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.

We propose novel fast algorithms for the Gromov–Wasserstein problem (GW) with cyclic symmetry of input data. This problem naturally appears as an object-matching task, which underlies various real-world computer vision applications, e.g., image registration, point cloud registration, stereo matching, and 3D reconstruction. Gradient-based algorithms have been widely used to solve GW, and our main idea is to utilize the following remarkable property that emerges in GW with cyclic symmetry: By setting the initial solution to have cyclic symmetry, all intermediate solutions and matrices that appear in the gradient-based algorithms have the same cyclic symmetry until convergence. Based on this property, our gradient-based algorithms restrict the solution space to have cyclic symmetry and update only one symmetric part of solutions and matrices at each iteration, resulting in faster computation. Moreover, our algorithms solve the optimal transport problem at each iteration, which also exhibits cyclic symmetry. This problem can be solved efficiently, and as a result, our algorithms perform significantly faster. Experiments showed the effectiveness of our algorithms in synthetic and real-world data with strict and approximate cyclic symmetry.

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.

We propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph processing. Our main idea is to reduce OT to a small optimization problem that has significantly fewer variables by utilizing cyclic symmetry and various optimization techniques. On the basis of this reduction, our algorithms solve the small optimization problem instead of the original OT. As a result, our algorithms obtain the optimal solution and the objective function value of the original OT faster than solving the original OT directly. In this paper, our focus is on two crucial OT formulations: the linear programming OT (LOT) and the strongly convex-regularized OT, which includes the well-known entropy-regularized OT (EROT). Experiments show the effectiveness of our algorithms for LOT and EROT in synthetic/real-world data that has a strict/approximate cyclic symmetry structure. Through theoretical and experimental results, this paper successfully introduces the concept of symmetry into the OT research field for the first time.

Crowd-sourcing has attracted much attention due to its growing importance to society, and numerous studies have been conducted on task allocation and wage determination. Recent works have focused on optimizing task allocation and workers' wages, simultaneously. However, existing methods do not provide good solutions for real-world crowd-sourcing platforms due to the low approximation ratio or myopic problem settings. We tackle an optimization problem for wage determination and online task allocation in crowd-sourcing and propose a fast 1-1/(k+3)^(1/2)-approximation algorithm, where k is the minimum of tasks' budgets (numbers of possible assignments). This approximation ratio is greater than or equal to the existing method. The proposed method reduces the tackled problem to a non-convex multi-period continuous optimization problem by approximating the objective function. Then, the method transforms the reduced problem into a minimum convex cost flow problem, which is a well-known combinatorial optimization problem, and solves it by the capacity scaling algorithm. Synthetic experiments and simulation experiments using real crowd-sourcing data show that the proposed method solves the problem faster and outputs higher objective values than existing methods.

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.

Online bipartite matching has attracted much attention due to its importance in various applications such as advertising, ride-sharing, and crowdsourcing. In most online matching problems, the rewards and node arrival probabilities are given in advance and are not controllable. However, many real-world matching services require them to be controllable and the decision-maker faces a non-trivial problem of optimizing them. In this study, we formulate a new optimization problem, Online Matching with Controllable Rewards and Arrival probabilities (OM-CRA), to simultaneously determine not only the matching strategy but also the rewards and arrival probabilities. Even though our problem is more complex than the existing ones, we propose a fast 1/2-approximation algorithm for OM-CRA. The proposed approach transforms OM-CRA to a saddle-point problem by approximating the objective function, and then solves it by the Primal-Dual Hybrid Gradient (PDHG) method with acceleration through the use of the problem structure. In simulations on real data from crowdsourcing and ride-sharing platforms, we show that the proposed algorithm can find solutions with high total rewards in practical times.

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.

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.

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.

Video magnification methods can magnify and reveal subtle changes invisible to the naked eye. However, in such subtle changes, meaningful ones caused by physical and natural phenomena are mixed with non-meaningful ones caused by photographic noise. Therefore, current methods often produce noisy and misleading magnification outputs due to the non-meaningful subtle changes. For detecting only meaningful subtle changes, several methods have been proposed but require human manipulations, additional resources, or input video scene limitations. In this paper, we present a novel method using fractional anisotropy (FA) to detect only meaningful subtle changes without the aforementioned requirements. FA has been used in neuroscience to evaluate anisotropic diffusion of water molecules in the body. On the basis of our observation that temporal distribution of meaningful subtle changes more clearly indicates anisotropic diffusion than that of non-meaningful ones, we used FA to design a fractional anisotropic filter that passes only meaningful subtle changes. Using the filter enables our method to obtain better and more impressive magnification results than those obtained with state-of-the-art 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.