Combining the stochastic and δN formalisms, we derive non-perturbative analytical expressions for all correlation functions of scalar perturbations in single-field, slow-roll inflation. The standard, classical formulas are recovered as saddle-point limits of the full results. This yields a classicality criterion that shows that stochastic effects are small only if the potential is sub-Planckian...

Correlation clustering is the problem of finding a crisp partition of the vertices of a correlation graph in such a way as to minimize the disagreements in the cluster assignments. In this paper, we discuss a relaxation to the original problem setting which allows probabilistic assignments of vertices to labels. By so doing, overlapping clusters can be captured. We also show that a known optimi...

In this report we examine the connection between Itti and Baldi’s ‘Bayesian suprise’ [1] and instantaneous predictive information [2], and show that the two are identical in certain classes of exchangeable random sequences. We also examine how these relationships can be used to compute the instantaneous predictive information in a Markov chain where the transition matrix is unknown. Samples fro...

This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structural-semantical de nitions of the probabilities of necessary or su cient causation (or both), we show how to bound these quantities from data obtained in experimental and observational studies, under general...

In this paper, we consider independence property between a random process and its first derivative. Then, for linear mixtures, we show that cross-correlations between mixtures and their derivatives provide a sufficient number of equations for analytically computing the unknown mixing matrix. In addition to its simplicity, the method is able to separate Gaussian sources, since it only requires s...

This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structural-semantical deenitions of the probabilities of necessary or suucient causation (or both), we show how to bound these quantities from data obtained in experimental and observational studies, under general...

received discrete-time Gaussian signals. Using two different methods, possible structures for the joint maximum likelihood (ML) estimator are proposed, when the observation interval is long compared to both the delay to estimate and the correlation time of the various random processes involved. These structures generalize the cross-correlation method with prefiltering that implements the ML est...