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The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…

Statistical Mechanics · Physics 2012-09-27 Julian Lee , Steve Pressé

Recent years have seen the rise of convolutional neural network techniques in exemplar-based image synthesis. These methods often rely on the minimization of some variational formulation on the image space for which the minimizers are…

Statistics Theory · Mathematics 2019-12-05 Valentin De Bortoli , Agnes Desolneux , Alain Durmus , Bruno Galerne , Arthur Leclaire

A major challenge for community ecology is using spatio-temporal data to infer parameters of dynamical models without conducting laborious experiments. We present a novel framework from statistical physics -- Maximum Caliber -- to…

Populations and Evolution · Quantitative Biology 2025-11-07 Zachary Jackson , Mathew A. Leibold , Robert D. Holt , BingKan Xue

This work derives a theoretical value for the entropy of a Linear Additive Markov Process (LAMP), an expressive model able to generate sequences with a given autocorrelation structure. While a first-order Markov Chain model generates new…

Information Theory · Computer Science 2023-01-10 Bridget Smart , Matthew Roughan , Lewis Mitchell

We present a framework to address a class of sequential decision making problems. Our framework features learning the optimal control policy with robustness to noisy data, determining the unknown state and action parameters, and performing…

Machine Learning · Computer Science 2022-01-20 Amber Srivastava , Srinivasa M Salapaka

In recent years, machine learning, and in particular generative adversarial neural networks (GANs) and attention-based neural networks (transformers), have been successfully used to compose and generate music, both melodies and polyphonic…

Mixtures of Hidden Markov Models (MHMMs) are frequently used for clustering of sequential data. An important aspect of MHMMs, as of any clustering approach, is that they can be interpretable, allowing for novel insights to be gained from…

Artificial Intelligence · Computer Science 2021-03-24 Negar Safinianaini , Henrik Boström

The Maximum Entropy Modeling Toolkit supports parameter estimation and prediction for statistical language models in the maximum entropy framework. The maximum entropy framework provides a constructive method for obtaining the unique…

cmp-lg · Computer Science 2008-02-03 Eric Sven Ristad

We present a model for capturing musical features and creating novel sequences of music, called the Convolutional Variational Recurrent Neural Network. To generate sequential data, the model uses an encoder-decoder architecture with latent…

Sound · Computer Science 2018-10-09 Eunjeong Stella Koh , Shlomo Dubnov , Dustin Wright

We present two novel models of document coherence and their application to information retrieval (IR). Both models approximate document coherence using discourse entities, e.g. the subject or object of a sentence. Our first model views text…

Information Retrieval · Computer Science 2016-10-31 Casper Petersen , Christina Lioma , Jakob Grue Simonsen , Birger Larsen

We study the problem of efficient exploration in order to learn an accurate model of an environment, modeled as a Markov decision process (MDP). Efficient exploration in this problem requires the agent to identify the regions in which…

Herding is a deterministic algorithm used to generate data points that can be regarded as random samples satisfying input moment conditions. The algorithm is based on the complex behavior of a high-dimensional dynamical system and is…

Machine Learning · Statistics 2023-05-10 Hiroshi Yamashita , Hideyuki Suzuki , Kazuyuki Aihara

Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally…

Machine Learning · Statistics 2019-06-05 Diego Granziol , Binxin Ru , Stefan Zohren , Xiaowen Doing , Michael Osborne , Stephen Roberts

Finding the correct encoding for a generic dynamical system's trajectory is a complicated task: the symbolic sequence needs to preserve the invariant properties from the system's trajectory. In theory, the solution to this problem is found…

Chaotic Dynamics · Physics 2018-04-18 Nicolás Rubido , Celso Grebogi , Murilo S. Baptista

In addressing the challenge of interpretability and generalizability of artificial music intelligence, this paper introduces a novel symbolic representation that amalgamates both explicit and implicit musical information across diverse…

Sound · Computer Science 2024-01-08 Yikai Qian , Tianle Wang , Xinyi Tong , Xin Jin , Duo Xu , Bo Zheng , Tiezheng Ge , Feng Yu , Song-Chun Zhu

Algorithmic composition of music has a long history and with the development of powerful deep learning methods, there has recently been increased interest in exploring algorithms and models to create art. We explore the utility of state…

Sound · Computer Science 2018-10-02 Anna K. Yanchenko , Sayan Mukherjee

In this paper, we consider a modified version of the control problem in a model free Markov decision process (MDP) setting with large state and action spaces. The control problem most commonly addressed in the contemporary literature is to…

Artificial Intelligence · Computer Science 2018-02-01 Ajin George Joseph , Shalabh Bhatnagar

We study the problem of synthesizing a policy that maximizes the entropy of a Markov decision process (MDP) subject to a temporal logic constraint. Such a policy minimizes the predictability of the paths it generates, or dually, maximizes…

Optimization and Control · Mathematics 2019-06-17 Yagiz Savas , Melkior Ornik , Murat Cubuktepe , Mustafa O. Karabag , Ufuk Topcu

We consider the problem of communicating exogenous information by means of Markov decision process trajectories. This setting, which we call a Markov coding game (MCG), generalizes both source coding and a large class of referential games.…

The pervasive presence spatial and size structure in biological populations challenges fundamental assumptions at the heart of continuum models of population dynamics based on mean densities (local or global) only. Individual-based models…

Populations and Evolution · Quantitative Biology 2012-02-29 Michael Raghib , Nicholas A. Hill , Ulf Dieckmann