Humans exhibit time-inconsistent behavior, in which planned actions diverge from executed actions. Understanding time inconsistency and designing appropriate interventions is a key research challenge in computer science and behavioral economics. Previous work focuses on progress-based tasks and derives a closed-form description of agent behavior, from which they obtain optimal intervention strategies. They model time-inconsistency using the β–δ discounting (quasi-hyperbolic discounting), but the analysis is limited to the case δ = 1. In this paper, we relax that constraint and show that a closed-form description of agent behavior remains possible for the general case 0 < δ ≤ 1. Based on this result, we derive the conditions under which agents abandon tasks and develop efficient methods for computing optimal interventions. Our analysis reveals that agent behavior and optimal interventions depend critically on the value of δ, suggesting that fixing δ = 1 in many prior studies may unduly simplify real-world decision-making processes.

Present bias, the tendency to overvalue immediate rewards while undervaluing future ones, is a well-known barrier to achieving long-term goals. As artificial intelligence and behavioral economics increasingly focus on this phenomenon, the need for robust mathematical models to predict behavior and guide effective interventions has become crucial. However, existing models are constrained by their reliance on the discreteness of time and limited discount functions. This study introduces a novel continuous-time mathematical model for agents influenced by present bias. Using the variational principle, we model human behavior, where individuals repeatedly act according to a sequence of states that minimize their perceived cost. Our model not only retains analytical tractability but also accommodates various discount functions. Using this model, we consider intervention optimization problems under exponential and hyperbolic discounting and theoretically derive optimal intervention strategies, offering new insights into managing present-biased behavior.

Time-inconsistency is a characteristic of human behavior in which people plan for long-term benefits but take actions that differ from the plan due to conflicts with short-term benefits. Such time-inconsistent behavior is believed to be caused by present bias, a tendency to overestimate immediate rewards and underestimate future rewards. It is essential in behavioral economics to investigate the relationship between present bias and time-inconsistency. In this paper, we propose a model for analyzing agent behavior with present bias in tasks to make progress toward a goal over a specific period. Unlike previous models, the state sequence of the agent can be described analytically in our model. Based on this property, we analyze three crucial problems related to agents under present bias: task abandonment, optimal goal setting, and optimal reward scheduling. Extensive analysis reveals how present bias affects the condition under which task abandonment occurs and optimal intervention strategies. Our findings are meaningful for preventing task abandonment and intervening through incentives in the real world.

Humans make decisions based on their internal value function, and its shape is known to be distorted and biased around a point, which the research community of behavior economics refers to as the reference point. People intensify activities that come to lie within the reach of their reference point, and abstain from acts that would incur losses once they've crossed the point. However, the impact of past experiences on decision making around the reference point has not been well studied. By analyzing a long series of user-level decisions gathered from a competitive programming website, we find that history has a clear impact on user's decision making around the reference point. Past experiences can strengthen, and sometimes weaken, the decision bias around the reference point. Experiences of past difficulties can strengthen the tendency towards loss aversion after achieving the reference point. When a person crosses a reference point for the first time, the cognitive decision bias is significant. However, repeating this crossing gradually weakens the effect. We also show the value of our insights in the task of predicting user behavior. Prediction models incorporating our insights may be used for motivating people to remain more active.

Abstract Collective graphical model (CGM) is a probabilistic model that provides a framework for analyzing aggregated count data. Maximum a posteriori (MAP) inference of unobserved variables under given observations is one of the essential operations in CGM. Because the MAP inference problem is known to be NP-hard in general, the current mainstream approach is to solve an alternative problem obtained by approximating the objective function and applying continuous relaxation. However, this approach has two significant drawbacks. First, the quality of the solution deteriorates when the values in the count data are negligible due to the inaccuracy of Stirling’s approximation. Second, the application of continuous relaxation causes the violation of integrality constraints. This paper proposes novel algorithms for MAP inference in CGMs on path graphs to overcome these problems. Our method is based on the discrete difference of convex algorithm (DCA); DCA is a general framework to minimize the sum of a convex function and a concave function by repeatedly minimizing surrogate functions. Utilizing the particular structure of path graphs, we efficiently solve the surrogate function minimization by minimum convex cost flow algorithms. Furthermore, our approach also leads to a new method of solving another important task; MAP inference of the sample size in CGM on path graphs. Our method is naturally applicable to this task, allowing us to design very efficient algorithms. Experimental results on synthetic and real-world datasets show the effectiveness of the proposed algorithms.

Massive spatio-temporal event data sets are now available that cover events such as disease outbreaks, armed conflicts and crimes. Predicting such events and revealing the underlying triggering patterns are a crucial task for many applications, ranging from disease control to global politics. Traditional event prediction models based on Hawkes processes capture the spatio-temporal relationships between events, but cannot incorporate complex and heterogeneous external features, including population distribution, weather and terrain. This paper proposes an event prediction method that effectively utilizes the rich external information present in sets of unstructured data (e.g., map images, satellite images and weather map). Specifically, we extend a convolutional neural network (CNN) by combining it with continuous kernel convolution; and design the conditional intensity of Hawkes process based on the extended neural network model that accepts images as its input. Our approach of using the continuous convolution kernel provides a flexible way to discover the complex effect of external factors on the triggering process, as well as yielding tractable optimization algorithms. We use real-world event data from different domains (i.e., disease outbreaks, armed conflicts and protests) to demonstrate that the proposed method has better prediction performance than existing methods.

The research field of stochastic matching has yielded many developments for various applications. In most stochastic matching problems, the probability distributions inherent in the nodes and edges are set a priori, and are not controllable. However, many matching services have options, which we call control variables, that affect the probability distributions and thus what constitutes an optimum matching. Although several methods for optimizing the values of the control variables have been developed, their optimization in consideration of the matching problem is still in its infancy. In this paper, we formulate an optimization problem for determining the values of the control variables so as to maximize the expected value of matching weights. Since this problem involves hard to evaluate objective values and is non-convex, we construct an approximation algorithm via a minimum-cost flow algorithm that can find 3-approximation solutions rapidly. Simulations on real data from a ride-hailing platform and a crowd-sourcing market show that the proposed method can find solutions with high profits of the service provider in practical time.

Sequences of events including infectious disease outbreaks, social network activities, and crimes are ubiquitous and the data on such events carry essential information about the underlying diffusion processes between communities (e.g., regions, online user groups). Modeling diffusion processes and predicting future events are crucial in many applications including epidemic control, viral marketing, and predictive policing. Hawkes processes offer a central tool for modeling the diffusion processes, in which the influence from the past events is described by the triggering kernel. However, the triggering kernel parameters, which govern how each community is influenced by the past events, are assumed to be static over time. In the real world, the diffusion processes depend not only on the influences from the past, but also the current (time-evolving) states of the communities, e.g., people's awareness of the disease and people's current interests. In this paper, we propose a novel Hawkes process model that is able to capture the underlying dynamics of community states behind the diffusion processes and predict the occurrences of events based on the dynamics. Specifically, we model the latent dynamic function that encodes these hidden dynamics by a mixture of neural networks. Then we design the triggering kernel using the latent dynamic function and its integral. The proposed method, termed DHP (Dynamic Hawkes Processes), offers a flexible way to learn complex representations of the time-evolving communities' states, while at the same time it allows to computing the exact likelihood, which makes parameter learning tractable. Extensive experiments on four real-world event datasets show that DHP outperforms five widely adopted methods for event prediction.

The importance of aggregated count data, which is calculated from the data of multiple individuals, continues to increase. Collective Graphical Model (CGM) is a probabilistic approach to the analysis of aggregated data. One of the most important operations in CGM is maximum a posteriori (MAP) inference of unobserved variables under given observations. Because the MAP inference problem for general CGMs has been shown to be NP-hard, an approach that solves an approximate problem has been proposed. However, this approach has two major drawbacks. First, the quality of the solution deteriorates when the values in the count tables are small, because the approximation becomes inaccurate. Second, since continuous relaxation is applied, the integrality constraints of the output are violated. To resolve these problems, this paper proposes a new method for MAP inference for CGMs on path graphs. Our method is based on the Difference of Convex Algorithm (DCA), which is a general methodology to minimize a function represented as the sum of a convex function and a concave function. In our algorithm, important subroutines in DCA can be efficiently calculated by minimum convex cost flow algorithms. Experiments show that the proposed method outputs higher quality solutions than the conventional approach.

The rapid adoption of wireless sensor devices has made it easier to record location information of people in a variety of spaces (e.g., exhibition halls). Location information is often aggregated due to privacy and/or cost concerns. The aggregated data we use as input consist of the numbers of incoming and outgoing people at each location and at each time step. Since the aggregated data lack tracking information of individuals, determining the flow of people between locations is not straightforward. In this article, we address the problem of inferring latent people flows, that is, transition populations between locations, from just aggregated population data gathered from observed locations. Existing models assume that everyone is always in one of the observed locations at every time step; this, however, is an unrealistic assumption, because we do not always have a large enough number of sensor devices to cover the large-scale spaces targeted. To overcome this drawback, we propose a probabilistic model with flow conservation constraints that incorporate travel duration distributions between observed locations. To handle noisy settings, we adopt noisy observation models for the numbers of incoming and outgoing people, where the noise is regarded as a factor that may disturb flow conservation, e.g., people may appear in or disappear from the predefined space of interest. We develop an approximate expectation-maximization (EM) algorithm that simultaneously estimates transition populations and model parameters. Our experiments demonstrate the effectiveness of the proposed model on real-world datasets of pedestrian data in exhibition halls, bike trip data and taxi trip data in New York City.

Collective Flow Diffusion Model (CFDM) is a general framework to find the hidden movements underlying aggregated population data. The key procedure in CFDM analysis is MAP inference of hidden variables. Unfortunately, existing approaches fail to offer exact MAP inferences, only approximate versions, and take a lot of computation time when applied to large scale problems. In this paper, we propose an exact and efficient method for MAP inference in CFDM. Our key idea is formulating the MAP inference problem as a combinatorial optimization problem called Minimum Convex Cost Flow Problem (C-MCFP) with no approximation or continuous relaxation. On the basis of this formulation, we propose an efficient inference method that employs the C-MCFP algorithm as a subroutine. Our experiments on synthetic and real datasets show that the proposed method is effective both in single MAP inference and people flow estimation with EM algorithm.

The importance of developing an application based on intervention technology that leads to a healthier life is widely recognized. A challenging part of realizing the application is the need for planning, i.e., considering a user's health goal (e.g., sleep at 10:00 p.m. to get enough sleep), providing intervention at the appropriate timing to help the user achieve the goal. The reinforcement learning (RL) approach is well suited to this type of problem since it is a methodology for planning; RL finds the optimal strategy as that which maximizes future expected profit. The purpose of this study is to clarify the effects of intervention based on RL to support healthy daily life. Therefore, we (i) collect real daily activity data from participants, (ii) generate a user model that imitates the user's response to system interventions, (iii) examine valuable goals and design them as rewards in RL and (iv) obtain optimal intervention strategies by RL via simulations given a user model and goals. We evaluate a generated user model and verify by simulations whether our method could successfully achieve the goal. In addition, we analyze the cases that demonstrated higher probability of achieving the goal and report the features.

Due to the difficulty of comprehensive data collection, created by factors such as privacy protection and sensor device limitations, we often need to analyze incomplete transition data where some information is missing from the ideal (complete) transition data. In this paper, we propose a new method that can estimate, in a unified manner, Markov chain parameters from incomplete transition data that consist of hidden transition data (data from which visited state information is partially hidden) and dropped transition data (data from which some state visits are dropped). A key to developing the method is regarding the hidden and dropped transition data as labeled and unlabeled multi-step transition data, where the labels represent the number of steps required for each transition. This allows us to describe the generative process of multi-step transition data, and thus develop a new probabilistic model. We confirm the effectiveness of the proposal by experiments on synthetic and real data.

We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity of target data. The proposed model can effectively make use of auxiliary data sets with various granularities by hierarchically incorporating Gaussian processes. With the proposed model, a distribution for each auxiliary data set on the continuous space is modeled using a Gaussian process, where the representation of uncertainty considers the levels of granularity. The finegrained target data are modeled by another Gaussian process that considers both the spatial correlation and the auxiliary data sets with their uncertainty. We integrate the Gaussian process with a spatial aggregation process that transforms the fine-grained target data into the coarse-grained target data, by which we can infer the fine-grained target Gaussian process from the coarse-grained data. Our model is designed such that the inference of model parameters based on the exact marginal likelihood is possible, in which the variables of finegrained target and auxiliary data are analytically integrated out. Our experiments on real-world spatial data sets demonstrate the effectiveness of the proposed model.

Predicting when and where events will occur in cities, like taxi pick-ups, crimes, and vehicle collisions, is a challenging and important problem with many applications in fields such as urban planning, transportation optimization and location-based marketing. Though many point processes have been proposed to model events in a continuous spatio-temporal space, none of them allow for the consideration of the rich contextual factors that affect event occurrence, such as weather, social activities, geographical characteristics, and traffic. In this paper, we propose DMPP (Deep Mixture Point Processes), a point process model for predicting spatio-temporal events with the use of rich contextual information; a key advance is its incorporation of the heterogeneous and high-dimensional context available in image and text data. Specifically, we design the intensity of our point process model as a mixture of kernels, where the mixture weights are modeled by a deep neural network. This formulation allows us to automatically learn the complex nonlinear effects of the contextual factors on event occurrence. At the same time, this formulation makes analytical integration over the intensity, which is required for point process estimation, tractable. We use real-world data sets from different domains to demonstrate that DMPP has better predictive performance than existing methods.

We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can only utilize the sufficiently fine-grained auxiliary data sets on the same domain (e.g., a city). With the proposed model, the functions for respective areal data sets are assumed to be a multivariate dependent Gaussian process (GP) that is modeled as a linear mixing of independent latent GPs. Sharing of latent GPs across multiple areal data sets allows us to effectively estimate the spatial correlation for each areal data set; moreover it can easily be extended to transfer learning across multiple domains. To handle the multivariate areal data, we design an observation model with a spatial aggregation process for each areal data set, which is an integral of the mixed GP over the corresponding region. By deriving the posterior GP, we can predict the data value at any location point by considering the spatial correlations and the dependences between areal data sets, simultaneously. Our experiments on real-world data sets demonstrate that our model can 1) accurately refine coarse-grained areal data, and 2) offer performance improvements by using the areal data sets from multiple domains.

Real-time spatiotemporal population data is attracting a great deal of attention for understanding crowd movements in cities.The data is the aggregation of personal location information and consists of just areas and the number of people in each area at certain time instants. Accordingly, it does not explicitly represent crowd movement. This paper proposes a probabilistic model based on collective graphical models that can estimate crowd movement from spatiotemporal population data. There are two technical challenges: (i) poor estimation accuracy as the traditional approach means the model would have too many degrees of freedom, (ii) excessive computation cost. Our key idea for overcoming these two difficulties is to model the transition probability between grid cells (cells hereafter) in a geospatial grid space by using three factors: departure probability of cells, gathering score of cells, and geographical distance between cells. These advances enable us to reduce the degrees of freedom of the model appropriately and derive an efficient estimation algorithm. To evaluate the performance of our method, we conduct experiments using real-world spatiotemporal population data. The results confirm the effectiveness of our method, both in estimation accuracy and computation cost.

Analyzing people flows is important for better navigation and location-based advertising. Since the location information of people is often aggregated for protecting privacy, it is not straightforward to estimate transition populations between locations from aggregated data. Here, aggregated data are incoming and outgoing people counts at each location; they do not contain tracking information of individuals. This paper proposes a probabilistic model for estimating unobserved transition populations between locations from only aggregated data. With the proposed model, temporal dynamics of people flows are assumed to be probabilistic diffusion processes over a network, where nodes are locations and edges are paths between locations. By maximizing the likelihood with flow conservation constraints that incorporate travel duration distributions between locations, our model can robustly estimate transition populations between locations. The statistically significant improvement of our model is demonstrated using real-world datasets of pedestrian data in exhibition halls, bike trip data and taxi trip data in New York City.

Mobile health applications, including those that track activities such as exercise, sleep, and diet, are becoming widely used. Accurately predicting human actions in the real world is essential for targeted recommendations that could improve our health and for personalization of these applications. However, making such predictions is extremely difficult due to the complexities of human behavior, which consists of a large number of potential actions that vary over time, depend on each other, and are periodic. Previous work has not jointly modeled these dynamics and has largely focused on item consumption patterns instead of broader types of behaviors such as eating, commuting or exercising. In this work, we develop a novel statistical model, called TIPAS, for Time-varying, Interdependent, and Periodic Action Sequences. Our approach is based on personalized, multivariate temporal point processes that model time-varying action propensities through a mixture of Gaussian intensities. Our model captures short-term and long-term periodic interdependencies between actions through Hawkes process-based self-excitations. We evaluate our approach on two activity logging datasets comprising 12 million real-world actions (e.g., eating, sleep, and exercise) taken by 20 thousand users over 17 months. We demonstrate that our approach allows us to make successful predictions of future user actions and their timing. Specifically, TIPAS improves predictions of actions, and their timing, over existing methods across multiple datasets by up to 156%, and up to 37%, respectively. Performance improvements are particularly large for relatively rare and periodic actions such as walking and biking, improving over baselines by up to 256%. This demonstrates that explicit modeling of dependencies and periodicities in real-world behavior enables successful predictions of future actions, with implications for modeling human behavior, app personalization, and targeting of health interventions.

This paper proposes a method for inferring from single-source data the factors that trigger purchases. Here, single-source data are the histories of item purchases and media advertisement views for each individual. We assume a sequence of purchase events to be a stochastic process incorporating the following three factors: (a) user preference, (b) social effects received from other users, and (c) media advertising effects. As our user-purchase model incorporates the latent relationships between users and advertisers, it can infer the latent triggers of purchases. Experiments on real single-source data show that our model can (a) achieve high prediction accuracy for purchases, (b) discover the key information, i.e., popular items, influential users, and influential advertisers, (c) estimate the relative impact of the three factors on purchases, and (d) find user segments according to the estimated factors.

Automatic check-in, which is to identify a user's visited points of interest (POIs) from his or her trajectories, is still an open problem because of positioning errors and the high POI density in small areas. In this study, we propose a probabilistic visited-POI identification method. The method uses a new hierarchical Bayesian model for identifying the latent visited-POI label of stay points, which are automatically extracted from trajectories. This model learns from labeled and unlabeled stay point data (i.e., semi-supervised learning) and takes into account personal preferences, stay locations including positioning errors, stay times for each category, and prior knowledge about typical user preferences and stay times. Experimental results with real user trajectories and POIs of Foursquare demonstrated that our method achieved statistically significant improvements in precision at 1 and recall at 3 over the nearest neighbor method and a conventional method that uses a supervised learning-to-rank algorithm.

The diffusion of information, rumors, and diseases are assumed to be probabilistic processes over some network structure. An event starts at one node of the network, and then spreads to the edges of the network. In most cases, the underlying network structure that generates the diffusion process is unobserved, and we only observe the times at which each node is altered/influenced by the process. This paper proposes a probabilistic model for inferring the diffusion network, which we call Probabilistic Latent Network Visualization (PLNV); it is based on cascade data, a record of observed times of node influence. An important characteristic of our approach is to infer the network by embedding it into a low-dimensional visualization space. We assume that each node in the network has latent coordinates in the visualization space, and diffusion is more likely to occur between nodes that are placed close together. Our model uses maximum a posteriori estimation to learn the latent coordinates of nodes that best explain the observed cascade data. The latent coordinates of nodes in the visualization space can 1) enable the system to suggest network layouts most suitable for browsing, and 2) lead to high accuracy in inferring the underlying network when analyzing the diffusion process of new or rare information, rumors, and disease.

Discovering interesting behavior patterns and profiles of users as they interact with E-commerce (EC) sites is an important task for site managers. We propose a probabilistic behavior model for extracting latent classes of items that impact the users' item selections but cannot be inferred from the current knowledge of the managers. The proposed model assumes that the current knowledge is represented by categories of items that are defined in the EC site, and a user selects items depending on both of their categories and latent classes. By estimating latent classes, each of which shows items accessed by users with common interests, we can find interesting factors for explaining user behavior. We evaluate our proposed model using item-access log data observed in an EC site. The results show that our model can accurately predict users' item selection, and actually discover latent classes of items having similar latent characteristic such as "colored design" and "impression" by using item categories such as "coat" and "hat" as the current knowledge of the managers.

This paper proposes a method that analyzes the location log data of multiple users to recommend locations to be visited. The method uses our new topic model, called Geo Topic Model, that can jointly estimate both the user's interests and activity area hosting the user's home, office and other personal places. By explicitly modeling geographical features of locations and users, the user's interests in other features of locations, which we call latent topics, can be inferred effectively. The topic interests estimated by our model 1) lead to high accuracy in predicting visit behavior as driven by personal interests, 2) make possible the generation of recommendations when the user is in an unfamiliar area (e.g. sightseeing), and 3) enable the recommender system to suggest an interpretable representation of the user profile that can be customized by the user. Experiments are conducted using real location logs of landmark and restaurant visits to evaluate the recommendation performance of the proposed method in terms of the accuracy of predicting visit selections. We also show that our model can estimate latent features of locations such as art, nature and atmosphere as latent topics, and describe each user's preference based on them.

The ability to create geotagged photos enables people to share their personal experiences as tourists at specific locations and times. Assuming that the collection of each photographer's geotagged photos is a sequence of visited locations, photo-sharing sites are important sources for gathering the location histories of tourists. By following their location sequences, we can find representative and diverse travel routes that link key landmarks. In this paper, we propose a travel route recommendation method that makes use of the photographers' histories as held by Flickr. Recommendations are performed by our photographer behavior model, which estimates the probability of a photographer visiting a landmark. We incorporate user preference and present location information into the probabilistic behavior model by combining topic models and Markov models. We demonstrate the effectiveness of the proposed method using a real-life dataset holding information from 71,718 photographers taken in the United States in terms of the prediction accuracy of travel behavior.

Integration of Web search with geographic information has recently attracted much attention. There are a number of local Web search systems enabling users to find location-specific Web content. In this paper, however, we point out that this integration is still at a superficial level. Most local Web search systems today only link local Web content to a map interface. They are extensions of a conventional stand-alone geographic information system (GIS), applied to a Web-based client-server architecture. In this paper, we discuss the directions available for tighter integration of Web search with a GIS, in terms of extraction, knowledge discovery, and presentation. We also describe implementations to support our argument that the integration must go beyond the simple map-and hyperlink architecture.