Related papers: Causal Rate Distortion Function and Relations to F…
In this paper the relation between nonanticipative rate distortion function (RDF) and Bayesian filtering theory is investigated using the topology of weak convergence of probability measures on Polish spaces. The relation is established via…
In Causal Perturbation Theory the process of renormalization is precisely equivalent to the extension of time ordered distributions to coincident points. This is achieved by a modified Taylor subtraction on the corresponding test functions.…
We introduce a new distortion measure for point processes called functional-covering distortion. It is inspired by intensity theory and is related to both the covering of point processes and logarithmic loss distortion. We obtain the…
A receiver wants to compute a function of two correlated sources separately observed by two transmitters. One of the transmitters may send a possibly private message to the other transmitter in a cooperation phase before both transmitters…
We define a Causal Decision Problem as a Decision Problem where the available actions, the family of uncertain events and the set of outcomes are related through the variables of a Causal Graphical Model $\mathcal{G}$. A solution criteria…
We characterize the rate-distortion function for zero-mean stationary Gaussian sources under the MSE fidelity criterion and subject to the additional constraint that the distortion is uncorrelated to the input. The solution is given by two…
In this paper the relation between nonanticipative rate distortion function (RDF) and Bayesian filtering theory is further investigated on general Polish spaces. The relation is established via an optimization on the space of conditional…
The purpose of this paper is to point out a new connection between information theory and dynamical systems. In the information theory side, we consider rate distortion theory, which studies lossy data compression of stochastic processes…
We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate distortion theory to use causal shielding---a natural principle of learning. We study two distinct cases of causal inference:…
A new source model, which consists of an intrinsic state part and an extrinsic observation part, is proposed and its information-theoretic characterization, namely its rate-distortion function, is defined and analyzed. Such a source model…
Statistical machine learning algorithms have achieved state-of-the-art results on benchmark datasets, outperforming humans in many tasks. However, the out-of-distribution data and confounder, which have an unpredictable causal relationship,…
A rate-distortion problem motivated by the consideration of semantic information is formulated and solved. The starting point is to model an information source as a pair consisting of an intrinsic state which is not observable,…
Rate-distortion formulation is the information-theoretic approach to the study of signal encoding systems. Since a more general approach to model the nonstationarity exhibited by real-world signals is to use appropriately fitted time…
Detecting and understanding reasons for defects and inadvertent behavior in software is challenging due to their increasing complexity. In configurable software systems, the combinatorics that arises from the multitude of features a user…
We present a definition of cause and effect in terms of decision-theoretic primitives and thereby provide a principled foundation for causal reasoning. Our definition departs from the traditional view of causation in that causal assertions…
Causal inference is capable of estimating the treatment effect (i.e., the causal effect of treatment on the outcome) to benefit the decision making in various domains. One fundamental challenge in this research is that the treatment…
In a world that constantly changes, it is crucial to understand how those changes impact different systems, such as industrial manufacturing or critical infrastructure. Explaining critical changes, referred to as concept drift in the field…
We propose a definition of causality for time series in terms of the effect of an intervention in one component of a multivariate time series on another component at some later point in time. Conditions for identifiability, comparable to…
Shannon proved that if we can transmit bits reliably at rates larger than the rate distortion function $R(D)$, then we can transmit this source to within a distortion $D$. We answer the converse question ``If we can transmit a source to…
The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…