Framework for Variable-lag Motif Following Relation Inference In Time Series using Matrix Profile analysis

Knowing who follows whom and what patterns they are following are crucial steps to understand collective behaviors (e.g. a group of human, a school of fish, or a stock market). Time series is one of resources that can be used to get insight regarding following relations. However, the concept of following patterns or motifs and the solution to find them in time series are not obvious. In this work, we formalize a concept of following motifs between two time series and present a framework to infer following patterns between two time series. The framework utilizes one of efficient and scalable methods to retrieve motifs from time series called the Matrix Profile Method. We compare our proposed framework with several baselines. The framework performs better than baselines in the simulation datasets. In the dataset of sound recording, the framework is able to retrieve the following motifs within a pair of time series that two singers sing following each other. In the cryptocurrency dataset, the framework is capable of capturing the following motifs within a pair of time series from two digital currencies, which implies that the values of one currency follow the values of another currency patterns. Our framework can be utilized in any field of time series to get insight regarding following patterns between time series.

Framework for inferring empirical causal graphs from binary data to support multidimensional poverty analysis

Poverty is one of the fundamental issues that mankind faces. Multidimensional Poverty Index (MPI) is deployed for measuring poverty issues in a population beyond monetary. However, MPI cannot provide information regarding associations and causal relations among poverty factors. Does education cause income inequality in a specific region? Is lacking education a cause of health issues? By not knowing causal relations, policy maker cannot pinpoint root causes of poverty issues of a specific population, which might not be the same across different population. Additionally, MPI requires binary data, which cannot be analyzed by most of causal inference frameworks. In this work, we proposed an exploratory-data-analysis framework for finding possible causal relations with confidence intervals among binary data. The proposed framework provides not only how severe the issue of poverty is, but it also provides the causal relations among poverty factors. Moreover, knowing a confidence interval of degree of causal direction lets us know how strong a causal relation is. We evaluated the proposed framework with several baseline approaches in simulation datasets as well as using two real-world datasets as case studies 1) Twin births of the United States: the relation between birth weight and mortality of twin, and 2) Thailand population surveys from 378k households of Chiang Mai and 353k households of Khon Kaen provinces. Our framework performed better than baselines in most cases. The first case study reveals almost all mortality cases in twins have issues of low birth weights but not all low-birth-weight twins were died. The second case study reveals that smoking associates with drinking alcohol in both provinces and there is a causal relation of smoking causes drinking alcohol in only Chiang Mai province. The framework can be applied beyond the poverty context.

Mining and modeling complex leadership-followership dynamics of movement data

Leadership and followership are essential parts of collective decision and organization in social animals, including humans. In nature, relationships of leaders and followers are dynamic and vary with context or temporal factors. Understanding dynamics of leadership and followership, such as how leaders and followers change, emerge, or converge, allows scientists to gain more insight into group decision-making and collective behavior in general. However, given only data of individual activities, it is challenging to infer the dynamics of leaders and followers. In this paper, we focus on mining and modeling frequent patterns of leading and following. We formalize new computational problems and propose a framework that can be used to address several questions regarding group movement. We use the leadership inference framework, mFLICA, to infer the time series of leaders and their factions from movement datasets and then propose an approach to mine and model frequent patterns of both leadership and followership dynamics. We evaluate our framework performance by using several simulated datasets, as well as the real-world dataset of baboon movement to demonstrate the applications of our framework. These are novel computational problems and, to the best of our knowledge, there are no existing comparable methods to address them. Thus, we modify and extend an existing leadership inference framework to provide a non-trivial baseline for comparison. Our framework performs better than this baseline in all datasets. Our framework opens the opportunities for scientists to generate testable scientific hypotheses about the dynamics of leadership in movement data.

Variable-lag Granger Causality and Transfer Entropy for Time Series Analysis

Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a fixed time delay. The assumption of fixed time delay also exists in Transfer Entropy, which is considered to be a non-linear version of Granger causality. However, the assumption of the fixed time delay does not hold in many applications, such as collective behavior, financial markets, and many natural phenomena. To address this issue, we develop Variable-lag Granger causality and Variable-lag Transfer Entropy, generalizations of both Granger causality and Transfer Entropy that relax the assumption of the fixed time delay and allow causes to influence effects with arbitrary time delays. In addition, we propose a method for inferring both variable-lag Granger causality and Transfer Entropy relations. We demonstrate our approaches on an application for studying coordinated collective behavior and other real-world casual-inference datasets and show that our proposed approaches perform better than several existing methods in both simulated and real-world datasets. Our approaches can be applied in any domain of time series analysis. The software of this work is available in the R-CRAN package: VLTimeCausality.

Variable-lag Granger Causality for Time Series Analysis

Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a fixed time delay. However, the assumption of the fixed time delay does not hold in many applications, such as collective behavior, financial markets, and many natural phenomena. To address this issue, we develop variable-lag Granger causality, a generalization of Granger causality that relaxes the assumption of the fixed time delay and allows causes to influence effects with arbitrary time delays. In addition, we propose a method for inferring variable-lag Granger causality relations. We demonstrate our approach on an application for studying coordinated collective behavior and show that it performs better than several existing methods in both simulated and real-world datasets. Our approach can be applied in any domain of time series analysis.

A nonparametric framework for inferring orders of categorical data from category-real ordered pairs

Given a dataset of careers and incomes, how large a difference of income between any pair of careers would be? Given a dataset of travel time records, how long do we need to spend more when choosing a public transportation mode $A$ instead of $B$ to travel? In this paper, we propose a framework that is able to infer orders of categories as well as magnitudes of difference of real numbers between each pair of categories using Estimation statistics framework. Not only reporting whether an order of categories exists, but our framework also reports the magnitude of difference of each consecutive pairs of categories in the order. In large dataset, our framework is scalable well compared with the existing framework. The proposed framework has been applied to two real-world case studies: 1) ordering careers by incomes based on information of 350,000 households living in Khon Kaen province, Thailand, and 2) ordering sectors by closing prices based on 1060 companies' closing prices of NASDAQ stock markets between years 2000 and 2016. The results of careers ordering show income inequality among different careers. The stock market results illustrate dynamics of sector domination that can change over time. Our approach is able to be applied in any research area that has category-real ordered pairs. Our proposed "Dominant-Distribution Network" provides a novel approach to gain new insight of analyzing category orders. The software of this framework is available for researchers or practitioners within R package: EDOIF.

Inferring Coordination Strategies from Time Series of Movement Data

How do groups of individuals achieve consensus in movement decisions? Do individuals follow their friends, the one predetermined leader, or whomever just happens to be nearby? To address these questions computationally, we formalize Coordination Strategy Inference Problem. In this setting, a group of multiple individuals moves in a coordinated manner towards a target path. Each individual uses a specific strategy to follow others (e.g. nearest neighbors, pre-defined leaders, preferred friends). Given a set of time series that includes coordinated movement and a set of candidate strategies as inputs, we provide the first methodology (to the best of our knowledge) to infer the set of strategies that each individual uses to achieve movement coordination at the group level. We evaluate and demonstrate the performance of the proposed framework by predicting the direction of movement of an individual in a group in both simulated datasets as well as two real-world datasets: a school of fish and a troop of baboons. Moreover, since there is no prior methodology for inferring individual-level strategies, we compare our framework with the state-of-the-art approach for the task of classification of group-level-coordination models. The results show that our approach is highly accurate in inferring the correct strategy in simulated datasets even in complicated mixed strategy settings, which no existing method can infer. In the task of classification of group-level-coordination models, our framework performs better than the state-of-the-art approach in all datasets. Animal data experiments show that fish, as expected, follow their neighbors, while baboons have a preference to follow specific individuals. Our methodology generalizes to arbitrary time series data of real numbers, beyond movement data.

Identifying Linear Models in Multi-Resolution Population Data using Minimum Description Length Principle to Predict Household Income

One shirt size cannot fit everybody, while we cannot make a unique shirt that fits perfectly for everyone because of resource limitation. This analogy is true for the policy making. Policy makers cannot establish a single policy to solve all problems for all regions because each region has its own unique issue. In the other extreme, policy makers also cannot create a policy for each small village due to the resource limitation. Would it be better if we can find a set of largest regions such that the population of each region within this set has common issues and we can establish a single policy for them? In this work, we propose a framework using regression analysis and minimum description length (MDL) to find a set of largest areas that have common indicators, which can be used to predict household incomes efficiently. Given a set of household features, and a multi-resolution partition that represents administrative divisions, our framework reports a set C* of largest subdivisions that have a common model for population-income prediction. We formalize a problem of finding C* and propose the algorithm as a solution. We use both simulation datasets as well as a real-world dataset of Thailand's population household information to demonstrate our framework performance and application. The results show that our framework performance is better than the baseline methods. We show the results of our method can be used to find indicators of income prediction for many areas in Thailand. By increasing these indicator values, we expect people in these areas to gain more incomes. Hence, the policy makers can plan to establish the policies by using these indicators in our results as a guideline to solve low-income issues. Our framework can be used to support policy makers to establish policies regarding any other dependent variable beyond incomes in order to combat poverty and other issues.

FLICA: A Framework for Leader Identification in Coordinated Activity

Leadership is an important aspect of social organization that affects the processes of group formation, coordination, and decision-making in human societies, as well as in the social system of many other animal species. The ability to identify leaders based on their behavior and the subsequent reactions of others opens opportunities to explore how group decisions are made. Understanding who exerts influence provides key insights into the structure of social organizations. In this paper, we propose a simple yet powerful leadership inference framework extracting group coordination periods and determining leadership based on the activity of individuals within a group. We are able to not only identify a leader or leaders but also classify the type of leadership model that is consistent with observed patterns of group decision-making. The framework performs well in differentiating a variety of leadership models (e.g. dictatorship, linear hierarchy, or local influence). We propose five simple features that can be used to categorize characteristics of each leadership model, and thus make model classification possible. The proposed approach automatically (1) identifies periods of coordinated group activity, (2) determines the identities of leaders, and (3) classifies the likely mechanism by which the group coordination occurred. We demonstrate our framework on both simulated and real-world data: GPS tracks of a baboon troop and video-tracking of fish schools, as well as stock market closing price data of the NASDAQ index. The results of our leadership model are consistent with ground-truthed biological data and the framework finds many known events in financial data which are not otherwise reflected in the aggregate NASDAQ index. Our approach is easily generalizable to any coordinated activity data from interacting entities.