Related papers: Low probability states, data statistics, and entro…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
Extracting low-dimensional summary statistics from large datasets is essential for efficient (likelihood-free) inference. We characterize three different classes of summaries and demonstrate their importance for correctly analyzing…
Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
We study the fundamental task of outlier-robust mean estimation for heavy-tailed distributions in the presence of sparsity. Specifically, given a small number of corrupted samples from a high-dimensional heavy-tailed distribution whose mean…
We show that the naive mean-field approximation correctly predicts the leading term of the logarithmic lower tail probabilities for the number of copies of a given subgraph in $G(n,p)$ and of arithmetic progressions of a given length in…
We propose a method for the accurate estimation of rare event or failure probabilities for expensive-to-evaluate numerical models in high dimensions. The proposed approach combines ideas from large deviation theory and adaptive importance…
State space models have long played an important role in signal processing. The Gaussian case can be treated algorithmically using the famous Kalman filter. Similarly since the 1970s there has been extensive application of Hidden Markov…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…
Estimating the density of states of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers. Density of states estimation has also…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…
The task of state estimation in active distribution systems faces a major challenge due to the integration of different measurements with multiple reporting rates. As a result, distribution systems are essentially unobservable in real time,…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…
Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it becomes difficult for high-dimensional problems, especially when multiple modes exist.…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
Estimating information-theoretic quantities such as entropy and mutual information is central to many problems in statistics and machine learning, but challenging in high dimensions. This paper presents estimators of entropy via inference…