Inferring linear and nonlinear Interaction networks using neighborhood support vector machines

Causality indices for bivariate time series data: a comparative review of performance

Inferring nonlinear and asymmetric causal relationships between multivariate longitudinal data is a challenging task with wide-ranging application areas including clinical medicine, mathematical biology, economics and environmental research. A number of methods for inferring causal relationships within complex dynamic and stochastic systems have been proposed but there is not a unified consistent definition of causality in this context. We evaluate the performance of ten prominent bivariate causality indices for time series data, across four simulated model systems that have different coupling…

Inferring Multidimensional Rates of Aging from Cross-Sectional Data

Modeling how individuals evolve over time is a fundamental problem in the natural and social sciences. However, existing datasets are often cross-sectional with each individual observed only once, making it impossible to apply traditional time-series methods. Motivated by the study of human aging, we present an interpretable latent-variable model that learns temporal dynamics from cross-sectional data. Our model represents each individual's features over time as a nonlinear function of a low-dimensional, linearly-evolving latent state. We prove that when this nonlinear function is constrained …

Interpretable Models for Granger Causality Using Self-explaining Neural Networks

Exploratory analysis of time series data can yield a better understanding of complex dynamical systems. Granger causality is a practical framework for analysing interactions in sequential data, applied in a wide range of domains. In this paper, we propose a novel framework for inferring multivariate Granger causality under nonlinear dynamics based on an extension of self-explaining neural networks. This framework is more interpretable than other neural-network-based techniques for inferring Granger causality, since in addition to relational inference, it also allows detecting signs of Granger-…

Deep Variational Koopman Models: Inferring Koopman Observations for Uncertainty-Aware Dynamics Modeling and Control

Koopman theory asserts that a nonlinear dynamical system can be mapped to a linear system, where the Koopman operator advances observations of the state forward in time. However, the observable functions that map states to observations are generally unknown. We introduce the Deep Variational Koopman (DVK) model, a method for inferring distributions over observations that can be propagated linearly in time. By sampling from the inferred distributions, we obtain a distribution over dynamical models, which in turn provides a distribution over possible outcomes as a modeled system advances in time…

Investigating Manifold Neighborhood size for Nonlinear Analysis of LIBS Amino Acid Spectra

Classification and identification of amino acids in aqueous solutions is important in the study of biomacromolecules. Laser Induced Breakdown Spectroscopy (LIBS) uses high energy laser-pulses for ablation of chemical compounds whose radiated spectra are captured and recorded to reveal molecular structure. Spectral peaks and noise from LIBS are impacted by experimental protocols. Current methods for LIBS spectral analysis achieves promising results using PCA, a linear method. It is well-known that the underlying physical processes behind LIBS are highly nonlinear. Our work set out to understand…

Learning Topic Models by Neighborhood Aggregation

Topic models are frequently used in machine learning owing to their high interpretability and modular structure. However, extending a topic model to include a supervisory signal, to incorporate pre-trained word embedding vectors and to include a nonlinear output function is not an easy task because one has to resort to a highly intricate approximate inference procedure. The present paper shows that topic modeling with pre-trained word embedding vectors can be viewed as implementing a neighborhood aggregation algorithm where messages are passed through a network defined over words. From the net…

Feedback System Neural Networks for Inferring Causality in Directed Cyclic Graphs

This paper presents a new causal network learning algorithm (FSNN, Feedback System Neural Network) based on the construction and analysis of a non-linear system of Ordinary Differential Equations (ODEs). The constructed system provides insight into the mechanisms responsible for generating the past and potential future behavior of dynamic systems. It is also interpretable in terms of real system variables, providing a wholistic, causally accurate, and systemic understanding of the real-life interactions governing observed phenomena. This paper demonstrates the generation of an n-dimensional or…

Deep Nonlinear Non-Gaussian Filtering for Dynamical Systems

Filtering is a general name for inferring the states of a dynamical system given observations. The most common filtering approach is Gaussian Filtering (GF) where the distribution of the inferred states is a Gaussian whose mean is an affine function of the observations. There are two restrictions in this model: Gaussianity and Affinity. We propose a model to relax both these assumptions based on recent advances in implicit generative models. Empirical results show that the proposed method gives a significant advantage over GF and nonlinear methods based on fixed nonlinear kernels.

从神经数据推断随机低秩循环神经网络

Inferring stochastic low-rank recurrent neural networks from neural data

本文提出用变分序贯蒙特卡洛方法拟合随机低秩循环神经网络，在神经数据上获得更低维潜在动力学，并实现多项式成本识别不动点，兼具可解释性与生成能力。

Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks

We present a procedure for effective estimation of entropy and mutual information from small-sample data, and apply it to the problem of inferring high-dimensional gene association networks. Specifically, we develop a James-Stein-type shrinkage estimator, resulting in a procedure that is highly efficient statistically as well as computationally. Despite its simplicity, we show that it outperforms eight other entropy estimation procedures across a diverse range of sampling scenarios and data-generating models, even in cases of severe undersampling. We illustrate the approach by analyzing E. col…

随机邻域嵌入与相对熵的梯度流

Stochastic neighborhood embedding and the gradient flow of relative entropy

研究随机邻域嵌入（SNE）及其变体t-SNE的数学模型，通过分析相对熵梯度流的长期行为，发现t-SNE的直径可能爆炸而SNE保持有界。