​Background
Patients who are readmitted to an intensive care unit (ICU) usually have a high risk of mortality and an increased length of stay. ICU readmission risk prediction may help physicians to re-evaluate the patient’s physical conditions before patients are discharged and avoid preventable readmissions. ICU readmission prediction models are often built based on physiological variables. Intuitively, snapshot measurements, especially the last measurements, are effective predictors that are widely used by researchers. However, methods that only use snapshot measurements neglect predictive information contained in the trends of physiological and medication variables. Mean, maximum or minimum values take multiple time points into account and capture their summary statistics, however, these statistics are not able to catch the detailed picture of temporal trends.
 
In this work, we find strong predictors with ability of capturing detailed temporal trends of variables for 30- day readmission risk and build prediction models with high accuracy.
 
Workflow
We convert patients’ time series into graphs, where each node represents a discretized measurement at a single point in time. Among these graphs, we discover the most important subgraphs and identify them as common temporal trends. We study the correlation between the important subgraphs, group them and use the groupings as an augmentation to snapshot features in building predictive models. A workflow is shown below.

​Study of Imputation on Temporal Data
Along the way, we study the impact of different imputation techniques and develop a tailored methodology, called customized linear interpolation, that outperforms all other state-of-the-art approaches. Multivariate Imputation by Chained Equations (MICE) is a popular imputation method. However, its performance on temporal data is not as strong as that on snapshot data. A comparison between imputed values from MICE and customized linear interpolation is shown below.

​Conclusions
As a result, our model outperforms the baseline model that only uses the snapshot features, suggesting that the temporal trends carry predictive information for ICU readmission risk. Additionally, our experiments show that some imputation methods work well on replacing missing values in snapshot measurements but not on temporal data, suggesting that the temporal pattern need to be taken into consideration in imputation.

More and more airlines are putting emphasis on “merchandizing.” But aren’t they doing this right now? Unfortunately, most of them are not. Traditional carriers rely on their complex distribution channels and most of their focus is on managing those channels such as OTAs, off-line travel agencies, etc. Selling through direct channel is lucrative yet most airlines are in their early stage. As one part of merchandising capability, personalization heavily relies on airlines’ understanding of their travelers’ data and the ability to collect data. That is also why more and more airlines are trying to bring their travelers to their own website and complete the booking.
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This trend however may disrupt current market ecosystem where global distribution system (GDS) sells the majority of fares. To prevent airlines’ corner overtaking strategies, GDS has to take some actions! Comparing to airlines’ database, GDS companies’ competitive advantage is that they have data from all different airlines who use GDS. Most importantly, some GDS companies have the ability to “shop-back” and match bookings with the itineraries displayed to travelers. But this process is computationally expensive. So, an interesting problem came to our mind that can we use unmatched itineraries (i.e. unlabeled data or data without observed label) to improve airlines’ understanding of a potential market?

Airlines can understand a market such as Chicago to Shanghai from different aspects. To predict their market share, they use discrete choice model and the basic one (i.e. multinomial logit model) assumes a traveler’s utility or impression on an itinerary is given by a linear function of weighted features plus a gumbel noise. The goal of this model is to predict probability of choosing one itinerary. And it can also be used to estimate an airline’s market share or to estimate a traveler’s preferred rank of returned itineraries. In a typical case, to estimate such a model we need to know choice sets and also booked itineraries within each set. But those unlabeled choice sets may also be used as a way to improve the typical model estimation.
 
How can we utilize those choice sets? There were lots of research focusing on improving classification model estimation with unlabeled data. So it is worthwhile to try similar algorithms onto our problem. Inspired by this, we adapted four different algorithms. Three of them were based on clustering methods while another one was based on expectation-maximization algorithm. To evaluate the methods, we designed cross-validation experiments based on a public hotel dataset and compared the prediction accuracy. Results are presented below. We gradually increase the percentage of booked data with respect to unlabeled data. The metric we used is based on Kendall’s tau and model used was based on a ranked-logit choice model. For this metric, the lower the better. And we can see the zero Y-axis is the baseline which is the prediction provided by a model we estimated with only booked data. It is clear that our algorithms have a better performance than the baseline model for up to 10%.

​Specifically, we applied clustering-and-label (CL), expectation maximization (EM), x-clustering-and-label-1 (XCL1) and x-clustering-and-label-2 (XCL2). XCL1 and XCL2 are advanced clustering methods which explores the clustering structure automatically without setting a target number. It indicates that XCL1 and XCL2 are better than the other two algorithms.
 
In all, we believe this research may benefit GDS companies to provide better solutions to airlines, especially those non-legacy carriers who have not the capability to build up its own channel or IT infrastructure.