Related papers: Discovering the Hidden Structure of Complex Dynami…

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…

Maximum likelihood estimation is effective for identifying dynamical systems, but applying it to large networks becomes computationally prohibitive. This paper introduces a maximum likelihood estimation method that enables identification of…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift,…

We propose a globally optimal Bayesian network structure discovery algorithm based on a progressively leveled scoring approach. Bayesian network structure discovery is a fundamental yet NP-hard problem in the field of probabilistic…

This paper concerns structure learning or discovery of discrete generative models. It focuses on Bayesian model selection and the assimilation of training data or content, with a special emphasis on the order in which data are ingested. A…

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…

We propose a general algorithmic framework for Bayesian model selection. A spike-and-slab Laplacian prior is introduced to model the underlying structural assumption. Using the notion of effective resistance, we derive an EM-type algorithm…

Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…

In the present paper, we propose the model of {\it structural information learning machines} (SiLeM for short), leading to a mathematical definition of learning by merging the theories of computation and information. Our model shows that…

Predicting epidemic dynamics is of great value in understanding and controlling diffusion processes, such as infectious disease spread and information propagation. This task is intractable, especially when surveillance resources are very…

Networked dynamic systems are ubiquitous in various domains, such as industrial processes, social networks, and biological systems. These systems produce high-dimensional data that reflect the complex interactions among the network nodes…

Structural equation models (SEMs) are widely used in sciences, ranging from economics to psychology, to uncover causal relationships underlying a complex system under consideration and estimate structural parameters of interest. We study…

Complex network reconstruction is a hot topic in many fields. Currently, the most popular data-driven reconstruction framework is based on lasso. However, it is found that, in the presence of noise, lasso loses efficiency for weighted…

This paper provides a tutorial discussion on analyzing structural equation modelling (SEM). SEM can be regarded as regression models with observed and unobserved indicators, have been extensively applied to practical and fundamental…

{\em Algorithms with predictions} incorporate machine learning predictions into algorithm design. A plethora of recent works incorporated predictions to improve on worst-case optimal bounds for online problems. In this paper, we initiate…

Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

In this paper, we present a guide to the foundations of learning Dynamic Bayesian Networks (DBNs) from data in the form of multiple samples of trajectories for some length of time. We present the formalism for a generic as well as a set of…

Over the past few years, equation discovery has gained popularity in different fields of science and engineering. However, existing equation discovery algorithms rely on the availability of noisy measurements of the state variables (i.e.,…

Continuous-time Bayesian Networks (CTBNs) represent a compact yet powerful framework for understanding multivariate time-series data. Given complete data, parameters and structure can be estimated efficiently in closed-form. However, if…