Inference With Cross-Lagged Effects - Problems in Time and New Interpretations

The interpretation of cross-effects from vector autoregressive models to infer structure and causality amongst constructs is widespread and sometimes problematic. I first explain how hypothesis testing and regularization are invalidated when processes that are thought to fluctuate continuously in time are, as is typically done, modeled as changing only in discrete steps. I then describe an alternative interpretation of cross-effect parameters that incorporates correlated random changes for a potentially more realistic view of how process are temporally coupled. Using an example based on wellbeing data, I demonstrate how some classical concerns such as sign flipping and counter intuitive effect directions can disappear when using this combined deterministic / stochastic interpretation. Models that treat processes as continuously interacting offer both a resolution to the hypothesis testing problem, and the possibility of the combined stochastic / deterministic interpretation.

Neural Circuits for Dynamics-Based Segmentation of Time Series

The brain must extract behaviorally relevant latent variables from the signals streamed by the sensory organs. Such latent variables are often encoded in the dynamics that generated the signal rather than in the specific realization of the waveform. Therefore, one problem faced by the brain is to segment time series based on underlying dynamics. We present two algorithms for performing this segmentation task that are biologically plausible, which we define as acting in a streaming setting and all learning rules being local. One algorithm is model based and can be derived from an optimization problem involving a mixture of autoregressive processes. This algorithm relies on feedback in the form of a prediction error and can also be used for forecasting future samples. In some brain regions, such as the retina, the feedback connections necessary to use the prediction error for learning are absent. For this case, we propose a second, model-free algorithm that uses a running estimate of the autocorrelation structure of the signal to perform the segmentation. We show that both algorithms do well when tasked with segmenting signals drawn from autoregressive models with piecewise-constant parameters. In particular, the segmentation accuracy is similar to that obtained from oracle-like methods in which the ground-truth parameters of the autoregressive models are known. We also test our methods on data sets generated by alternating snippets of voice recordings. We provide implementations of our algorithms at https://github.com/ttesileanu/bio-time-series.

Short-Term Economic Forecasting by Complex-Valued Autoregressions

One of the directions that can expand the instrumental base for modeling the economy is complex-valued economics – ​a section of economic and mathematical modeling devoted to the use of models and methods of the theory of the function of a complex variable in economics. The article discusses the possibility of short-term economic forecasting using autoregressive models of complex variables. A classification of possible modifications of complex-valued autoregressive models is given, and the main properties of each of the classes of these models are shown. One of the varieties of these complex-valued models uses current and past errors of approximation, which means that it can be compared with the widely used model of autoregressive real variables ARIMA(p, d, q). The article makes such a comparison, both on a theoretical level and on a practical example.

Comparison of compression estimations under the penalty functions of different violent crimes on campus through deep learning and linear spatial autoregressive models

To reduce the probability of violent crimes, the deep learning (DL) technology and linear spatial autoregressive models (ARMs) are utilised to estimate the model parameters through different penalty functions. In addition, under a determinate space, the influences of environmental factors on violent crimes are discussed. By taking campus violence cases as examples, the major influencing factors of violent crimes are found through data analysis. The results show that campus violence cases are usually caused by the complex surrounding environments and persons. Also, campus security measures only cover a small range, and the security management is difficult. In the meantime, due to the younger ages and lack of self-protection awareness, students may easily become the targets of criminals. Therefore, the results have a positive significance for authorities to analyse the crime rates in a determinate area and take preventive measures against violent crimes.