arXiv subjects

Santtu Tikka

Publications and source records attributed to Santtu Tikka.

At least 19 recordsLinked to original sources

arXiv2026

Early Warning Signals Appear Long Before Dropping Out: An Idiographic Approach Grounded in Complex Dynamic Systems Theory

The ability to sustain engagement and recover from setbacks (i.e., resilience) -- is fundamental for learning. When resilience weakens, students are at risk of disengagement and may drop out and miss on opportunities. Therefore, predicting disengagement long before it happens during the window of hope is important. In this article, we test whether early warning signals of resilience loss, grounded in the concept of critical slowing down (CSD) can forecast disengagement before dropping out. CSD has been widely observed across ecological, climate, and neural systems, where it precedes tipping points into catastrophic failure (dropping out in our case). Using 1.67 million practice attempts from 9,401 students who used a digital math learning environment, we computed CSD indicators: autocorrelation, return rate, variance, skewness, kurtosis, and coefficient of variation. We found that 88.2% of students exhibited CSD signals prior to disengagement, with warnings clustering late in activity and before practice ceased (dropping out). Our results provide the first evidence of CSD in education, suggesting that universal resilience dynamics also govern social systems such as human learning. These findings offer a practical indicator for early detection of vulnerability and supporting learners across different applications and contexts long before critical events happen. Most importantly, CSD indicators arise universally, independent of the mechanisms that generate the data, offering new opportunities for portability across contexts, data types, and learning environments.

cs.CY↗

arXiv2025

Clustering and Pruning in Causal Data Fusion

Data fusion, the process of combining observational and experimental data, can enable the identification of causal effects that would otherwise remain non-identifiable. Although identification algorithms have been developed for specific scenarios, do-calculus remains the only general-purpose tool for causal data fusion, particularly when variables are present in some data sources but not others. However, approaches based on do-calculus may encounter computational challenges as the number of variables increases and the causal graph grows in complexity. Consequently, there exists a need to reduce the size of such models while preserving the essential features. For this purpose, we propose pruning (removing unnecessary variables) and clustering (combining variables) as preprocessing operations for causal data fusion. We generalize earlier results on a single data source and derive conditions for applying pruning and clustering in the case of multiple data sources. We give sufficient conditions for inferring the identifiability or non-identifiability of a causal effect in a larger graph based on a smaller graph and show how to obtain the corresponding identifying functional for identifiable causal effects. Examples from epidemiology and social science demonstrate the use of the results.

stat.ML↗

arXiv2024

Transition Network Analysis: A Novel Framework for Modeling, Visualizing, and Identifying the Temporal Patterns of Learners and Learning Processes

This paper presents a novel learning analytics method: Transition Network Analysis (TNA), a method that integrates Stochastic Process Mining and probabilistic graph representation to model, visualize, and identify transition patterns in the learning process data. Combining the relational and temporal aspects into a single lens offers capabilities beyond either framework, including centralities to capture important learning events, community detection to identify behavior patterns, and clustering to reveal temporal patterns. Furthermore, TNA introduces several significance tests that go beyond either method and add rigor to the analysis. Here, we introduce the theoretical and mathematical foundations of TNA and we demonstrate the functionalities of TNA with a case study where students (n=191) engaged in small-group collaboration to map patterns of group dynamics using the theories of co-regulation and socially-shared regulated learning. The analysis revealed that TNA can map the regulatory processes as well as identify important events, patterns, and clusters. Bootstrap validation established the significant transitions and eliminated spurious transitions. As such, TNA can capture learning dynamics and provide a robust framework for investigating the temporal evolution of learning processes. Future directions include -- inter alia -- expanding estimation methods, reliability assessment, and building longitudinal TNA.

cs.SI↗

arXiv2024

Monotone Missing Data: A Blessing and a Curse

Monotone missingness is commonly encountered in practice when a missing measurement compels another measurement to be missing. Because of the simpler missing data pattern, monotone missing data is often viewed as beneficial from the perspective of practical data analysis. However, in graphical missing data models, monotonicity has implications for the identifiability of the full law, i.e., the joint distribution of actual variables and response indicators. In the general nonmonotone case, the full law is known to be nonparametrically identifiable if and only if specific graphical structures are not present. We show that while monotonicity may enable the identification of the full law despite some of these structures, it also prevents the identification in certain cases that are identifiable without monotonicity. The results emphasize the importance of proper treatment of monotone missingness in the analysis of incomplete data.

stat.ME↗

arXiv2024

Multiple Imputation Guided by Full Law and Target Law Identifiability under the Missing Not At Random Assumption

The central challenges in missing data models concern the identifiability of two distributions: the target law and the full law. The target law refers to the joint distribution of the data variables, whereas the full law refers to the joint distribution of the data variables and their corresponding response indicators. However, the relationship between the identifiability of these two distributions and the feasibility of multiple imputation has not been clearly established when the data are missing not at random (MNAR). We present a procedure in which the choice of imputation method is guided by identifiability considerations. The identifiability of the full law implies the applicability of conditionally complete imputation methods that draw imputations for all missing data patterns. By contrast, the non-identifiability of the full law implies that any multiple imputation method aiming to implement conditionally complete imputation will produce biased estimates, thereby also restricting the options for estimating the target law. We demonstrate that alternative imputation strategies can sometimes enable the estimation of the target law in such cases. Specifically, we introduce factorizable imputation where certain observed values are also imputed and the imputed data are weighted in the analysis.

math.ST↗

arXiv2024

Full Law Identification under Missing Data with Categorical Variables

Missing data may be disastrous for the identifiability of causal and statistical estimands. In graphical missing data models, colluders are dependence structures that have a special importance for identification considerations. It has been shown that the presence of a colluder makes the full law, i.e., the joint distribution of variables and response indicators, non-parametrically non-identifiable. However, when the variables related to the colluder structure are categorical, it is sometimes possible to regain the identifiability of the full law. We present a necessary and sufficient condition for the identification of the full law in the presence of colluder structures with arbitrary categorical variables. Maximum likelihood estimation of the full law in identifiable models with categorical variables is demonstrated with simulated and real data.

stat.ME↗

arXiv2023

Simulating counterfactuals

Counterfactual inference considers a hypothetical intervention in a parallel world that shares some evidence with the factual world. If the evidence specifies a conditional distribution on a manifold, counterfactuals may be analytically intractable. We present an algorithm for simulating values from a counterfactual distribution where conditions can be set on both discrete and continuous variables. We show that the proposed algorithm can be presented as a particle filter leading to asymptotically valid inference. The algorithm is applied to fairness analysis in credit-scoring.

stat.ML↗

arXiv2023

Price Optimization Combining Conjoint Data and Purchase History: A Causal Modeling Approach

Pricing decisions of companies require an understanding of the causal effect of a price change on the demand. When real-life pricing experiments are infeasible, data-driven decision-making must be based on alternative data sources such as purchase history (sales data) and conjoint studies where a group of customers is asked to make imaginary purchases in an artificial setup. We present an approach for price optimization that combines population statistics, purchase history and conjoint data in a systematic way. We build on the recent advances in causal inference to identify and quantify the effect of price on the purchase probability at the customer level. The identification task is a transportability problem whose solution requires a parametric assumption on the differences between the conjoint study and real purchases. The causal effect is estimated using Bayesian methods that take into account the uncertainty of the data sources. The pricing decision is made by comparing the estimated posterior distributions of gross profit for different prices. The approach is demonstrated with simulated data resembling the features of real-world data.

stat.AP↗

arXiv2023

dynamite: An R Package for Dynamic Multivariate Panel Models

dynamite is an R package for Bayesian inference of intensive panel (time series) data comprising multiple measurements per multiple individuals measured in time. The package supports joint modeling of multiple response variables, time-varying and time-invariant effects, a wide range of discrete and continuous distributions, group-specific random effects, latent factors, and customization of prior distributions of the model parameters. Models in the package are defined via a user-friendly formula interface, and estimation of the posterior distribution of the model parameters takes advantage of state-of-the-art Markov chain Monte Carlo methods. The package enables efficient computation of both individual-level and aggregated predictions and offers a comprehensive suite of tools for visualization and model diagnostics.

stat.ME↗

arXiv2022

Identifying Counterfactual Queries with the R Package cfid

In the framework of structural causal models, counterfactual queries describe events that concern multiple alternative states of the system under study. Counterfactual queries often take the form of "what if" type questions such as "would an applicant have been hired if they had over 10 years of experience, when in reality they only had 5 years of experience?" Such questions and counterfactual inference in general are crucial, for example when addressing the problem of fairness in decision-making. Because counterfactual events contain contradictory states of the world, it is impossible to conduct a randomized experiment to address them without making several restrictive assumptions. However, it is sometimes possible to identify such queries from observational and experimental data by representing the system under study as a causal model, and the available data as symbolic probability distributions. Shpitser and Pearl (2007) constructed two algorithms, called ID* and IDC*, for identifying counterfactual queries and conditional counterfactual queries, respectively. These two algorithms are analogous to the ID and IDC algorithms by Shpitser and Pearl (2006) for identification of interventional distributions, which were implemented in R by Tikka and Karvanen (2017) in the causaleffect package. We present the R package cfid that implements the ID* and IDC* algorithms. Identification of counterfactual queries and the features of cfid are demonstrated via examples.

stat.ME↗

arXiv2021

Clustering and Structural Robustness in Causal Diagrams

Graphs are commonly used to represent and visualize causal relations. For a small number of variables, this approach provides a succinct and clear view of the scenario at hand. As the number of variables under study increases, the graphical approach may become impractical, and the clarity of the representation is lost. Clustering of variables is a natural way to reduce the size of the causal diagram, but it may erroneously change the essential properties of the causal relations if implemented arbitrarily. We define a specific type of cluster, called transit cluster, that is guaranteed to preserve the identifiability properties of causal effects under certain conditions. We provide a sound and complete algorithm for finding all transit clusters in a given graph and demonstrate how clustering can simplify the identification of causal effects. We also study the inverse problem, where one starts with a clustered graph and looks for extended graphs where the identifiability properties of causal effects remain unchanged. We show that this kind of structural robustness is closely related to transit clusters.

stat.ML↗

arXiv2020

Identifying Causal Effects via Context-specific Independence Relations

Causal effect identification considers whether an interventional probability distribution can be uniquely determined from a passively observed distribution in a given causal structure. If the generating system induces context-specific independence (CSI) relations, the existing identification procedures and criteria based on do-calculus are inherently incomplete. We show that deciding causal effect non-identifiability is NP-hard in the presence of CSIs. Motivated by this, we design a calculus and an automated search procedure for identifying causal effects in the presence of CSIs. The approach is provably sound and it includes standard do-calculus as a special case. With the approach we can obtain identifying formulas that were unobtainable previously, and demonstrate that a small number of CSI-relations may be sufficient to turn a previously non-identifiable instance to identifiable.

cs.AI↗

arXiv2020

Simulation Framework for Realistic Large-scale Individual-level Data Generation with an Application in the Health Domain

We propose a framework for realistic data generation and simulation of complex systems and demonstrate its capabilities in the health domain. The main use cases of the framework are predicting the development of risk factors and disease occurrence, evaluating the impact of interventions and policy decisions, and statistical method development. We present the fundamentals of the framework using rigorous mathematical definitions. The framework supports calibration to a real population as well as various manipulations and data collection processes. The freely available open-source implementation in R embraces efficient data structures, parallel computing and fast random number generation which ensure reproducibility and scalability. With the framework it is possible to run daily-level simulations for populations of millions of individuals for decades of simulated time. An example on the occurrence of stroke, type 2 diabetes and mortality illustrates the usage of the framework in the Finnish context. In the example, we demonstrate the data-collection functionality by studying the impact of non-participation on the estimated risk models and interventions related to controlling the additional salt intake.

stat.ME↗

arXiv2020

Do-search -- a tool for causal inference and study design with multiple data sources

Epidemiological evidence is based on multiple data sources including clinical trials, cohort studies, surveys, registries and expert opinions. Merging information from different sources opens up new possibilities for the estimation of causal effects. We show how causal effects can be identified and estimated by combining experiments and observations in real and realistic scenarios. As a new tool, we present do-search, a recently developed algorithmic approach that can determine the identifiability of a causal effect. The approach is based on do-calculus, and it can utilize data with non-trivial missing data and selection bias mechanisms. When the effect is identifiable, do-search outputs an identifying formula on which numerical estimation can be based. When the effect is not identifiable, we can use do-search to recognize additional data sources and assumptions that would make the effect identifiable. Throughout the paper, we consider the effect of salt-adding behavior on blood pressure mediated by the salt intake as an example. The identifiability of this effect is resolved in various scenarios with different assumptions on confounding. There are scenarios where the causal effect is identifiable from a chain of experiments but not from survey data, as well as scenarios where the opposite is true. As an illustration, we use survey data from NHANES 2013--2016 and the results from a meta-analysis of randomized controlled trials and estimate the reduction in average systolic blood pressure under an intervention where the use of table salt is discontinued.

stat.AP↗

arXiv2020

Estimation of causal effects with small data in the presence of trapdoor variables

We consider the problem of estimating causal effects of interventions from observational data when well-known back-door and front-door adjustments are not applicable. We show that when an identifiable causal effect is subject to an implicit functional constraint that is not deducible from conditional independence relations, the estimator of the causal effect can exhibit bias in small samples. This bias is related to variables that we call trapdoor variables. We use simulated data to study different strategies to account for trapdoor variables and suggest how the related trapdoor bias might be minimized. The importance of trapdoor variables in causal effect estimation is illustrated with real data from the Life Course 1971-2002 study. Using this dataset, we estimate the causal effect of education on income in the Finnish context. Bayesian modelling allows us to take the parameter uncertainty into account and to present the estimated causal effects as posterior distributions.

stat.ME↗

arXiv2020

The gallium anomaly reassessed using a Bayesian approach

The solar-neutrino detectors GALLEX and SAGE were calibrated by electron-neutrino flux from the $^{37}$Ar and $^{51}$Cr calibration sources. A deficit in the measured neutrino flux was recorded by counting the number of neutrino-induced conversions of the $^{71}$Ga nuclei to $^{71}$Ge nuclei. This deficit was coined ``gallium anomaly'' and it has lead to speculations about beyond-the-standard-model physics in the form of eV-mass sterile neutrinos. Notably, this anomaly has already defied final solution for more than 20 years. Here we reassess the statistical significance of this anomaly and improve the related statistical approaches by treating the neutrino experiments as repeated Bernoulli trials taking into account the fact that the number of the detected $^{71}$Ge nuclei is quite small, thus calling for a Bayesian statistical approach. In addition, we take into account the systematic errors of the experiments, their correlations, theoretical uncertainties and the number of background solar-neutrino events as a Poisson-distributed random variable. To compare with the previously reported statistical significances of the anomaly we convert the posterior intervals of our Bayesian approach to standard deviations $\sigma$ of the frequentist approach. We find that our approach reduces the statistical significance of the anomaly by $0.8\,\sigma$ for all the adopted theoretical approaches. This renders the gallium anomaly a statistically weakly supported concept. Furthermore, the implications of our approach go far beyond the gallium anomaly since the results of many rare-events experiments should be reassessed for their limited number of recorded events.

hep-ph↗

arXiv2019

Causal Effect Identification from Multiple Incomplete Data Sources: A General Search-based Approach

Causal effect identification considers whether an interventional probability distribution can be uniquely determined without parametric assumptions from measured source distributions and structural knowledge on the generating system. While complete graphical criteria and procedures exist for many identification problems, there are still challenging but important extensions that have not been considered in the literature. To tackle these new settings, we present a search algorithm directly over the rules of do-calculus. Due to generality of do-calculus, the search is capable of taking more advanced data-generating mechanisms into account along with an arbitrary type of both observational and experimental source distributions. The search is enhanced via a heuristic and search space reduction techniques. The approach, called do-search, is provably sound, and it is complete with respect to identifiability problems that have been shown to be completely characterized by do-calculus. When extended with additional rules, the search is capable of handling missing data problems as well. With the versatile search, we are able to approach new problems such as combined transportability and selection bias, or multiple sources of selection bias. We perform a systematic analysis of bivariate missing data problems and study causal inference under case-control design. We also present the R package dosearch that provides an interface for a C++ implementation of the search.

stat.ML↗

arXiv2018

Simplifying Probabilistic Expressions in Causal Inference

Obtaining a non-parametric expression for an interventional distribution is one of the most fundamental tasks in causal inference. Such an expression can be obtained for an identifiable causal effect by an algorithm or by manual application of do-calculus. Often we are left with a complicated expression which can lead to biased or inefficient estimates when missing data or measurement errors are involved. We present an automatic simplification algorithm that seeks to eliminate symbolically unnecessary variables from these expressions by taking advantage of the structure of the underlying graphical model. Our method is applicable to all causal effect formulas and is readily available in the R package causaleffect.

stat.ML↗