Related papers: The Past and the Future in the Present

We develop a model of social learning from overabundant information: Short-lived agents sequentially choose from a large set of (flexibly correlated) information sources for prediction of an unknown state. Signal realizations are public. We…

In classical information theory, a causal relationship between two variables is typically modelled by assuming that, for every possible state of one of the variables, there exists a particular distribution of states of the second variable.…

Using results from neurobiology on perceptual decision making and value-based decision making, the problem of decision making between lotteries is reformulated in an abstract space where uncertain prospects are mapped to corresponding…

We consider the problem of performing predecessor searches in a bounded universe while achieving query times that depend on the distribution of queries. We obtain several data structures with various properties: in particular, we give data…

The definition of thermodynamic entropy is dependent on one's assignment of physical microstates to observed macrostates. As a result, low entropy in the distant past could be equivalently explained by selection of a particular observer. In…

The analysis of temporal networks heavily depends on the analysis of time-respecting paths. However, before being able to model and analyze the time-respecting paths, we have to infer the timescales at which the temporal edges influence…

We investigate how undecidability enters into computations of classical physical systems and contributes to the increase of entropy and loss of information. In actual computation with finite bit of information capacity we accept…

Partial orders have been used to model several experimental setups, going from classical thermodynamics and general relativity to the quantum realm with its resource theories. In order to study such experimental setups, one typically…

The characterisation of information processing is an important task in complex systems science. Information dynamics is a quantitative methodology for modelling the intrinsic information processing conducted by a process represented as a…

Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies…

Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods…

Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…

Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments;…

The paper argues that a part of the current statistical discussion is not based on the standard firm foundations of the field. Among the examples we consider are prediction into the future, semi-supervised classification, and causality…

Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex…

We investigate correlations in information carriers, e.g. texts and pieces of music, which are represented by strings of letters. For information carrying strings generated by one source (i.e. a novel or a piece of music) we find…

We propose a partial information decomposition based on the newly introduced framework of causal tensors, i.e., multilinear stochastic maps that transform source data into destination data. This framework enables us to express an indirect…

We consider prediction theory for stationary stochastic processes in continuous time. We discuss prediction using the whole (infinite) past, and using only a finite section of the past. The solutions to both these classical problems have…

The excess work required to drive a stochastic system out of thermodynamic equilibrium through a time-dependent external perturbation is directly related to the amount of entropy produced during the driving process, allowing excess work and…

The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer…