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Identifying meaningful signal buried in noise is a problem of interest arising in diverse scenarios of data-driven modeling. We present here a theoretical framework for exploiting intrinsic geometry in data that resists noise corruption,…
The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data…
A randomized algorithm for finding sparse cuts is given which is based on constructing a dual markov chain called multiscale rings process(MRP) and a new concept of entropy. It is shown how the time to absorption of the dual process…
We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle…
An inverse modeling technique is introduced that combines elements of coupled logistic map models and wavelet analysis for the purpose of analyzing partial synchronization states in high-dimensional systems. Using Embedded Complex Logistic…
Information-theoretic quantities play a crucial role in understanding non-linear relationships between random variables and are widely used across scientific disciplines. However, estimating these quantities remains an open problem,…
This paper establishes a Markov chain model as a unified framework for understanding information consumption processes in complex networks, with clear implications to the Internet and big-data technologies. In particular, the proposed model…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…
Low-dimensional embeddings are a cornerstone in the modelling and analysis of complex networks. However, most existing approaches for mining network embedding spaces rely on computationally intensive machine learning systems to facilitate…
We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $\varphi : H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-equivariant ones. We formulate…
Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying…
Vector representations of graphs and relational structures, whether hand-crafted feature vectors or learned representations, enable us to apply standard data analysis and machine learning techniques to the structures. A wide range of…
Graph embedding provides a feasible methodology to conduct pattern classification for graph-structured data by mapping each data into the vectorial space. Various pioneering works are essentially coding method that concentrates on a…
We introduce an adaptive refinement procedure for smart, and scalable abstraction of dynamical systems. Our technique relies on partitioning the state space depending on the observation of future outputs. However, this knowledge is…
Logic-Geometric Programming (LGP) is a powerful motion and manipulation planning framework, which represents hierarchical structure using logic rules that describe discrete aspects of problems, e.g., touch, grasp, hit, or push, and solves…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…
Multistate Markov models are a canonical parametric approach for data modeling of observed or latent stochastic processes supported on a finite state space. Continuous-time Markov processes describe data that are observed irregularly over…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…