Interpretable Categorization of Heterogeneous Time Series Data

Understanding heterogeneous multivariate time series data is important in many applications ranging from smart homes to aviation. Learning models of heterogeneous multivariate time series that are also human-interpretable is challenging and not adequately addressed by the existing literature. We propose grammar-based decision trees (GBDTs) and an algorithm for learning them. GBDTs extend decision trees with a grammar framework. Logical expressions derived from a context-free grammar are used for branching in place of simple thresholds on attributes. The added expressivity enables support for a wide range of data types while retaining the interpretability of decision trees. In particular, when a grammar based on temporal logic is used, we show that GBDTs can be used for the interpretable classi cation of high-dimensional and heterogeneous time series data. Furthermore, we show how GBDTs can also be used for categorization, which is a combination of clustering and generating interpretable explanations for each cluster. We apply GBDTs to analyze the classic Australian Sign Language dataset as well as data on near mid-air collisions (NMACs). The NMAC data comes from aircraft simulations used in the development of the next-generation Airborne Collision Avoidance System (ACAS X).Comment: 9 pages, 5 figures, 2 tables, SIAM International Conference on Data Mining (SDM) 201

We Are Not Your Real Parents: Telling Causal from Confounded using MDL

Given data over variables $(X_1,...,X_m, Y)$ we consider the problem of finding out whether $X$ jointly causes $Y$ or whether they are all confounded by an unobserved latent variable $Z$. To do so, we take an information-theoretic approach based on Kolmogorov complexity. In a nutshell, we follow the postulate that first encoding the true cause, and then the effects given that cause, results in a shorter description than any other encoding of the observed variables. The ideal score is not computable, and hence we have to approximate it. We propose to do so using the Minimum Description Length (MDL) principle. We compare the MDL scores under the models where $X$ causes $Y$ and where there exists a latent variables $Z$ confounding both $X$ and $Y$ and show our scores are consistent. To find potential confounders we propose using latent factor modeling, in particular, probabilistic PCA (PPCA). Empirical evaluation on both synthetic and real-world data shows that our method, CoCa, performs very well -- even when the true generating process of the data is far from the assumptions made by the models we use. Moreover, it is robust as its accuracy goes hand in hand with its confidence

Methods for generating and evaluating synthetic longitudinal patient data: a systematic review

The proliferation of data in recent years has led to the advancement and utilization of various statistical and deep learning techniques, thus expediting research and development activities. However, not all industries have benefited equally from the surge in data availability, partly due to legal restrictions on data usage and privacy regulations, such as in medicine. To address this issue, various statistical disclosure and privacy-preserving methods have been proposed, including the use of synthetic data generation. Synthetic data are generated based on some existing data, with the aim of replicating them as closely as possible and acting as a proxy for real sensitive data. This paper presents a systematic review of methods for generating and evaluating synthetic longitudinal patient data, a prevalent data type in medicine. The review adheres to the PRISMA guidelines and covers literature from five databases until the end of 2022. The paper describes 17 methods, ranging from traditional simulation techniques to modern deep learning methods. The collected information includes, but is not limited to, method type, source code availability, and approaches used to assess resemblance, utility, and privacy. Furthermore, the paper discusses practical guidelines and key considerations for developing synthetic longitudinal data generation methods

Bayesian Model Selection in Complex Linear Systems, as Illustrated in Genetic Association Studies

Motivated by examples from genetic association studies, this paper considers the model selection problem in a general complex linear model system and in a Bayesian framework. We discuss formulating model selection problems and incorporating context-dependent {\it a priori} information through different levels of prior specifications. We also derive analytic Bayes factors and their approximations to facilitate model selection and discuss their theoretical and computational properties. We demonstrate our Bayesian approach based on an implemented Markov Chain Monte Carlo (MCMC) algorithm in simulations and a real data application of mapping tissue-specific eQTLs. Our novel results on Bayes factors provide a general framework to perform efficient model comparisons in complex linear model systems

Network analysis of multivariate data in psychological science

Stress and Psychopatholog