Search Results for author: James P. Crutchfield

Found 20 papers, 3 papers with code

Topology, Convergence, and Reconstruction of Predictive States

no code implementations19 Sep 2021 Samuel P. Loomis, James P. Crutchfield

Predictive equivalence in discrete stochastic processes have been applied with great success to identify randomness and structure in statistical physics and chaotic dynamical systems and to inferring hidden Markov models.

Time Series

Discovering Causal Structure with Reproducing-Kernel Hilbert Space $ε$-Machines

1 code implementation23 Nov 2020 Nicolas Brodu, James P. Crutchfield

A structural representation -- a finite- or infinite-state kernel $\epsilon$-machine -- is extracted by a reduced-dimension transform that gives an efficient representation of causal states and their topology.

Spacetime Autoencoders Using Local Causal States

1 code implementation12 Oct 2020 Adam Rupe, James P. Crutchfield

Local causal states are latent representations that capture organized pattern and structure in complex spatiotemporal systems.

Shannon Entropy Rate of Hidden Markov Processes

no code implementations29 Aug 2020 Alexandra M. Jurgens, James P. Crutchfield

We also show how this method gives the minimal set of infinite predictive features.

INFERENCE, PREDICTION, AND ENTROPY RATE OF CONTINUOUS-TIME, DISCRETE-EVENT PROCESSES

no code implementations ICLR 2020 Sarah Marzen, James P. Crutchfield

The inference of models, prediction of future symbols, and entropy rate estimation of discrete-time, discrete-event processes is well-worn ground.

Time Series

Towards Unsupervised Segmentation of Extreme Weather Events

no code implementations16 Sep 2019 Adam Rupe, Karthik Kashinath, Nalini Kumar, Victor Lee, Prabhat, James P. Crutchfield

Extreme weather is one of the main mechanisms through which climate change will directly impact human society.

Representation Learning

Local Causal States and Discrete Coherent Structures

no code implementations1 Jan 2018 Adam Rupe, James P. Crutchfield

The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates.

The Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications

no code implementations18 Oct 2017 James P. Crutchfield

The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified.

Time Series

Unique Information via Dependency Constraints

no code implementations19 Sep 2017 Ryan G. James, Jeffrey Emenheiser, James P. Crutchfield

The dependency decomposition then allows us to define a measure of the information about a target that can be uniquely attributed to a particular source as the least amount which the source-target statistical dependency can influence the information shared between the sources and the target.

Nearly Maximally Predictive Features and Their Dimensions

no code implementations27 Feb 2017 Sarah E. Marzen, James P. Crutchfield

Scientific explanation often requires inferring maximally predictive features from a given data set.

Trimming the Independent Fat: Sufficient Statistics, Mutual Information, and Predictability from Effective Channel States

no code implementations7 Feb 2017 Ryan G. James, John R. Mahoney, James P. Crutchfield

The theoretically ideal implementation is the use of minimal sufficient statistics, where it is well-known that either X or Y can be replaced by their minimal sufficient statistic about the other while preserving the mutual information.

Leveraging Environmental Correlations: The Thermodynamics of Requisite Variety

no code implementations17 Sep 2016 Alexander B. Boyd, Dibyendu Mandal, James P. Crutchfield

Employing computational mechanics and a new information-processing Second Law of Thermodynamics (IPSL) we remove these restrictions, analyzing general finite-state ratchets interacting with structured environments that generate correlated input signals.

Multivariate Dependence Beyond Shannon Information

no code implementations5 Sep 2016 Ryan G. James, James P. Crutchfield

Accurately determining dependency structure is critical to discovering a system's causal organization.

The Elusive Present: Hidden Past and Future Dependency and Why We Build Models

no code implementations2 Jul 2015 Pooneh M. Ara, Ryan G. James, James P. Crutchfield

When this occurs, the present captures all of the dependency between past and future.

Time Resolution Dependence of Information Measures for Spiking Neurons: Atoms, Scaling, and Universality

no code implementations18 Apr 2015 Sarah E. Marzen, Michael R. DeWeese, James P. Crutchfield

A first step towards that larger goal is to develop information measures for individual output processes, including information generation (entropy rate), stored information (statistical complexity), predictable information (excess entropy), and active information accumulation (bound information rate).

Model Selection

Signatures of Infinity: Nonergodicity and Resource Scaling in Prediction, Complexity, and Learning

no code implementations1 Apr 2015 James P. Crutchfield, Sarah Marzen

We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes.

Understanding and Designing Complex Systems: Response to "A framework for optimal high-level descriptions in science and engineering---preliminary report"

no code implementations30 Dec 2014 James P. Crutchfield, Ryan G. James, Sarah Marzen, Dowman P. Varn

We recount recent history behind building compact models of nonlinear, complex processes and identifying their relevant macroscopic patterns or "macrostates".

Circumventing the Curse of Dimensionality in Prediction: Causal Rate-Distortion for Infinite-Order Markov Processes

no code implementations9 Dec 2014 Sarah Marzen, James P. Crutchfield

Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length.

Bayesian Structural Inference for Hidden Processes

no code implementations5 Sep 2013 Christopher C. Strelioff, James P. Crutchfield

Properties of epsilon-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data.

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