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Mutual Information (MI) and Conditional Mutual Information (CMI) are multi-purpose tools from information theory that are able to naturally measure the statistical dependencies between random variables, thus they are usually of central…
We demonstrate that the quantum mutual information (QMI) is a useful probe to study many-body localization (MBL). First, we focus on the detection of a metal--insulator transition for two different models, the noninteracting…
In this paper, we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way. Examples include Ising Models on lattices, and Mean-Field type Ising Models…
The way in which different types of dynamics unfold in complex networks is intrinsically related to the propagation of activation along nodes, which is strongly affected by the network connectivity. In this work we investigate to which…
Quantifying the dependence between high-dimensional random variables is central to statistical learning and inference. Two classical methods are canonical correlation analysis (CCA), which identifies maximally correlated projected versions…
We consider the problem of estimating mutual information between dependent data, an important problem in many science and engineering applications. We propose a data-driven, non-parametric estimator of mutual information in this paper. The…
Periodic neural activity not locked to the stimulus or to motor responses is usually ignored. Here, we present new tools for modeling and quantifying the information transmission based on periodic neural activity that occurs with…
Segregation is a multi-scale phenomenon that requires careful measurement. A segregation index implicitly defines how the demographic compositions of locations are compared. We identify two properties -- mean-minimisation and invariance --…
The total correlation(TC) is a crucial index to measure the correlation between marginal distribution in multidimensional random variables, and it is frequently applied as an inductive bias in representation learning. Previous research has…
We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…
There has been much recent interest in modifying Bayesian inference for misspecified models so that it is useful for specific purposes. One popular modified Bayesian inference method is "cutting feedback" which can be used when the model…
By employing various empirical estimators for the Mutual Information (MI) measure, we calculate and compare the estimates and their confidence intervals for both normal and non-normal bivariate data samples. We find that certain nonlinear…
Real-world applications often require improved models by leveraging a range of cheap incidental supervision signals. These could include partial labels, noisy labels, knowledge-based constraints, and cross-domain or cross-task annotations…
A restrictive assumption in change point analysis is "stationarity under the null hypothesis of no change-point", which is crucial for asymptotic theory but not very realistic from a practical point of view. For example, if change point…
In a novel approach to the multiple testing problem, Efron (2004; 2007) formulated estimators of the distribution of test statistics or nominal p-values under a null distribution suitable for modeling the data of thousands of unaffected…
The Kullback-Leibler (KL) divergence is a foundational measure for comparing probability distributions. Yet in multivariate settings, its single value often obscures the underlying reasons for divergence, conflating mismatches in individual…
Phase-amplitude coupling (PAC), a form of cross-frequency interaction, has been implicated in various cognitive functions and, by extension, in neural communication and information integration. Accurately detecting and characterising PAC is…
In this paper, we study stabilizability of discrete-time switched linear systems where the switching signal is considered as an arbitrary disturbance (and not a control variable). We characterize feedback stabilization via necessary and…
We propose a distributed Bayesian quickest change detection algorithm for sensor networks, based on a random gossip inter-sensor communication structure. Without a control or fusion center, each sensor executes its local change detection…