7,547 research outputs found
The Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications
The principle goal of computational mechanics is to define pattern and
structure so that the organization of complex systems can be detected and
quantified. Computational mechanics developed from efforts in the 1970s and
early 1980s to identify strange attractors as the mechanism driving weak fluid
turbulence via the method of reconstructing attractor geometry from measurement
time series and in the mid-1980s to estimate equations of motion directly from
complex time series. In providing a mathematical and operational definition of
structure it addressed weaknesses of these early approaches to discovering
patterns in natural systems.
Since then, computational mechanics has led to a range of results from
theoretical physics and nonlinear mathematics to diverse applications---from
closed-form analysis of Markov and non-Markov stochastic processes that are
ergodic or nonergodic and their measures of information and intrinsic
computation to complex materials and deterministic chaos and intelligence in
Maxwellian demons to quantum compression of classical processes and the
evolution of computation and language.
This brief review clarifies several misunderstandings and addresses concerns
recently raised regarding early works in the field (1980s). We show that
misguided evaluations of the contributions of computational mechanics are
groundless and stem from a lack of familiarity with its basic goals and from a
failure to consider its historical context. For all practical purposes, its
modern methods and results largely supersede the early works. This not only
renders recent criticism moot and shows the solid ground on which computational
mechanics stands but, most importantly, shows the significant progress achieved
over three decades and points to the many intriguing and outstanding challenges
in understanding the computational nature of complex dynamic systems.Comment: 11 pages, 123 citations;
http://csc.ucdavis.edu/~cmg/compmech/pubs/cmr.ht
Switching Regression Models and Causal Inference in the Presence of Discrete Latent Variables
Given a response and a vector of predictors,
we investigate the problem of inferring direct causes of among the vector
. Models for that use all of its causal covariates as predictors enjoy
the property of being invariant across different environments or interventional
settings. Given data from such environments, this property has been exploited
for causal discovery. Here, we extend this inference principle to situations in
which some (discrete-valued) direct causes of are unobserved. Such cases
naturally give rise to switching regression models. We provide sufficient
conditions for the existence, consistency and asymptotic normality of the MLE
in linear switching regression models with Gaussian noise, and construct a test
for the equality of such models. These results allow us to prove that the
proposed causal discovery method obtains asymptotic false discovery control
under mild conditions. We provide an algorithm, make available code, and test
our method on simulated data. It is robust against model violations and
outperforms state-of-the-art approaches. We further apply our method to a real
data set, where we show that it does not only output causal predictors, but
also a process-based clustering of data points, which could be of additional
interest to practitioners.Comment: 46 pages, 14 figures; real-world application added in Section 5.2;
additional numerical experiments added in the Appendix
The Infinite Latent Events Model
We present the Infinite Latent Events Model, a nonparametric hierarchical Bayesian distribution over infinite dimensional Dynamic Bayesian Networks with binary state representations and noisy-OR-like transitions. The distribution can be used to learn structure in discrete timeseries data by simultaneously inferring a set of latent events, which events fired at each timestep, and how those events are causally linked. We illustrate the model on a sound factorization task, a network topology identification task, and a video game task.NTT Communication Science LaboratoriesUnited States. Air Force Office of Scientific Research (AFOSR FA9550-07-1-0075)United States. Office of Naval Research (ONR N00014-07-1-0937)National Science Foundation (U.S.) (Graduate Research Fellowship)United States. Army Research Office (ARO W911NF-08-1-0242)James S. McDonnell Foundation (Causal Learning Collaborative Initiative
Causal Discovery from Temporal Data: An Overview and New Perspectives
Temporal data, representing chronological observations of complex systems,
has always been a typical data structure that can be widely generated by many
domains, such as industry, medicine and finance. Analyzing this type of data is
extremely valuable for various applications. Thus, different temporal data
analysis tasks, eg, classification, clustering and prediction, have been
proposed in the past decades. Among them, causal discovery, learning the causal
relations from temporal data, is considered an interesting yet critical task
and has attracted much research attention. Existing casual discovery works can
be divided into two highly correlated categories according to whether the
temporal data is calibrated, ie, multivariate time series casual discovery, and
event sequence casual discovery. However, most previous surveys are only
focused on the time series casual discovery and ignore the second category. In
this paper, we specify the correlation between the two categories and provide a
systematical overview of existing solutions. Furthermore, we provide public
datasets, evaluation metrics and new perspectives for temporal data casual
discovery.Comment: 52 pages, 6 figure
Invariant Causal Prediction for Sequential Data
We investigate the problem of inferring the causal predictors of a response
from a set of explanatory variables . Classical
ordinary least squares regression includes all predictors that reduce the
variance of . Using only the causal predictors instead leads to models that
have the advantage of remaining invariant under interventions, loosely speaking
they lead to invariance across different "environments" or "heterogeneity
patterns". More precisely, the conditional distribution of given its causal
predictors remains invariant for all observations. Recent work exploits such a
stability to infer causal relations from data with different but known
environments. We show that even without having knowledge of the environments or
heterogeneity pattern, inferring causal relations is possible for time-ordered
(or any other type of sequentially ordered) data. In particular, this allows
detecting instantaneous causal relations in multivariate linear time series
which is usually not the case for Granger causality. Besides novel methodology,
we provide statistical confidence bounds and asymptotic detection results for
inferring causal predictors, and present an application to monetary policy in
macroeconomics.Comment: 55 page
Vanilla PP for Philosophers: A Primer on Predictive Processing
The goal of this short chapter, aimed at philosophers, is to provide an overview and brief explanation of some central concepts involved in predictive processing (PP). Even those who consider themselves experts on the topic may find it helpful to see how the central terms are used in this collection. To keep things simple, we will first informally define a set of features important to predictive processing, supplemented by some short explanations and an alphabetic glossary.
The features described here are not shared in all PP accounts. Some may not be necessary for an individual model; others may be contested. Indeed, not even all authors of this collection will accept all of them. To make this transparent, we have encouraged contributors to indicate briefly which of the features are necessary to support the arguments they provide, and which (if any) are incompatible with their account. For the sake of clarity, we provide the complete list here, very roughly ordered by how central we take them to be for “Vanilla PP” (i.e., a formulation of predictive processing that will probably be accepted by most researchers working on this topic). More detailed explanations will be given below. Note that these features do not specify individually necessary and jointly sufficient conditions for the application of the concept of “predictive processing”. All we currently have is a semantic cluster, with perhaps some overlapping sets of jointly sufficient criteria. The framework is still developing, and it is difficult, maybe impossible, to provide theory-neutral explanations of all PP ideas without already introducing strong background assumptions
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