that arises in many industries such as retailing and airlines. One of the key challenges in an assortment planning problem is to identify the “right” model for the substitution behavior of customers from the data. Error in model selection can lead to highly suboptimal decisions. In this paper, we consider a Markov chain based choice model and show that it provides a simultaneous approximation for all random utility based discrete choice models including the multinomial logit (MNL), the probit, the nested logit and mixtures of multinomial logit models. In the Markov chain model, substitution from one product to another is modeled as a state transition in the Markov chain. We show that the choice probabilities computed by the Markov chain based model are a good approximation to the true choice probabilities for any random utility based choice model under mild conditions. Moreover, they are exact if the underlying model is a generalized attraction model (GAM) of which the MNL model is a special case. We also show that the assortment optimization problem for our choice model can be solved efficiently in polynomial time. In addition to the theoretical bounds, we also conduct numerical experiments and observe that the average maximum relative error of the choice probabilities of our model with respect to the true probabilities for any offer set is less than 3 where the average is taken over different offer sets. Therefore, our model provides a tractable approach to choice modeling and assortment optimization that is robust to model selection errors. Moreover, the state transition primitive for substitution provides interesting insights to model the substitution behavior in many real-world applications. Recommender systems are an important component of many websites. Two of the most popular approaches are based on matrix factorization (MF) and Markov chains (MC). MF methods learn the general taste of a user by factorizing the matrix over observed user-item preferences. On the other hand, MC methods model sequential behavior by learning a transition graph over items that is used to predict the next action based on the recent actions of a user. In this paper, we present a method bringing both approaches together. Our method is based on personalized transition graphs over underlying Markov chains. That means for each user an own transition matrix is learned - thus in total the method uses a transition cube. As the observations for estimating the transitions are usually very limited, our method factorizes the transition cube with a pairwise interaction model which is a special case of the Tucker Decomposition. We show that our factorized personalized MC (FPMC) model subsumes both a common Markov chain and the normal matrix factorization model. For learning the model parameters, we introduce an adaption of the Bayesian Personalized Ranking (BPR) framework for sequential basket data. Empirically, we show that our FPMC model outperforms both the common matrix factorization and the unpersonalized MC model both learned with and without factorization. Abstract The enormous growth in the number of documents in the World Wide Web increases the need for improved link navigation and path analysis models. Link prediction and path analysis are important problems with a wide range of applications ranging from personalization to Web server request prediction. The sheer size of the World Wide Web coupled with the variation in users' navigation patterns makes this a very difficult sequence modelling problem. In this paper, the notion of probabilistic link prediction and path analysis using Markov chains is proposed and evaluated. Markov chains allow the system to dynamically model the URL access patterns that are observed in navigation logs based on the previous state. Furthermore, the Markov chain model can also be used in a generative mode to automatically obtain tours. The Markov transition matrix can be analysed further using eigenvector decomposition to obtain personalized hubs authorities'. The utility of the Markov chain approach is demonstrated in many domains: HTTP request prediction, system-driven adaptive Web navigation, tour generation, and detection of personalized hubs authorities' from user navigation profiles. The generality and power of Markov chains is a first step towards the application of powerful probabilistic models to Web path analysis and link prediction.