Related papers: Machine learning and optimization-based approaches…

Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…

We characterize equilibrium properties and relaxation dynamics of a two-dimensional lattice containing, at each site, two particles connected by a double-well potential (dumbbell). Dumbbells are oriented in the orthogonal direction with…

We link optimal filtering for hidden Markov models to the notion of duality for Markov processes. We show that when the signal is dual to a process that has two components, one deterministic and one a pure death process, and with respect to…

The Hamiltonian formalism offers a natural framework for discussing the notion of Poisson Lie T-duality. This is because the duality is inherent in the Poisson structures alone and exists regardless of the choice of Hamiltonian. Thus one…

It is known that the normal three-dimensional (3D) Ising model on a cubic lattice is dual to the Wegner's 3D $Z_2$ lattice gauge theory. Here we find an unusual $Z_2$ lattice gauge theory which is dual to the 3D Ising model with not only…

We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…

In this paper, we are interested in building a domain knowledge based deep learning framework to solve the chiller plants energy optimization problems. Compared to the hotspot applications of deep learning (e.g. image classification and…

This paper provides an introduction to Double/Debiased Machine Learning (DML). DML is a general approach to performing inference about a target parameter in the presence of nuisance functions: objects that are needed to identify the target…

Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions;…

We present an algorithm to approximate partition functions of 3-body classical Ising models on two-dimensional lattices of arbitrary genus, in the real-temperature regime. Even though our algorithm is purely classical, it is designed by…

Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known…

Orthogonal statistical learning and double machine learning have emerged as general frameworks for two-stage statistical prediction in the presence of a nuisance component. We establish non-asymptotic bounds on the excess risk of orthogonal…

This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…

Learning Gibbs distributions using only sufficient statistics has long been recognized as a computationally hard problem. On the other hand, computationally efficient algorithms for learning Gibbs distributions rely on access to full sample…

Modern retrieval problems are characterised by training sets with potentially billions of labels, and heterogeneous data distributions across subpopulations (e.g., users of a retrieval system may be from different countries), each of which…

A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et…

We consider Lagrangian duality based approaches to design and analyze algorithms for online energy-efficient scheduling. First, we present a primal-dual framework. Our approach makes use of the Lagrangian weak duality and convexity to…

We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient…

A discrete spatial lattice can be cast as a network structure over which spatially-correlated outcomes are observed. A second network structure may also capture similarities among measured features, when such information is available.…

As a popular form of knowledge and experience, patterns and their identification have been critical tasks in most data mining applications. However, as far as we are aware, no study has systematically examined the dynamics of pattern values…