Unified Causality Analysis Based on the Degrees of Freedom

Temporally evolving systems are typically modeled by dynamic equations. A key challenge in accurate modeling is understanding the causal relationships between subsystems, as well as identifying the presence and influence of unobserved hidden drivers on the observed dynamics. This paper presents a unified method capable of identifying fundamental causal relationships between pairs of systems, whether deterministic or stochastic. Notably, the method also uncovers hidden common causes beyond the observed variables. By analyzing the degrees of freedom in the system, our approach provides a more comprehensive understanding of both causal influence and hidden confounders. This unified framework is validated through theoretical models and simulations, demonstrating its robustness and potential for broader application.

Learning ECG signal features without backpropagation

Representation learning has become a crucial area of research in machine learning, as it aims to discover efficient ways of representing raw data with useful features to increase the effectiveness, scope and applicability of downstream tasks such as classification and prediction. In this paper, we propose a novel method to generate representations for time series-type data. This method relies on ideas from theoretical physics to construct a compact representation in a data-driven way, and it can capture both the underlying structure of the data and task-specific information while still remaining intuitive, interpretable and verifiable. This novel methodology aims to identify linear laws that can effectively capture a shared characteristic among samples belonging to a specific class. By subsequently utilizing these laws to generate a classifier-agnostic representation in a forward manner, they become applicable in a generalized setting. We demonstrate the effectiveness of our approach on the task of ECG signal classification, achieving state-of-the-art performance.

Feature space reduction method for ultrahigh-dimensional, multiclass data: Random forest-based multiround screening (RFMS)

In recent years, numerous screening methods have been published for ultrahigh-dimensional data that contain hundreds of thousands of features; however, most of these features cannot handle data with thousands of classes. Prediction models built to authenticate users based on multichannel biometric data result in this type of problem. In this study, we present a novel method known as random forest-based multiround screening (RFMS) that can be effectively applied under such circumstances. The proposed algorithm divides the feature space into small subsets and executes a series of partial model builds. These partial models are used to implement tournament-based sorting and the selection of features based on their importance. To benchmark RFMS, a synthetic biometric feature space generator known as BiometricBlender is employed. Based on the results, the RFMS is on par with industry-standard feature screening methods while simultaneously possessing many advantages over these methods.

LLT: An R package for Linear Law-based Feature Space Transformation

The goal of the linear law-based feature space transformation (LLT) algorithm is to assist with the classification of univariate and multivariate time series. The presented R package, called LLT, implements this algorithm in a flexible yet user-friendly way. This package first splits the instances into training and test sets. It then utilizes time-delay embedding and spectral decomposition techniques to identify the governing patterns (called linear laws) of each input sequence (initial feature) within the training set. Finally, it applies the linear laws of the training set to transform the initial features of the test set. These steps are performed by three separate functions called trainTest, trainLaw, and testTrans. Their application requires a predefined data structure; however, for fast calculation, they use only built-in functions. The LLT R package and a sample dataset with the appropriate data structure are publicly available on GitHub.

Predicting the Price Movement of Cryptocurrencies Using Linear Law-based Transformation

The aim of this paper is to investigate the effect of a novel method called linear law-based feature space transformation (LLT) on the accuracy of intraday price movement prediction of cryptocurrencies. To do this, the 1-minute interval price data of Bitcoin, Ethereum, Binance Coin, and Ripple between 1 January 2019 and 22 October 2022 were collected from the Binance cryptocurrency exchange. Then, 14-hour nonoverlapping time windows were applied to sample the price data. The classification was based on the first 12 hours, and the two classes were determined based on whether the closing price rose or fell after the next 2 hours. These price data were first transformed with the LLT, then they were classified by traditional machine learning algorithms with 10-fold cross-validation. Based on the results, LLT greatly increased the accuracy for all cryptocurrencies, which emphasizes the potential of the LLT algorithm in predicting price movements.

BiometricBlender: Ultra-high dimensional, multi-class synthetic data generator to imitate biometric feature space

The lack of freely available (real-life or synthetic) high or ultra-high dimensional, multi-class datasets may hamper the rapidly growing research on feature screening, especially in the field of biometrics, where the usage of such datasets is common. This paper reports a Python package called BiometricBlender, which is an ultra-high dimensional, multi-class synthetic data generator to benchmark a wide range of feature screening methods. During the data generation process, the overall usefulness and the intercorrelations of blended features can be controlled by the user, thus the synthetic feature space is able to imitate the key properties of a real biometric dataset.

Reconstruction of observed mechanical motions with Artificial Intelligence tools

The goal of this paper is to determine the laws of observed trajectories assuming that there is a mechanical system in the background and using these laws to continue the observed motion in a plausible way. The laws are represented by neural networks with a limited number of parameters. The training of the networks follows the Extreme Learning Machine idea. We determine laws for different levels of embedding, thus we can represent not only the equation of motion but also the symmetries of different kinds. In the recursive numerical evolution of the system, we require the fulfillment of all the observed laws, within the determined numerical precision. In this way, we can successfully reconstruct both integrable and chaotic motions, as we demonstrate in the example of the gravity pendulum and the double pendulum.

Linear Laws of Markov Chains with an Application for Anomaly Detection in Bitcoin Prices

The goals of this paper are twofold: (1) to present a new method that is able to find linear laws governing the time evolution of Markov chains and (2) to apply this method for anomaly detection in Bitcoin prices. To accomplish these goals, first, the linear laws of Markov chains are derived by using the time embedding of their (categorical) autocorrelation function. Then, a binary series is generated from the first difference of Bitcoin exchange rate (against the United States Dollar). Finally, the minimum number of parameters describing the linear laws of this series is identified through stepped time windows. Based on the results, linear laws typically became more complex (containing an additional third parameter that indicates hidden Markov property) in two periods: before the crash of cryptocurrency markets inducted by the COVID-19 pandemic (12 March 2020), and before the record-breaking surge in the price of Bitcoin (Q4 2020 - Q1 2021). In addition, the locally high values of this third parameter are often related to short-term price peaks, which suggests price manipulation.